Research ArticleDetection and Prediction of Internal Damage in the AncientTimber Structure Based on Optimal Combined Model
Ziyi Wang 123 Donghui Ma234 Wei Qian 234 Wei Wang 234 Xiaodong Guo234
Qingfeng Xu5 Junhong Huan 13 and Zhongwei Gao 13
1College of Architecture and Civil Engineering Beijing University of Technology Beijing 100124 China2Institute of Earthquake Resistance and Disaster Reduction Beijing University of Technology Beijing 100124 China3Key Science Research Base of Safety Assessment and Disaster Mitigation for TraditionalTimber Structure (Beijing University of Technology) State Administration for Cultural Heritage Beijing 100124 China4Beijing Engineering Research Center of Historic Buildings Protection Beijing 100124 China5Shanghai Research Institute of Building Sciences Shanghai 200032 China
Correspondence should be addressed to Wei Qian qianweibjuteducn and Wei Wang ieewwbjuteducn
Received 11 April 2019 Revised 27 June 2019 Accepted 4 July 2019 Published 14 August 2019
Academic Editor Jorge Branco
Copyright copy 2019 Ziyi Wang et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
It is currently known that using stress wave and drilling resistance to detect the internal damage in the ancient timber structure isnot a highly precise process To improve the detection precision of this process a simulation test was used to detect the internaldamage of poplar and elm in ancient buildings In this empirical study we compared the detection precision of these two detectionmethods Based on the idea of variable weight we introduced three combined forecasting models based on the IOWA operatorIOWGA operator and IOWHA operator to predict the internal damage in the ancient timber structure +e results show that thecombined forecasting model based on the IOWA operator is more effective in predicting compared to a single detection methodand other combined forecasting models To be more specific the results show that the detection precision of the combined modelis increased by 258 and 47 respectively compared to the precision of the stress wave and drilling resistance tests +e errorindicators of the combined forecastingmodel based on the IOWAoperator are better than those of the other combined forecastingmodels In addition the analysis results based upon cross-validation theory show the combined forecasting model based on theIOWA operator has the best applicability which provides a new practical method for evaluating internal damage of timbercomponents in ancient buildings
1 Introduction
Ancient timber structures have high historical value artisticvalue and cultural value Because wood is a natural materialit is easily affected by environmental factors during its lifecycle Split insect attacks hollow decay and other damages(see Figure 1) are easily found in the wooden components ofancient buildings +ese may often result in some structuralabnormalities of timber components [1] +erefore ap-propriately and precisely predicting the internal damage oftimber components in ancient buildings is of great im-portance for sustaining the health and safety of ancienttimber structures
In recent years national and international scholars haveconducted many studies in detecting the internal damage oftimber components in ancient buildings and have achievedgood results Commonly used nondestructive testingmethods [2] for detecting the internal damage of timbercomponents mainly include stress wave [3ndash5] X-ray scan-ning [6ndash8] drilling resistance [9ndash11] and ultrasonic wave[12ndash14] However it is difficult to achieve precise detectionby using only one single detection method because each ofthese methods has its own advantages and disadvantages[15]
+e basic principle of stress wave nondestructive testingis that one end of the wood is subjected to the impact force
HindawiAdvances in Civil EngineeringVolume 2019 Article ID 7108262 18 pageshttpsdoiorg10115520197108262
and the stress wave propagates inside +e properties of thewood material are determined by measuring the change ofthe stress wave propagation velocity Riggio et al [8] statedstress waves could be used on-site for the identification ofinternal macroscopic defects in wooden structures How-ever the described technique permits only qualitative andlarge-scale analysis Other previous researches howeverhave also shown the stress wave detection method is simpleconvenient fast accurate and of low cost and it is not easilyaffected by the detection environment and suitable for fielddetection [16 17] In contrast other studies found that thestress wave detection method should be improved Forinstance Li et al [18] presented the stress wave velocitymodel to diagnosis the internal defects in urban treesAccording to Guntekin et al [19] the imaging results anddetection precision still need to be improved althoughmanystress wave detection devices are capable of generating two-dimensional or three-dimensional tomographic images ofwood cross sections Sun andWang [20] found that the two-dimensional image detected by the stress wave was notaccurate enough to show the shape of the decayed area
For X-ray scanning since wood parts and wood defectshave different X-ray absorption capacities the image formedby the X-ray scanning technique is also different and theinternal defects of the wood can be measured according to acertain process identification analysis Lechner et al [6]found that X-rays allowed a view into the structural memberor the connections Riggio et al [2] used X-rays to test theoriginal roof timbers of the Saint Annersquos Church in PragueCzech Republic +e results showed when the loss of woodcould not be determined visually it is possible to estimatethe extent of the void by measuring the dark area on theradiograph Wei et al [21] however pointed out that X-rayshad a low spatial resolution of the images when detectingwood defects In addition because of the high costsequipment mobility issues and health risks this method isusually employed only in industrial environments [22] Forinstance Yu et al [23] reported that the use of X-rays wasneither portable nor practical in field assessment and thisapproach posed a radiation hazard toward the users
+e drilling resistance method can quickly obtain thedefect results inside the wood according to the resistancecurve Nowak et al [11] used the drilling resistance methodin in situ assessment of structural timber to assess the extentof wood damage in the tested elements Nowak et al alsofound that the drilling resistance graph was influenced bymany factors including angle and direction of drilling
interwoodmoisture and drill bit sharpness Chang et al [24]and An et al [25] found that the result detected by drillingresistance could only reflect the wood damage condition onthe probe path thus it was difficult to give a specific andintuitive three-dimensional image In order to obtain moreprecise information more drilling resistance paths should beprovided [26]
+e ultrasonic spectrum technology primarily detectswood defects based on changes in the velocity of the ul-trasonic waves in the wood+e last commonly used methodto be examined is the ultrasonic wave method Dackermannet al [5] adopted the ultrasonic echo technique to obtain thedirect localization of a reflector such as a backwall or anyinhomogeneity or damage in the wood element But it isdifficult to locate the exact position of damage within thespecimen and distinguish between one large irregularitysuch as a knot and a cluster of small ones Perlin et al [22]also used ultrasound to determine an accurate pith locationWhen applied to a given wood structure this method canimprove its structural assessment given by other non-destructive methods such as drilling resistance stress wavetransmission and stress wave tomography Due to thecomplexity of the wood structure there are still problems tobe solved by applying the ultrasonic technology For ex-ample the air gap between the ultrasonic probe and woodrequires a good coupling agent [16]
Although many methods provide nondestructive as-sessment of the internal damage of old wood in timberstructures no single method can provide a complete data setfor analysis [11] In recent years many scholars have used acombination of detection methods to detect internal damageof wood components [8 15 20 24ndash31] However currentlythere are not many methods to quantify uniformly thedetection results detected by different methods In order toovercome the loss of information caused by a single de-tection method and quantify uniformly the detection resultscombined forecasting methods [32] are introduced to detectand predict the internal defects of wooden componentsChang et al [24] proposed a combined forecasting methodbased on the Shapley value to predict the internal defects ofwooden components +e weight coefficients of the stresswave and drilling resistance tests were fixed under eachworking condition without considering the dynamics of thedetected effects However the detected precision of thisdetection method is not the same under different workingconditions +e detected precision is high under a certainworking condition but when it is under another different
working condition it may be low +erefore this combinedforecasting method could not provide a consistent preciseprediction and still needs to be improved
In order to overcome the disadvantage of assigningweight in the previous combined forecasting model thispaper introduced the idea of variable weight According tothe detected precision of a single detection method undervarious working conditions the weight coefficients weregiven in an order from high to low +is greatly reduced thesensitivity of the result to a poor detection method Addi-tionally it effectively improved the forecasting precision ofthe internal damage of wooden components in ancientbuildings +e following four steps are used for evaluatingthe internal defect of wood components in ancient buildingsbased on the optimal combined forecasting model
Step 1 considering the relative lower costs of equip-ment and simpler execution in field applications testmethods based on stress wave and drilling resistancewere used to detect the internal defects of poplar andelm based on the idea of reverse simulationStep 2 based on the idea of variable weight and takingthe square sum of error square sum of logarithmicerror and square sum of reciprocal error as a guidelinethree combined forecasting models were establishedbased on the IOWA (induced ordered weighted av-erage) operator [33ndash35] IOWGA (induced orderedweighted geometric average) operator [36 37] andIOWHA (induced ordered weighted harmonic aver-age) operator [38 39] Additionally the combinedforecasting models based on the entropy value [40 41]and Shapley value [24ndash42] were used to compare withthe proposed methodsStep 3 based on the five indicators a comprehensiveevaluation index was developed to select the optimalcombined forecasting modelStep 4 according to the cross-validation theory [43]the optimal combined forecasting method was gener-alized into a model
2 Nondestructive Tests
21 Specimen Fabrication Poplar and elm commonly usedin ancient building timber components (eg beams andcolumns in the Guanyin Temple Changzhi City ShanxiProvince) were selected as test specimens to simulate thehollow and insect attacks in the wooden structure +e rawmaterials were sawed into a cylindrical shape of 100mmheight (see Figure 2(a)) and the sawing plane of the testpiece was required to be flat Based on the cross-sectionalarea (S) of the test piece there are five simulated damageratios which are respectively 132 116 18 14 and 12 ofthe cross-sectional area (S) of the test piece (see Figure 2(b))According to the method of reverse simulation the internalhollow and insect attacks were simulated by manual digging(see Figure 2(c)) and drilling (see Figure 2(d)) in the crosssections of the wood component
22 Test Hypothesis Considering that wood is an aniso-tropic material the physical properties of wood differ indifferent positions in the same tree When the water contentis the same the wave propagation velocity increases linearlywith the increase of density [44] In the radial direction of thetrunk the change in wood density is divided into three cases(1) increase from the bark to the pith (2) first increase andthen decrease from the bark to the pith and (3) decreasefrom the bark to the pith [45] To reduce the effect of thisdifference on the test results we designed the damaged areaof the test piece to be circular Additionally circular dam-aged areas of different sizes can better reflect the degree ofinternal damage of the wood +erefore we made two kindsof assumptions
(1) It is assumed that the circumference of the specimenis a complete circle regardless of the special shape ofthe wood
(2) It is assumed that the damage type of each specimenis a standard circle (see Figure 3)
23 Test Conditions +e indoor temperature is 20degC and theair relative humidity is 65 which meet the requirements ofthe ldquoStandard for test methods of timber structuresrdquo (GBT50329-2012) Test equipment includes Fakopp (stress wavetest equipment) made in Hungary IML-RESI PD500(drilling resistance test equipment) and GANN-HT85T(wood hygrometer) made in Germany and electric per-cussion drill (BOSCH) which are shown in Figure 4
+ere are 18 working conditions in total Each workingcondition simulates the detection of different defective areasof different tree species under different damage types Forexample the working condition 7 in Table 1 simulates acondition that the internal damage type of elm is hollow andthe proportion of the damaged area is 14 +rough visualinspection surface percussion and pressing there are noobvious joints splits and other defects Four specimens withan average moisture content of 918 are prepared for thistest +ey meet the requirements of the ldquoStandard for designof timber structuresrdquo (GB 50005-2017) [46] and ldquoStandardfor test methods of timber structuresrdquo (GBT 50329-2012)[47] +e specific parameters of the specimen are shown inTable 1
24 StressWaveDetection Fakopp 3D Acoustic Tomographis able to nondestructively detect the size and location of thedefective part in wood It works based on sound velocitymeasurement between several sensors around the trunk Ifthere is a hole the sound waves will have to pass around thehole +us they require more time to reach the oppositesensors In order to explain the complex velocity model atwo-dimensional image is constructed Healthy wood isshown in green decaying wood is shown in red and hollowis shown in blue +is test selected 10 sensors to detect theinternal damage of the specimen (see Figure 5) +e specifictest steps were as follows
Advances in Civil Engineering 3
(1) 10 Sensors were placed around the specimen con-necting to the wood with steel nails
(2) Sensors were connected to amplifier boxes(3) Bluetooth connection is established to PC(4) Each sensor is tapped 3 times by a hammer(5) +e data are transmitted to a laptop to calculate the
two-dimensional image
25 Drilling Resistance Tests Drilling resistance tests arebased on microdrilling of wood at a constant velocity by astandard drill IML-RESI PD500 has a small needle driven bya motor to penetrate into the wood at a constant speedWhen the drilling needle enters the interior of the wood it
encounters relative resistance in both directions which arethe forward direction and the direction of rotation +erelative resistance value varies with the density of each treespecies and the instrument records the relative resistanceduring the test +e resistance image processing software(PD-Tools Pro) is applied to export the data information toExcel which can be used to draw two-dimensional images ofrelative resistance In the figure the abscissa represents thepath length and the ordinate represents the relative re-sistance that the drilling needle encounters Based on themeasured impedance curve the width of the damaged areacan be determined according to the changes in the peaks andtroughs in the curve (see Figures 6(b) and 6(d)) +e decayinside the wood can be judged [48 49] and the test steps areas follows
Figure 3 Shape of the simulated defective area
(a) (b) (c) (d)
Figure 4 Specimen and test equipment (a) Fakopp (b) IML-RESI PD500 (c) GANN-HT85T (d) BOSCH
(a) (b) (c) (d)
Figure 2 Fabrication of test specimens (a) sawing (b) damage ratio (c) manual digging (d) manual drilling
4 Advances in Civil Engineering
Table 1 Parameters of test specimens
Working condition Damagedproportion
Simulationtype Tree species Radius (mm) Height (mm) Moisture
(1) +ree paths are selected for the test specimen(2) +e bit should be perpendicular to the direction of
the rings (see Figures 6(a) and 6(c))(3) +e drilling needle rotation rate and advance rate
parameters of the test equipment are set re-spectively +e stability of the drilling resistance testequipment should be ensured
3 Discussion and Analysis of Test Results
31 Two-Dimensional Images For example in specimen 2the tree species is elm and the simulated defect type ishollow Because of limited pages Figure 7 only shows therelative impedance curve in one path direction
When there is no internal damage in the specimen (seeFigure 7(a)) the two-dimensional image detected by stresswave tests is green and the relative impedance curve de-tected by drilling resistance tests is continuous Two de-tection methods indicate that the specimen is healthy woodWhile the internal hollow is small (when the damagedproportion is less than 18) pale yellow (see Figure 7(b)) andred (see Figure 7(c)) colors are presented in the center of thetwo-dimensional image detected by stress wave testsHowever the relative impedance curve image detected bythe drilling resistance tests starts to appear ldquoblankrdquo reflectingthe approximate width of the hollow area With the ex-pansion of the internal hollow area the center part of thetwo-dimensional image detected by stress wave tests shows abright blue color +e stress wave tests are more accurate inidentifying the size and location of internal hollow (seeFigures 7(d)ndash7(f)) +e stress wave tests visually express thelocation and size of internal hollow through colors but the
boundary of the hollow is relatively fuzzy For drilling re-sistance tests the length of the ldquoblankrdquo on the relative im-pedance curve increases with the expansion of the internalhollow area which is basically similar to the test resultsdetected by stress wave tests
To sum up the stress wave tests can quickly make anintuitive judgment on the general position and degree ofdamage but the judgment on the damage type is weak andthe boundary division of internal defects is fuzzy Howeverthe drilling resistance tests only reflect the internal damageof the wooden components under one path according to therelative impedance curve It is not possible to detect everyposition of a cross section and there is no great referencevalue when used alone If enough information is neededmore drilling resistance paths should be provided +roughanalysis it is found that the stress wave image and the re-sistance curve have a good correspondence relationship inthis test Putting the results of the two together for com-parative analysis can make up for their respectiveshortcomings
32DetectionData +edetection data listed in Table 2 showthat the detected precision of the same detection method isdifferent while it is working in various working conditions+e mean error and mean precision obtained by stress wavetests are 1113 cm2 and 729 respectively while the meanerror and mean precision obtained by drilling resistancetests are 847 cm2 and 876 respectively +e correlationcoefficients between the detected data obtained by stresswave and drilling resistance tests and the actual value are09894 and 09989 +e overall detection effect of drilling
(a)
100
Am
plitu
de (
) 80
60
40
20
00 2 4 6 8 10
Drilling depth (cm)
Hollow
12 14 16 18 20 22
(b)
(c)
100
Am
plitu
de (
) 80
60
40
20
00 2 4 6 8 10
Drilling depth (cm)
Insect attacks
12 14 16 18 20 22
(d)
Figure 6 Drilling resistance tests (a) hollow and (b) its two-dimensional image (c) insect attacks and (d) their two-dimensional image
6 Advances in Civil Engineering
resistance tests is more precise compared to that of stresswave tests
Although the correlation coefficients between the twosets of test data and the real value are very high the de-tected precision is still low under some conditions es-pecially when the stress wave detection is used We findthat the detected precision of the stress wave tests underworking condition 1 working condition 4 workingcondition 9 working condition 14 and working condition15 is relatively low +e proportion of damage simulatedunder the five working conditions is also small +ereforeit is of great engineering value to study the precision ofstress wave detection with such a small internal damagedproportion
When we examined the curves of detected precision underdifferent working conditions (see Figure 8) we found that thedetected precision obtained by stress wave tests increases withthe increase of the internal damaged area in the wood
As far as drilling resistance tests are concerned thedetected precision increases with the increase of the internaldefects in the wood when the internal damage type is hollow(see Figures 8(a) and 8(b))While the internal damage type isinsect attacks the detected precision of specimen 3 does notchange much with the increase of insect attack area (seeFigures 8(c) and 8(d))
In addition when the internal defects are small thedetected precision of drilling resistance tests is higher thanthat of stress wave tests With the further increase of
simulated damaged area the detected precision of bothdetection methods tends to be close to each other When theinternal damaged proportion of wood exceeds 14 thedetected precision of stress wave tests is higher than that ofdrilling resistance tests (see Figures 8(b)ndash8(d))
To sum up comprehensive use of stress wave and drillingresistance tests can screen the type position and size ofinternal damage of timber components However the de-tection results of the two detectionmethods are quite differentwith low detected precision In order to comprehensively usethe information provided by the two detection methods thispaper introduces several new combined forecasting modelswhich are different from the literature [24] in order to im-prove the prediction precision of the internal damage inancient building wood components
4 Combined Forecasting Model
41 Model Building Based on the OWA operator [50]OWGAoperator [51] andOWHAoperator [38] great deals ofextensions have been developed +ese extensions are theIOWA operator IOWGA operator and IOWHA operator Inthis study we reordered the arguments by an inducing variable
If there arem feasible single detection methods to detectinternal defects of the timber components in ancientbuildings under a certain working condition the detectionvalue of the i-th detection method in the t-th workingcondition is xit where i 1 2 m and t 1 2 N
If lm is the weight of the m-th single detection in thecombined forecasting model the weight satisfy the nor-malization and nonnegativity such that
116 18 1455
60
65
70
75
80
85
90
95D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(a)
132 116 18 14 1230
40
50
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(b)
132 116 18 14 12
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(c)
132 116 18 14 1230
40
50
60
70
80
90
100D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(d)
Figure 8 Curves of detected precision under different working conditions (a) Specimen 1 (b) Specimen 2 (c) Specimen 3 (d) Specimen 4
where ait represents the detected precision of the i-th de-tection method under the t-th working condition ait isin [0 1]When ait is regarded as the inducement value of xit it canformm two-dimensional arrays which are (a1t x1t) (a2t x2t) (amt xmt) +e detected precision sequence (a1t a2t amt) of m detection methods under the t-th working con-dition is arranged from high to low Let us hypothesize thata-index(it) is a subscript of the i-th largest value among thedetection sequence
(1) Model based on the IOWA operator [34] the squaresum of error is taken as the criterion to establish thecombined forecasting model According to the de-tected precision sequence the combined forecastingvalue based on the IOWA operator can be obtainedby
IL a1t x1t( 1113857 a2t x2t( 1113857 amt xmt( 11138571113858 1113859
1113944m
i1lixaminusindex(it)
(2)
+e optimal combined forecasting model based onthe IOWA operator with the square sum of error asthe criterion can be expressed as follows
SIOWA 1113944N
t1xt minus 1113944
m
i1lixaminusindex(it)
⎛⎝ ⎞⎠
2
(3)
(2) Model based on the IOWGA operator [36] thesquare sum of logarithmic error is taken as thecriterion to establish the combined forecastingmodel According to the detected precision se-quence the combined forecasting value based on theIOWGA operator can be obtained by
+eoptimal combined forecastingmodel based on theIOWGA operator with the square sum of logarithmicerror as the criterion can be expressed as follows
SIOWGA 1113944N
t1lnxt minus ln1113945
m
i1x
liaminusindex(it)
⎞⎠
2
⎛⎝ (5)
(3) Model based on the IOWHA operator [38] thesquare sum of reciprocal error is taken as the cri-terion to establish the combined forecasting modelAccording to the detected precision sequence thecombined forecasting value based on the IOWHAoperator can be obtained by
+e optimal combined forecasting model based onthe IOWHA operator with the square sum of re-ciprocal error as the criterion can be expressed asfollows
SIOWHA 1113944N
t11113944
m
i1li
1xt
minus1
xaminusindex(it)
1113888 1113889⎛⎝ ⎞⎠
2
(7)
42 Solving Model Taking the simulated hollow test ofspecimen 1 as an example we can list the two-dimensionalarray of detection values and its detected precision under thet-th working condition as follows
(0576 3722) (0817 2134)
(0650 7059) (0844 4412)
(0808 12464) (0909 9502)
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (8)
+e prediction value based on the IOWA operator iscalculated according to equation (2) +e solving process isshown as follows
By substituting them into equation (3) the optimalcombined forecasting model based on the IOWA operator isarranged as follows
min SIOWA l1 l2( 1113857 2613minus 2134l1 minus 3722l2( 11138572
+ 5227minus 4412l1 minus 7059l2( 11138572
+ 10454minus 9502l1 minus 12464l2( 11138572
stl1 + l2 1
l1 ge 0 l2 ge 01113896
(10)
Advances in Civil Engineering 9
+e MATLAB software is used to solve the optimalweight (li) Some parameters of the genetic algorithm are setas follows
Generations 50StallGenLimi 100PopInitRange [zeros(1 m) ones(1 m)]PopulationSize 10000
After 50 genetic iterations the MATLAB softwareshows that (l1 l2) is (069 031) respectively +e black andblue points in Figure 9 are the best fitness value and themean fitness value respectively It is found that the meanfitness value of the population represents a smoothdownward trend with the increase of the number of iter-ations and gradually moves towards the best fitness value(see Figure 9)
Similarly the solving processes of the models basedon the IOWGA operator and IOWHA operator are thesame as that of the model based on the IOWA operator Inorder to select the optimal model the traditional com-bined forecasting models based on the entropy valueand Shapley value are introduced in this paper forcomparison
43 Analyzing Precision of Different Combined ForecastingModels In Table 3 the mean precision from large to small isP1 P2 P3 P4 and P5 Compared to detected precision ofstress wave tests the precision is improved by 258 254252 215 and 176 respectively While compared todetected precision of drilling resistance tests the precision isimproved by 47 43 42 11 and 22 respectivelyAdditionally the mean absolute error from small to large ise1 e2 e3 e5 and e4 So we find that the models based on theIOWA operator IOWGA operator and IOWHA operatorhave better forecasting effects compared to others (seeFigure 10)
Other than that through statistical analysis of workingcondition 1 working condition 4 working condition 9working condition 14 and working condition 15 (seeTable 4) we also find that the combined forecasting modelsbased on the IOWA operator IOWGA operator andIOWHA operator are more effective compared to thecombined forecasting models based on the entropy valueand Shapley value in improving the detected precision ofstress wave tests in the case of small defects inside thewood
44 Forecasting Effect Evaluation According to the eval-uation principle of the forecasting effect SSE MSEMAE MAPE and MSPE are selected as evaluation in-dexes to reflect the effectiveness of the combined fore-casting models +e calculation results are shown inTable 5
In Table 5 it is found that the first four indexes of thecombined forecasting method based on the IOWA oper-ator are significantly lower than those of others AlthoughMSPE of the combined forecasting method based on theIOWA operator is not the least it is close to MSPE ofcombined forecasting methods based on the IOWGAoperator and IOWHA operator +erefore the combinedforecasting model based on the IOWA operator has thebest effect Meanwhile by normalizing the above fiveindexes the expression of the comprehensive evaluationindex C is obtained as follows
Ci 1n
1113944
n
j1
min Ej1113872 1113873
Eij
(12)
Best 011231 mean 0497158
Best fitness Mean fitness
Fitn
ess v
alue
0 5 10 15 20 25 30 35 40 45 50Generation
180
160
140
120
100
80
60
40
20
0
Figure 9 Best fitness value and mean fitness value
10 Advances in Civil Engineering
where Ci is the comprehensive evaluation index of the i-thmethod i 1 2 M Eij is the j-th index of the i-thmethod j 1 2 n and min(Ej) is the minimum valueamong the j-th indexes of m methods +e higher the C isthe better the corresponding combined forecasting model is+e index C of each method is developed by bringing the fiveindex values in Table 5 into equation (12)
Figure 11 shows that the comprehensive evaluationindex of each combined forecasting model is significantlyhigher than that of the two single detection methods in-dicating that the combined forecasting model can improvethe forecasting precision of the internal defects of the timber
components Furthermore the C of the combined fore-casting model based on the IOWA operator is 972 higherthan others All the analysis shows that the combinedforecasting model based on the IOWA operator is the op-timal model followed by the combined forecasting modelsbased on the IOWGA operator and IOWHA operator
5 Applicability Assessment
An applicability assessment is performed for the combinedforecasting models based on the IOWA operator IOWGAoperator and IOWHA operator
51 Cross-Validation 9eory Since there are a total of 18working conditions in this test each working conditionhas a corresponding set of actual values and detectedvalues obtained by stress wave and drilling resistance tests(see Table 2) Because of the small number of data samplesand each combined forecasting model is tested only oncethe randomness is large which does not prove that theabove optimal models have good universality In order tomake full use of the data samples a cross-validationmethod is applied to carry out the test +e researchprocess is shown in Figure 12
Firstly by setting random samples we randomlyextracted N (N 5 6 17) working conditions from 18working conditions as a training set (IN) and then thecorresponding remaining 18minusN working conditions areconsidered as a testing set (IN) For the number (N) ofrandomly selected samples there are CN
18 subsets for both thetraining set and the testing set (see Table 6) For example ifN 5 both the training set (I5) and the testing set (I5) willhave 8568 subsets
Table 3 Results of each combined forecasting model
If I5 working condition 1 working condition 2working condition 3 working condition 4 working con-dition 5 then I5 working condition 6 working condi-tion 7 working condition 8 working condition 9 workingcondition 10 working condition 11 working condition 12working condition 13 working condition 14 workingcondition 15 working condition 16 working condition17
By analogy we can get 8568 subsets for the training set(I5) and the testing set (I5)
Secondly based on random sample data in each trainingset (IN) three combined forecasting models based on theIOWA operator IOWGA operator and IOWHA operatorare established to solve three sets of corresponding optimalweights Based on the cross-validation method three sets ofweights are substituted into the corresponding testing set(IN) For the training set and testing set we can get thecomprehensive evaluation index C corresponding to eachcombined forecasting model using equation (12)
Finally we calculate the mean value (EC) and variance(VC) of the comprehensive evaluation index C +rough thestatistical analysis of the change law of the mean value (EC)and variance (VC) the universality of the optimal combinedforecasting model is judged
52 Cross-Validation Result Analysis +e mean value (EC)and the variance (VC) of the comprehensive evaluationindexes are evaluated by each combined forecasting modelin the training sets (see Table 7)
In Table 7 we find that EC-IOWA of each training set has asignificantly higher value compared to EC-IOWGA and EC-IOWHA+e higher the EC is the better the overall forecasting precisionis +e alignment of the variance of the comprehensive evalu-ation indexes is VC-IOWAltVC-IOWGAltVC-IOWHA +e smallerthe VC is the smaller the dispersion of the C value is and themore stable the data change is+is indicates that the combinedforecasting model based on the IOWA operator is wellapplicable
In Figure 13 the distribution maps of EC and VC corre-sponding to each training set show a roughly linear changingtrend When the sample data in the training set (IN) increaseEC-IOWA and EC-IOWH increase and EC-IOWGA decreases Withthe increase of the number of sample data in the training setsthe VC of the three combined forecasting models decreasesBut the change of VC-IOWA is smallest indicating that the Cdoes not fluctuate much and the data are very stable
Based on the cross-validation theory the optimalweights obtained by each training set are brought into thecorresponding testing set EC and VC of the testing sets arelisted in Table 8 and the distribution maps of EC and VCcalculated by each testing set are shown in Figure 14
In Table 8 EC-IOWA of testing sets is significantlyhigher than EC-IOWGA and EC-IOWHA while VC-IOWA issignificantly lower than VC-IOWGA and VC-IOWHA How-ever it is noted the values of EC-IOWGA and EC-IOWHA orVC-IOWGA and VC-IOWHA are very close to each otherMeanwhile it is found from Figure 14 that EC corre-sponding to each testing set decreases with the decrease ofthe sample number in the testing sets Contrarily VCincreases with the decrease of the sample number in thetesting sets +e distribution map of VC-IOWA has littlechange in slope meaning the corresponding C value ismore stable +e results show that the combined fore-casting model based on the IOWA operator has thehighest overall forecasting precision and best level ofapplicability among the three models
6 Nondestructive Tests for Double-CiroldLongevity Pavilion
Double-Cirold Longevity Pavilion is located in the BeijingTiantan Park It was built in the Middle Qing Dynasty andhas a history of 277 years Double-Cirold Longevity Pavilionis a combination of two round pavilions with double eavesand spires Its structure is peculiar and precise and its shapeis novel and well proportioned +is kind of pavilion hashigh scientific artistic and cultural value in the Chinesetimber structure Affected by the natural environment andhuman factors all year round timber components aredamaged Eventually it leads to the loss of the externalprotective layer for timber components and the accelerationof the internal and external damage of timber components
Nondestructive tests of timber components of thedouble-ring marsupial pavilion were performed by stresswave and drilling resistance (see Figure 15) It was found thatthe beams and the columns had internal defects +e B2column of Double-Cirold Longevity Pavilion is an examplewith a moisture content of 98 +e perimeter of thewooden column is 1099 cm and the detected section area is96163 cm2 According to the two-dimensional image ob-tained by the stress wave tests the internal defects werelocated Drilling resistance tests were conducted pertinently+ere were two detected paths in drilling resistance tests andeach path passed through the location of defects
+rough nondestructive tests it was found that there wasan uncompacted sound when knocking the position of theB2 column 400mm from the ground A certain degree ofdefect is found in the interior wood by the stress wave tests(see Figure 16) +e damaged area detected by the stresswave tests accounts for 18 of the detected section and thedamaged area is 17309 cm2 +e drilling resistance testsshow the damaged area is 49 cm2 +e damaged area of theB2 column calculated by the combined forecasting model
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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and the stress wave propagates inside +e properties of thewood material are determined by measuring the change ofthe stress wave propagation velocity Riggio et al [8] statedstress waves could be used on-site for the identification ofinternal macroscopic defects in wooden structures How-ever the described technique permits only qualitative andlarge-scale analysis Other previous researches howeverhave also shown the stress wave detection method is simpleconvenient fast accurate and of low cost and it is not easilyaffected by the detection environment and suitable for fielddetection [16 17] In contrast other studies found that thestress wave detection method should be improved Forinstance Li et al [18] presented the stress wave velocitymodel to diagnosis the internal defects in urban treesAccording to Guntekin et al [19] the imaging results anddetection precision still need to be improved althoughmanystress wave detection devices are capable of generating two-dimensional or three-dimensional tomographic images ofwood cross sections Sun andWang [20] found that the two-dimensional image detected by the stress wave was notaccurate enough to show the shape of the decayed area
For X-ray scanning since wood parts and wood defectshave different X-ray absorption capacities the image formedby the X-ray scanning technique is also different and theinternal defects of the wood can be measured according to acertain process identification analysis Lechner et al [6]found that X-rays allowed a view into the structural memberor the connections Riggio et al [2] used X-rays to test theoriginal roof timbers of the Saint Annersquos Church in PragueCzech Republic +e results showed when the loss of woodcould not be determined visually it is possible to estimatethe extent of the void by measuring the dark area on theradiograph Wei et al [21] however pointed out that X-rayshad a low spatial resolution of the images when detectingwood defects In addition because of the high costsequipment mobility issues and health risks this method isusually employed only in industrial environments [22] Forinstance Yu et al [23] reported that the use of X-rays wasneither portable nor practical in field assessment and thisapproach posed a radiation hazard toward the users
+e drilling resistance method can quickly obtain thedefect results inside the wood according to the resistancecurve Nowak et al [11] used the drilling resistance methodin in situ assessment of structural timber to assess the extentof wood damage in the tested elements Nowak et al alsofound that the drilling resistance graph was influenced bymany factors including angle and direction of drilling
interwoodmoisture and drill bit sharpness Chang et al [24]and An et al [25] found that the result detected by drillingresistance could only reflect the wood damage condition onthe probe path thus it was difficult to give a specific andintuitive three-dimensional image In order to obtain moreprecise information more drilling resistance paths should beprovided [26]
+e ultrasonic spectrum technology primarily detectswood defects based on changes in the velocity of the ul-trasonic waves in the wood+e last commonly used methodto be examined is the ultrasonic wave method Dackermannet al [5] adopted the ultrasonic echo technique to obtain thedirect localization of a reflector such as a backwall or anyinhomogeneity or damage in the wood element But it isdifficult to locate the exact position of damage within thespecimen and distinguish between one large irregularitysuch as a knot and a cluster of small ones Perlin et al [22]also used ultrasound to determine an accurate pith locationWhen applied to a given wood structure this method canimprove its structural assessment given by other non-destructive methods such as drilling resistance stress wavetransmission and stress wave tomography Due to thecomplexity of the wood structure there are still problems tobe solved by applying the ultrasonic technology For ex-ample the air gap between the ultrasonic probe and woodrequires a good coupling agent [16]
Although many methods provide nondestructive as-sessment of the internal damage of old wood in timberstructures no single method can provide a complete data setfor analysis [11] In recent years many scholars have used acombination of detection methods to detect internal damageof wood components [8 15 20 24ndash31] However currentlythere are not many methods to quantify uniformly thedetection results detected by different methods In order toovercome the loss of information caused by a single de-tection method and quantify uniformly the detection resultscombined forecasting methods [32] are introduced to detectand predict the internal defects of wooden componentsChang et al [24] proposed a combined forecasting methodbased on the Shapley value to predict the internal defects ofwooden components +e weight coefficients of the stresswave and drilling resistance tests were fixed under eachworking condition without considering the dynamics of thedetected effects However the detected precision of thisdetection method is not the same under different workingconditions +e detected precision is high under a certainworking condition but when it is under another different
working condition it may be low +erefore this combinedforecasting method could not provide a consistent preciseprediction and still needs to be improved
In order to overcome the disadvantage of assigningweight in the previous combined forecasting model thispaper introduced the idea of variable weight According tothe detected precision of a single detection method undervarious working conditions the weight coefficients weregiven in an order from high to low +is greatly reduced thesensitivity of the result to a poor detection method Addi-tionally it effectively improved the forecasting precision ofthe internal damage of wooden components in ancientbuildings +e following four steps are used for evaluatingthe internal defect of wood components in ancient buildingsbased on the optimal combined forecasting model
Step 1 considering the relative lower costs of equip-ment and simpler execution in field applications testmethods based on stress wave and drilling resistancewere used to detect the internal defects of poplar andelm based on the idea of reverse simulationStep 2 based on the idea of variable weight and takingthe square sum of error square sum of logarithmicerror and square sum of reciprocal error as a guidelinethree combined forecasting models were establishedbased on the IOWA (induced ordered weighted av-erage) operator [33ndash35] IOWGA (induced orderedweighted geometric average) operator [36 37] andIOWHA (induced ordered weighted harmonic aver-age) operator [38 39] Additionally the combinedforecasting models based on the entropy value [40 41]and Shapley value [24ndash42] were used to compare withthe proposed methodsStep 3 based on the five indicators a comprehensiveevaluation index was developed to select the optimalcombined forecasting modelStep 4 according to the cross-validation theory [43]the optimal combined forecasting method was gener-alized into a model
2 Nondestructive Tests
21 Specimen Fabrication Poplar and elm commonly usedin ancient building timber components (eg beams andcolumns in the Guanyin Temple Changzhi City ShanxiProvince) were selected as test specimens to simulate thehollow and insect attacks in the wooden structure +e rawmaterials were sawed into a cylindrical shape of 100mmheight (see Figure 2(a)) and the sawing plane of the testpiece was required to be flat Based on the cross-sectionalarea (S) of the test piece there are five simulated damageratios which are respectively 132 116 18 14 and 12 ofthe cross-sectional area (S) of the test piece (see Figure 2(b))According to the method of reverse simulation the internalhollow and insect attacks were simulated by manual digging(see Figure 2(c)) and drilling (see Figure 2(d)) in the crosssections of the wood component
22 Test Hypothesis Considering that wood is an aniso-tropic material the physical properties of wood differ indifferent positions in the same tree When the water contentis the same the wave propagation velocity increases linearlywith the increase of density [44] In the radial direction of thetrunk the change in wood density is divided into three cases(1) increase from the bark to the pith (2) first increase andthen decrease from the bark to the pith and (3) decreasefrom the bark to the pith [45] To reduce the effect of thisdifference on the test results we designed the damaged areaof the test piece to be circular Additionally circular dam-aged areas of different sizes can better reflect the degree ofinternal damage of the wood +erefore we made two kindsof assumptions
(1) It is assumed that the circumference of the specimenis a complete circle regardless of the special shape ofthe wood
(2) It is assumed that the damage type of each specimenis a standard circle (see Figure 3)
23 Test Conditions +e indoor temperature is 20degC and theair relative humidity is 65 which meet the requirements ofthe ldquoStandard for test methods of timber structuresrdquo (GBT50329-2012) Test equipment includes Fakopp (stress wavetest equipment) made in Hungary IML-RESI PD500(drilling resistance test equipment) and GANN-HT85T(wood hygrometer) made in Germany and electric per-cussion drill (BOSCH) which are shown in Figure 4
+ere are 18 working conditions in total Each workingcondition simulates the detection of different defective areasof different tree species under different damage types Forexample the working condition 7 in Table 1 simulates acondition that the internal damage type of elm is hollow andthe proportion of the damaged area is 14 +rough visualinspection surface percussion and pressing there are noobvious joints splits and other defects Four specimens withan average moisture content of 918 are prepared for thistest +ey meet the requirements of the ldquoStandard for designof timber structuresrdquo (GB 50005-2017) [46] and ldquoStandardfor test methods of timber structuresrdquo (GBT 50329-2012)[47] +e specific parameters of the specimen are shown inTable 1
24 StressWaveDetection Fakopp 3D Acoustic Tomographis able to nondestructively detect the size and location of thedefective part in wood It works based on sound velocitymeasurement between several sensors around the trunk Ifthere is a hole the sound waves will have to pass around thehole +us they require more time to reach the oppositesensors In order to explain the complex velocity model atwo-dimensional image is constructed Healthy wood isshown in green decaying wood is shown in red and hollowis shown in blue +is test selected 10 sensors to detect theinternal damage of the specimen (see Figure 5) +e specifictest steps were as follows
Advances in Civil Engineering 3
(1) 10 Sensors were placed around the specimen con-necting to the wood with steel nails
(2) Sensors were connected to amplifier boxes(3) Bluetooth connection is established to PC(4) Each sensor is tapped 3 times by a hammer(5) +e data are transmitted to a laptop to calculate the
two-dimensional image
25 Drilling Resistance Tests Drilling resistance tests arebased on microdrilling of wood at a constant velocity by astandard drill IML-RESI PD500 has a small needle driven bya motor to penetrate into the wood at a constant speedWhen the drilling needle enters the interior of the wood it
encounters relative resistance in both directions which arethe forward direction and the direction of rotation +erelative resistance value varies with the density of each treespecies and the instrument records the relative resistanceduring the test +e resistance image processing software(PD-Tools Pro) is applied to export the data information toExcel which can be used to draw two-dimensional images ofrelative resistance In the figure the abscissa represents thepath length and the ordinate represents the relative re-sistance that the drilling needle encounters Based on themeasured impedance curve the width of the damaged areacan be determined according to the changes in the peaks andtroughs in the curve (see Figures 6(b) and 6(d)) +e decayinside the wood can be judged [48 49] and the test steps areas follows
Figure 3 Shape of the simulated defective area
(a) (b) (c) (d)
Figure 4 Specimen and test equipment (a) Fakopp (b) IML-RESI PD500 (c) GANN-HT85T (d) BOSCH
(a) (b) (c) (d)
Figure 2 Fabrication of test specimens (a) sawing (b) damage ratio (c) manual digging (d) manual drilling
4 Advances in Civil Engineering
Table 1 Parameters of test specimens
Working condition Damagedproportion
Simulationtype Tree species Radius (mm) Height (mm) Moisture
(1) +ree paths are selected for the test specimen(2) +e bit should be perpendicular to the direction of
the rings (see Figures 6(a) and 6(c))(3) +e drilling needle rotation rate and advance rate
parameters of the test equipment are set re-spectively +e stability of the drilling resistance testequipment should be ensured
3 Discussion and Analysis of Test Results
31 Two-Dimensional Images For example in specimen 2the tree species is elm and the simulated defect type ishollow Because of limited pages Figure 7 only shows therelative impedance curve in one path direction
When there is no internal damage in the specimen (seeFigure 7(a)) the two-dimensional image detected by stresswave tests is green and the relative impedance curve de-tected by drilling resistance tests is continuous Two de-tection methods indicate that the specimen is healthy woodWhile the internal hollow is small (when the damagedproportion is less than 18) pale yellow (see Figure 7(b)) andred (see Figure 7(c)) colors are presented in the center of thetwo-dimensional image detected by stress wave testsHowever the relative impedance curve image detected bythe drilling resistance tests starts to appear ldquoblankrdquo reflectingthe approximate width of the hollow area With the ex-pansion of the internal hollow area the center part of thetwo-dimensional image detected by stress wave tests shows abright blue color +e stress wave tests are more accurate inidentifying the size and location of internal hollow (seeFigures 7(d)ndash7(f)) +e stress wave tests visually express thelocation and size of internal hollow through colors but the
boundary of the hollow is relatively fuzzy For drilling re-sistance tests the length of the ldquoblankrdquo on the relative im-pedance curve increases with the expansion of the internalhollow area which is basically similar to the test resultsdetected by stress wave tests
To sum up the stress wave tests can quickly make anintuitive judgment on the general position and degree ofdamage but the judgment on the damage type is weak andthe boundary division of internal defects is fuzzy Howeverthe drilling resistance tests only reflect the internal damageof the wooden components under one path according to therelative impedance curve It is not possible to detect everyposition of a cross section and there is no great referencevalue when used alone If enough information is neededmore drilling resistance paths should be provided +roughanalysis it is found that the stress wave image and the re-sistance curve have a good correspondence relationship inthis test Putting the results of the two together for com-parative analysis can make up for their respectiveshortcomings
32DetectionData +edetection data listed in Table 2 showthat the detected precision of the same detection method isdifferent while it is working in various working conditions+e mean error and mean precision obtained by stress wavetests are 1113 cm2 and 729 respectively while the meanerror and mean precision obtained by drilling resistancetests are 847 cm2 and 876 respectively +e correlationcoefficients between the detected data obtained by stresswave and drilling resistance tests and the actual value are09894 and 09989 +e overall detection effect of drilling
(a)
100
Am
plitu
de (
) 80
60
40
20
00 2 4 6 8 10
Drilling depth (cm)
Hollow
12 14 16 18 20 22
(b)
(c)
100
Am
plitu
de (
) 80
60
40
20
00 2 4 6 8 10
Drilling depth (cm)
Insect attacks
12 14 16 18 20 22
(d)
Figure 6 Drilling resistance tests (a) hollow and (b) its two-dimensional image (c) insect attacks and (d) their two-dimensional image
6 Advances in Civil Engineering
resistance tests is more precise compared to that of stresswave tests
Although the correlation coefficients between the twosets of test data and the real value are very high the de-tected precision is still low under some conditions es-pecially when the stress wave detection is used We findthat the detected precision of the stress wave tests underworking condition 1 working condition 4 workingcondition 9 working condition 14 and working condition15 is relatively low +e proportion of damage simulatedunder the five working conditions is also small +ereforeit is of great engineering value to study the precision ofstress wave detection with such a small internal damagedproportion
When we examined the curves of detected precision underdifferent working conditions (see Figure 8) we found that thedetected precision obtained by stress wave tests increases withthe increase of the internal damaged area in the wood
As far as drilling resistance tests are concerned thedetected precision increases with the increase of the internaldefects in the wood when the internal damage type is hollow(see Figures 8(a) and 8(b))While the internal damage type isinsect attacks the detected precision of specimen 3 does notchange much with the increase of insect attack area (seeFigures 8(c) and 8(d))
In addition when the internal defects are small thedetected precision of drilling resistance tests is higher thanthat of stress wave tests With the further increase of
simulated damaged area the detected precision of bothdetection methods tends to be close to each other When theinternal damaged proportion of wood exceeds 14 thedetected precision of stress wave tests is higher than that ofdrilling resistance tests (see Figures 8(b)ndash8(d))
To sum up comprehensive use of stress wave and drillingresistance tests can screen the type position and size ofinternal damage of timber components However the de-tection results of the two detectionmethods are quite differentwith low detected precision In order to comprehensively usethe information provided by the two detection methods thispaper introduces several new combined forecasting modelswhich are different from the literature [24] in order to im-prove the prediction precision of the internal damage inancient building wood components
4 Combined Forecasting Model
41 Model Building Based on the OWA operator [50]OWGAoperator [51] andOWHAoperator [38] great deals ofextensions have been developed +ese extensions are theIOWA operator IOWGA operator and IOWHA operator Inthis study we reordered the arguments by an inducing variable
If there arem feasible single detection methods to detectinternal defects of the timber components in ancientbuildings under a certain working condition the detectionvalue of the i-th detection method in the t-th workingcondition is xit where i 1 2 m and t 1 2 N
If lm is the weight of the m-th single detection in thecombined forecasting model the weight satisfy the nor-malization and nonnegativity such that
116 18 1455
60
65
70
75
80
85
90
95D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(a)
132 116 18 14 1230
40
50
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(b)
132 116 18 14 12
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(c)
132 116 18 14 1230
40
50
60
70
80
90
100D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(d)
Figure 8 Curves of detected precision under different working conditions (a) Specimen 1 (b) Specimen 2 (c) Specimen 3 (d) Specimen 4
where ait represents the detected precision of the i-th de-tection method under the t-th working condition ait isin [0 1]When ait is regarded as the inducement value of xit it canformm two-dimensional arrays which are (a1t x1t) (a2t x2t) (amt xmt) +e detected precision sequence (a1t a2t amt) of m detection methods under the t-th working con-dition is arranged from high to low Let us hypothesize thata-index(it) is a subscript of the i-th largest value among thedetection sequence
(1) Model based on the IOWA operator [34] the squaresum of error is taken as the criterion to establish thecombined forecasting model According to the de-tected precision sequence the combined forecastingvalue based on the IOWA operator can be obtainedby
IL a1t x1t( 1113857 a2t x2t( 1113857 amt xmt( 11138571113858 1113859
1113944m
i1lixaminusindex(it)
(2)
+e optimal combined forecasting model based onthe IOWA operator with the square sum of error asthe criterion can be expressed as follows
SIOWA 1113944N
t1xt minus 1113944
m
i1lixaminusindex(it)
⎛⎝ ⎞⎠
2
(3)
(2) Model based on the IOWGA operator [36] thesquare sum of logarithmic error is taken as thecriterion to establish the combined forecastingmodel According to the detected precision se-quence the combined forecasting value based on theIOWGA operator can be obtained by
+eoptimal combined forecastingmodel based on theIOWGA operator with the square sum of logarithmicerror as the criterion can be expressed as follows
SIOWGA 1113944N
t1lnxt minus ln1113945
m
i1x
liaminusindex(it)
⎞⎠
2
⎛⎝ (5)
(3) Model based on the IOWHA operator [38] thesquare sum of reciprocal error is taken as the cri-terion to establish the combined forecasting modelAccording to the detected precision sequence thecombined forecasting value based on the IOWHAoperator can be obtained by
+e optimal combined forecasting model based onthe IOWHA operator with the square sum of re-ciprocal error as the criterion can be expressed asfollows
SIOWHA 1113944N
t11113944
m
i1li
1xt
minus1
xaminusindex(it)
1113888 1113889⎛⎝ ⎞⎠
2
(7)
42 Solving Model Taking the simulated hollow test ofspecimen 1 as an example we can list the two-dimensionalarray of detection values and its detected precision under thet-th working condition as follows
(0576 3722) (0817 2134)
(0650 7059) (0844 4412)
(0808 12464) (0909 9502)
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (8)
+e prediction value based on the IOWA operator iscalculated according to equation (2) +e solving process isshown as follows
By substituting them into equation (3) the optimalcombined forecasting model based on the IOWA operator isarranged as follows
min SIOWA l1 l2( 1113857 2613minus 2134l1 minus 3722l2( 11138572
+ 5227minus 4412l1 minus 7059l2( 11138572
+ 10454minus 9502l1 minus 12464l2( 11138572
stl1 + l2 1
l1 ge 0 l2 ge 01113896
(10)
Advances in Civil Engineering 9
+e MATLAB software is used to solve the optimalweight (li) Some parameters of the genetic algorithm are setas follows
Generations 50StallGenLimi 100PopInitRange [zeros(1 m) ones(1 m)]PopulationSize 10000
After 50 genetic iterations the MATLAB softwareshows that (l1 l2) is (069 031) respectively +e black andblue points in Figure 9 are the best fitness value and themean fitness value respectively It is found that the meanfitness value of the population represents a smoothdownward trend with the increase of the number of iter-ations and gradually moves towards the best fitness value(see Figure 9)
Similarly the solving processes of the models basedon the IOWGA operator and IOWHA operator are thesame as that of the model based on the IOWA operator Inorder to select the optimal model the traditional com-bined forecasting models based on the entropy valueand Shapley value are introduced in this paper forcomparison
43 Analyzing Precision of Different Combined ForecastingModels In Table 3 the mean precision from large to small isP1 P2 P3 P4 and P5 Compared to detected precision ofstress wave tests the precision is improved by 258 254252 215 and 176 respectively While compared todetected precision of drilling resistance tests the precision isimproved by 47 43 42 11 and 22 respectivelyAdditionally the mean absolute error from small to large ise1 e2 e3 e5 and e4 So we find that the models based on theIOWA operator IOWGA operator and IOWHA operatorhave better forecasting effects compared to others (seeFigure 10)
Other than that through statistical analysis of workingcondition 1 working condition 4 working condition 9working condition 14 and working condition 15 (seeTable 4) we also find that the combined forecasting modelsbased on the IOWA operator IOWGA operator andIOWHA operator are more effective compared to thecombined forecasting models based on the entropy valueand Shapley value in improving the detected precision ofstress wave tests in the case of small defects inside thewood
44 Forecasting Effect Evaluation According to the eval-uation principle of the forecasting effect SSE MSEMAE MAPE and MSPE are selected as evaluation in-dexes to reflect the effectiveness of the combined fore-casting models +e calculation results are shown inTable 5
In Table 5 it is found that the first four indexes of thecombined forecasting method based on the IOWA oper-ator are significantly lower than those of others AlthoughMSPE of the combined forecasting method based on theIOWA operator is not the least it is close to MSPE ofcombined forecasting methods based on the IOWGAoperator and IOWHA operator +erefore the combinedforecasting model based on the IOWA operator has thebest effect Meanwhile by normalizing the above fiveindexes the expression of the comprehensive evaluationindex C is obtained as follows
Ci 1n
1113944
n
j1
min Ej1113872 1113873
Eij
(12)
Best 011231 mean 0497158
Best fitness Mean fitness
Fitn
ess v
alue
0 5 10 15 20 25 30 35 40 45 50Generation
180
160
140
120
100
80
60
40
20
0
Figure 9 Best fitness value and mean fitness value
10 Advances in Civil Engineering
where Ci is the comprehensive evaluation index of the i-thmethod i 1 2 M Eij is the j-th index of the i-thmethod j 1 2 n and min(Ej) is the minimum valueamong the j-th indexes of m methods +e higher the C isthe better the corresponding combined forecasting model is+e index C of each method is developed by bringing the fiveindex values in Table 5 into equation (12)
Figure 11 shows that the comprehensive evaluationindex of each combined forecasting model is significantlyhigher than that of the two single detection methods in-dicating that the combined forecasting model can improvethe forecasting precision of the internal defects of the timber
components Furthermore the C of the combined fore-casting model based on the IOWA operator is 972 higherthan others All the analysis shows that the combinedforecasting model based on the IOWA operator is the op-timal model followed by the combined forecasting modelsbased on the IOWGA operator and IOWHA operator
5 Applicability Assessment
An applicability assessment is performed for the combinedforecasting models based on the IOWA operator IOWGAoperator and IOWHA operator
51 Cross-Validation 9eory Since there are a total of 18working conditions in this test each working conditionhas a corresponding set of actual values and detectedvalues obtained by stress wave and drilling resistance tests(see Table 2) Because of the small number of data samplesand each combined forecasting model is tested only oncethe randomness is large which does not prove that theabove optimal models have good universality In order tomake full use of the data samples a cross-validationmethod is applied to carry out the test +e researchprocess is shown in Figure 12
Firstly by setting random samples we randomlyextracted N (N 5 6 17) working conditions from 18working conditions as a training set (IN) and then thecorresponding remaining 18minusN working conditions areconsidered as a testing set (IN) For the number (N) ofrandomly selected samples there are CN
18 subsets for both thetraining set and the testing set (see Table 6) For example ifN 5 both the training set (I5) and the testing set (I5) willhave 8568 subsets
Table 3 Results of each combined forecasting model
If I5 working condition 1 working condition 2working condition 3 working condition 4 working con-dition 5 then I5 working condition 6 working condi-tion 7 working condition 8 working condition 9 workingcondition 10 working condition 11 working condition 12working condition 13 working condition 14 workingcondition 15 working condition 16 working condition17
By analogy we can get 8568 subsets for the training set(I5) and the testing set (I5)
Secondly based on random sample data in each trainingset (IN) three combined forecasting models based on theIOWA operator IOWGA operator and IOWHA operatorare established to solve three sets of corresponding optimalweights Based on the cross-validation method three sets ofweights are substituted into the corresponding testing set(IN) For the training set and testing set we can get thecomprehensive evaluation index C corresponding to eachcombined forecasting model using equation (12)
Finally we calculate the mean value (EC) and variance(VC) of the comprehensive evaluation index C +rough thestatistical analysis of the change law of the mean value (EC)and variance (VC) the universality of the optimal combinedforecasting model is judged
52 Cross-Validation Result Analysis +e mean value (EC)and the variance (VC) of the comprehensive evaluationindexes are evaluated by each combined forecasting modelin the training sets (see Table 7)
In Table 7 we find that EC-IOWA of each training set has asignificantly higher value compared to EC-IOWGA and EC-IOWHA+e higher the EC is the better the overall forecasting precisionis +e alignment of the variance of the comprehensive evalu-ation indexes is VC-IOWAltVC-IOWGAltVC-IOWHA +e smallerthe VC is the smaller the dispersion of the C value is and themore stable the data change is+is indicates that the combinedforecasting model based on the IOWA operator is wellapplicable
In Figure 13 the distribution maps of EC and VC corre-sponding to each training set show a roughly linear changingtrend When the sample data in the training set (IN) increaseEC-IOWA and EC-IOWH increase and EC-IOWGA decreases Withthe increase of the number of sample data in the training setsthe VC of the three combined forecasting models decreasesBut the change of VC-IOWA is smallest indicating that the Cdoes not fluctuate much and the data are very stable
Based on the cross-validation theory the optimalweights obtained by each training set are brought into thecorresponding testing set EC and VC of the testing sets arelisted in Table 8 and the distribution maps of EC and VCcalculated by each testing set are shown in Figure 14
In Table 8 EC-IOWA of testing sets is significantlyhigher than EC-IOWGA and EC-IOWHA while VC-IOWA issignificantly lower than VC-IOWGA and VC-IOWHA How-ever it is noted the values of EC-IOWGA and EC-IOWHA orVC-IOWGA and VC-IOWHA are very close to each otherMeanwhile it is found from Figure 14 that EC corre-sponding to each testing set decreases with the decrease ofthe sample number in the testing sets Contrarily VCincreases with the decrease of the sample number in thetesting sets +e distribution map of VC-IOWA has littlechange in slope meaning the corresponding C value ismore stable +e results show that the combined fore-casting model based on the IOWA operator has thehighest overall forecasting precision and best level ofapplicability among the three models
6 Nondestructive Tests for Double-CiroldLongevity Pavilion
Double-Cirold Longevity Pavilion is located in the BeijingTiantan Park It was built in the Middle Qing Dynasty andhas a history of 277 years Double-Cirold Longevity Pavilionis a combination of two round pavilions with double eavesand spires Its structure is peculiar and precise and its shapeis novel and well proportioned +is kind of pavilion hashigh scientific artistic and cultural value in the Chinesetimber structure Affected by the natural environment andhuman factors all year round timber components aredamaged Eventually it leads to the loss of the externalprotective layer for timber components and the accelerationof the internal and external damage of timber components
Nondestructive tests of timber components of thedouble-ring marsupial pavilion were performed by stresswave and drilling resistance (see Figure 15) It was found thatthe beams and the columns had internal defects +e B2column of Double-Cirold Longevity Pavilion is an examplewith a moisture content of 98 +e perimeter of thewooden column is 1099 cm and the detected section area is96163 cm2 According to the two-dimensional image ob-tained by the stress wave tests the internal defects werelocated Drilling resistance tests were conducted pertinently+ere were two detected paths in drilling resistance tests andeach path passed through the location of defects
+rough nondestructive tests it was found that there wasan uncompacted sound when knocking the position of theB2 column 400mm from the ground A certain degree ofdefect is found in the interior wood by the stress wave tests(see Figure 16) +e damaged area detected by the stresswave tests accounts for 18 of the detected section and thedamaged area is 17309 cm2 +e drilling resistance testsshow the damaged area is 49 cm2 +e damaged area of theB2 column calculated by the combined forecasting model
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Navigation and Observation
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Hindawi
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Submit your manuscripts atwwwhindawicom
working condition it may be low +erefore this combinedforecasting method could not provide a consistent preciseprediction and still needs to be improved
In order to overcome the disadvantage of assigningweight in the previous combined forecasting model thispaper introduced the idea of variable weight According tothe detected precision of a single detection method undervarious working conditions the weight coefficients weregiven in an order from high to low +is greatly reduced thesensitivity of the result to a poor detection method Addi-tionally it effectively improved the forecasting precision ofthe internal damage of wooden components in ancientbuildings +e following four steps are used for evaluatingthe internal defect of wood components in ancient buildingsbased on the optimal combined forecasting model
Step 1 considering the relative lower costs of equip-ment and simpler execution in field applications testmethods based on stress wave and drilling resistancewere used to detect the internal defects of poplar andelm based on the idea of reverse simulationStep 2 based on the idea of variable weight and takingthe square sum of error square sum of logarithmicerror and square sum of reciprocal error as a guidelinethree combined forecasting models were establishedbased on the IOWA (induced ordered weighted av-erage) operator [33ndash35] IOWGA (induced orderedweighted geometric average) operator [36 37] andIOWHA (induced ordered weighted harmonic aver-age) operator [38 39] Additionally the combinedforecasting models based on the entropy value [40 41]and Shapley value [24ndash42] were used to compare withthe proposed methodsStep 3 based on the five indicators a comprehensiveevaluation index was developed to select the optimalcombined forecasting modelStep 4 according to the cross-validation theory [43]the optimal combined forecasting method was gener-alized into a model
2 Nondestructive Tests
21 Specimen Fabrication Poplar and elm commonly usedin ancient building timber components (eg beams andcolumns in the Guanyin Temple Changzhi City ShanxiProvince) were selected as test specimens to simulate thehollow and insect attacks in the wooden structure +e rawmaterials were sawed into a cylindrical shape of 100mmheight (see Figure 2(a)) and the sawing plane of the testpiece was required to be flat Based on the cross-sectionalarea (S) of the test piece there are five simulated damageratios which are respectively 132 116 18 14 and 12 ofthe cross-sectional area (S) of the test piece (see Figure 2(b))According to the method of reverse simulation the internalhollow and insect attacks were simulated by manual digging(see Figure 2(c)) and drilling (see Figure 2(d)) in the crosssections of the wood component
22 Test Hypothesis Considering that wood is an aniso-tropic material the physical properties of wood differ indifferent positions in the same tree When the water contentis the same the wave propagation velocity increases linearlywith the increase of density [44] In the radial direction of thetrunk the change in wood density is divided into three cases(1) increase from the bark to the pith (2) first increase andthen decrease from the bark to the pith and (3) decreasefrom the bark to the pith [45] To reduce the effect of thisdifference on the test results we designed the damaged areaof the test piece to be circular Additionally circular dam-aged areas of different sizes can better reflect the degree ofinternal damage of the wood +erefore we made two kindsof assumptions
(1) It is assumed that the circumference of the specimenis a complete circle regardless of the special shape ofthe wood
(2) It is assumed that the damage type of each specimenis a standard circle (see Figure 3)
23 Test Conditions +e indoor temperature is 20degC and theair relative humidity is 65 which meet the requirements ofthe ldquoStandard for test methods of timber structuresrdquo (GBT50329-2012) Test equipment includes Fakopp (stress wavetest equipment) made in Hungary IML-RESI PD500(drilling resistance test equipment) and GANN-HT85T(wood hygrometer) made in Germany and electric per-cussion drill (BOSCH) which are shown in Figure 4
+ere are 18 working conditions in total Each workingcondition simulates the detection of different defective areasof different tree species under different damage types Forexample the working condition 7 in Table 1 simulates acondition that the internal damage type of elm is hollow andthe proportion of the damaged area is 14 +rough visualinspection surface percussion and pressing there are noobvious joints splits and other defects Four specimens withan average moisture content of 918 are prepared for thistest +ey meet the requirements of the ldquoStandard for designof timber structuresrdquo (GB 50005-2017) [46] and ldquoStandardfor test methods of timber structuresrdquo (GBT 50329-2012)[47] +e specific parameters of the specimen are shown inTable 1
24 StressWaveDetection Fakopp 3D Acoustic Tomographis able to nondestructively detect the size and location of thedefective part in wood It works based on sound velocitymeasurement between several sensors around the trunk Ifthere is a hole the sound waves will have to pass around thehole +us they require more time to reach the oppositesensors In order to explain the complex velocity model atwo-dimensional image is constructed Healthy wood isshown in green decaying wood is shown in red and hollowis shown in blue +is test selected 10 sensors to detect theinternal damage of the specimen (see Figure 5) +e specifictest steps were as follows
Advances in Civil Engineering 3
(1) 10 Sensors were placed around the specimen con-necting to the wood with steel nails
(2) Sensors were connected to amplifier boxes(3) Bluetooth connection is established to PC(4) Each sensor is tapped 3 times by a hammer(5) +e data are transmitted to a laptop to calculate the
two-dimensional image
25 Drilling Resistance Tests Drilling resistance tests arebased on microdrilling of wood at a constant velocity by astandard drill IML-RESI PD500 has a small needle driven bya motor to penetrate into the wood at a constant speedWhen the drilling needle enters the interior of the wood it
encounters relative resistance in both directions which arethe forward direction and the direction of rotation +erelative resistance value varies with the density of each treespecies and the instrument records the relative resistanceduring the test +e resistance image processing software(PD-Tools Pro) is applied to export the data information toExcel which can be used to draw two-dimensional images ofrelative resistance In the figure the abscissa represents thepath length and the ordinate represents the relative re-sistance that the drilling needle encounters Based on themeasured impedance curve the width of the damaged areacan be determined according to the changes in the peaks andtroughs in the curve (see Figures 6(b) and 6(d)) +e decayinside the wood can be judged [48 49] and the test steps areas follows
Figure 3 Shape of the simulated defective area
(a) (b) (c) (d)
Figure 4 Specimen and test equipment (a) Fakopp (b) IML-RESI PD500 (c) GANN-HT85T (d) BOSCH
(a) (b) (c) (d)
Figure 2 Fabrication of test specimens (a) sawing (b) damage ratio (c) manual digging (d) manual drilling
4 Advances in Civil Engineering
Table 1 Parameters of test specimens
Working condition Damagedproportion
Simulationtype Tree species Radius (mm) Height (mm) Moisture
(1) +ree paths are selected for the test specimen(2) +e bit should be perpendicular to the direction of
the rings (see Figures 6(a) and 6(c))(3) +e drilling needle rotation rate and advance rate
parameters of the test equipment are set re-spectively +e stability of the drilling resistance testequipment should be ensured
3 Discussion and Analysis of Test Results
31 Two-Dimensional Images For example in specimen 2the tree species is elm and the simulated defect type ishollow Because of limited pages Figure 7 only shows therelative impedance curve in one path direction
When there is no internal damage in the specimen (seeFigure 7(a)) the two-dimensional image detected by stresswave tests is green and the relative impedance curve de-tected by drilling resistance tests is continuous Two de-tection methods indicate that the specimen is healthy woodWhile the internal hollow is small (when the damagedproportion is less than 18) pale yellow (see Figure 7(b)) andred (see Figure 7(c)) colors are presented in the center of thetwo-dimensional image detected by stress wave testsHowever the relative impedance curve image detected bythe drilling resistance tests starts to appear ldquoblankrdquo reflectingthe approximate width of the hollow area With the ex-pansion of the internal hollow area the center part of thetwo-dimensional image detected by stress wave tests shows abright blue color +e stress wave tests are more accurate inidentifying the size and location of internal hollow (seeFigures 7(d)ndash7(f)) +e stress wave tests visually express thelocation and size of internal hollow through colors but the
boundary of the hollow is relatively fuzzy For drilling re-sistance tests the length of the ldquoblankrdquo on the relative im-pedance curve increases with the expansion of the internalhollow area which is basically similar to the test resultsdetected by stress wave tests
To sum up the stress wave tests can quickly make anintuitive judgment on the general position and degree ofdamage but the judgment on the damage type is weak andthe boundary division of internal defects is fuzzy Howeverthe drilling resistance tests only reflect the internal damageof the wooden components under one path according to therelative impedance curve It is not possible to detect everyposition of a cross section and there is no great referencevalue when used alone If enough information is neededmore drilling resistance paths should be provided +roughanalysis it is found that the stress wave image and the re-sistance curve have a good correspondence relationship inthis test Putting the results of the two together for com-parative analysis can make up for their respectiveshortcomings
32DetectionData +edetection data listed in Table 2 showthat the detected precision of the same detection method isdifferent while it is working in various working conditions+e mean error and mean precision obtained by stress wavetests are 1113 cm2 and 729 respectively while the meanerror and mean precision obtained by drilling resistancetests are 847 cm2 and 876 respectively +e correlationcoefficients between the detected data obtained by stresswave and drilling resistance tests and the actual value are09894 and 09989 +e overall detection effect of drilling
(a)
100
Am
plitu
de (
) 80
60
40
20
00 2 4 6 8 10
Drilling depth (cm)
Hollow
12 14 16 18 20 22
(b)
(c)
100
Am
plitu
de (
) 80
60
40
20
00 2 4 6 8 10
Drilling depth (cm)
Insect attacks
12 14 16 18 20 22
(d)
Figure 6 Drilling resistance tests (a) hollow and (b) its two-dimensional image (c) insect attacks and (d) their two-dimensional image
6 Advances in Civil Engineering
resistance tests is more precise compared to that of stresswave tests
Although the correlation coefficients between the twosets of test data and the real value are very high the de-tected precision is still low under some conditions es-pecially when the stress wave detection is used We findthat the detected precision of the stress wave tests underworking condition 1 working condition 4 workingcondition 9 working condition 14 and working condition15 is relatively low +e proportion of damage simulatedunder the five working conditions is also small +ereforeit is of great engineering value to study the precision ofstress wave detection with such a small internal damagedproportion
When we examined the curves of detected precision underdifferent working conditions (see Figure 8) we found that thedetected precision obtained by stress wave tests increases withthe increase of the internal damaged area in the wood
As far as drilling resistance tests are concerned thedetected precision increases with the increase of the internaldefects in the wood when the internal damage type is hollow(see Figures 8(a) and 8(b))While the internal damage type isinsect attacks the detected precision of specimen 3 does notchange much with the increase of insect attack area (seeFigures 8(c) and 8(d))
In addition when the internal defects are small thedetected precision of drilling resistance tests is higher thanthat of stress wave tests With the further increase of
simulated damaged area the detected precision of bothdetection methods tends to be close to each other When theinternal damaged proportion of wood exceeds 14 thedetected precision of stress wave tests is higher than that ofdrilling resistance tests (see Figures 8(b)ndash8(d))
To sum up comprehensive use of stress wave and drillingresistance tests can screen the type position and size ofinternal damage of timber components However the de-tection results of the two detectionmethods are quite differentwith low detected precision In order to comprehensively usethe information provided by the two detection methods thispaper introduces several new combined forecasting modelswhich are different from the literature [24] in order to im-prove the prediction precision of the internal damage inancient building wood components
4 Combined Forecasting Model
41 Model Building Based on the OWA operator [50]OWGAoperator [51] andOWHAoperator [38] great deals ofextensions have been developed +ese extensions are theIOWA operator IOWGA operator and IOWHA operator Inthis study we reordered the arguments by an inducing variable
If there arem feasible single detection methods to detectinternal defects of the timber components in ancientbuildings under a certain working condition the detectionvalue of the i-th detection method in the t-th workingcondition is xit where i 1 2 m and t 1 2 N
If lm is the weight of the m-th single detection in thecombined forecasting model the weight satisfy the nor-malization and nonnegativity such that
116 18 1455
60
65
70
75
80
85
90
95D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(a)
132 116 18 14 1230
40
50
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(b)
132 116 18 14 12
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(c)
132 116 18 14 1230
40
50
60
70
80
90
100D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(d)
Figure 8 Curves of detected precision under different working conditions (a) Specimen 1 (b) Specimen 2 (c) Specimen 3 (d) Specimen 4
where ait represents the detected precision of the i-th de-tection method under the t-th working condition ait isin [0 1]When ait is regarded as the inducement value of xit it canformm two-dimensional arrays which are (a1t x1t) (a2t x2t) (amt xmt) +e detected precision sequence (a1t a2t amt) of m detection methods under the t-th working con-dition is arranged from high to low Let us hypothesize thata-index(it) is a subscript of the i-th largest value among thedetection sequence
(1) Model based on the IOWA operator [34] the squaresum of error is taken as the criterion to establish thecombined forecasting model According to the de-tected precision sequence the combined forecastingvalue based on the IOWA operator can be obtainedby
IL a1t x1t( 1113857 a2t x2t( 1113857 amt xmt( 11138571113858 1113859
1113944m
i1lixaminusindex(it)
(2)
+e optimal combined forecasting model based onthe IOWA operator with the square sum of error asthe criterion can be expressed as follows
SIOWA 1113944N
t1xt minus 1113944
m
i1lixaminusindex(it)
⎛⎝ ⎞⎠
2
(3)
(2) Model based on the IOWGA operator [36] thesquare sum of logarithmic error is taken as thecriterion to establish the combined forecastingmodel According to the detected precision se-quence the combined forecasting value based on theIOWGA operator can be obtained by
+eoptimal combined forecastingmodel based on theIOWGA operator with the square sum of logarithmicerror as the criterion can be expressed as follows
SIOWGA 1113944N
t1lnxt minus ln1113945
m
i1x
liaminusindex(it)
⎞⎠
2
⎛⎝ (5)
(3) Model based on the IOWHA operator [38] thesquare sum of reciprocal error is taken as the cri-terion to establish the combined forecasting modelAccording to the detected precision sequence thecombined forecasting value based on the IOWHAoperator can be obtained by
+e optimal combined forecasting model based onthe IOWHA operator with the square sum of re-ciprocal error as the criterion can be expressed asfollows
SIOWHA 1113944N
t11113944
m
i1li
1xt
minus1
xaminusindex(it)
1113888 1113889⎛⎝ ⎞⎠
2
(7)
42 Solving Model Taking the simulated hollow test ofspecimen 1 as an example we can list the two-dimensionalarray of detection values and its detected precision under thet-th working condition as follows
(0576 3722) (0817 2134)
(0650 7059) (0844 4412)
(0808 12464) (0909 9502)
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (8)
+e prediction value based on the IOWA operator iscalculated according to equation (2) +e solving process isshown as follows
By substituting them into equation (3) the optimalcombined forecasting model based on the IOWA operator isarranged as follows
min SIOWA l1 l2( 1113857 2613minus 2134l1 minus 3722l2( 11138572
+ 5227minus 4412l1 minus 7059l2( 11138572
+ 10454minus 9502l1 minus 12464l2( 11138572
stl1 + l2 1
l1 ge 0 l2 ge 01113896
(10)
Advances in Civil Engineering 9
+e MATLAB software is used to solve the optimalweight (li) Some parameters of the genetic algorithm are setas follows
Generations 50StallGenLimi 100PopInitRange [zeros(1 m) ones(1 m)]PopulationSize 10000
After 50 genetic iterations the MATLAB softwareshows that (l1 l2) is (069 031) respectively +e black andblue points in Figure 9 are the best fitness value and themean fitness value respectively It is found that the meanfitness value of the population represents a smoothdownward trend with the increase of the number of iter-ations and gradually moves towards the best fitness value(see Figure 9)
Similarly the solving processes of the models basedon the IOWGA operator and IOWHA operator are thesame as that of the model based on the IOWA operator Inorder to select the optimal model the traditional com-bined forecasting models based on the entropy valueand Shapley value are introduced in this paper forcomparison
43 Analyzing Precision of Different Combined ForecastingModels In Table 3 the mean precision from large to small isP1 P2 P3 P4 and P5 Compared to detected precision ofstress wave tests the precision is improved by 258 254252 215 and 176 respectively While compared todetected precision of drilling resistance tests the precision isimproved by 47 43 42 11 and 22 respectivelyAdditionally the mean absolute error from small to large ise1 e2 e3 e5 and e4 So we find that the models based on theIOWA operator IOWGA operator and IOWHA operatorhave better forecasting effects compared to others (seeFigure 10)
Other than that through statistical analysis of workingcondition 1 working condition 4 working condition 9working condition 14 and working condition 15 (seeTable 4) we also find that the combined forecasting modelsbased on the IOWA operator IOWGA operator andIOWHA operator are more effective compared to thecombined forecasting models based on the entropy valueand Shapley value in improving the detected precision ofstress wave tests in the case of small defects inside thewood
44 Forecasting Effect Evaluation According to the eval-uation principle of the forecasting effect SSE MSEMAE MAPE and MSPE are selected as evaluation in-dexes to reflect the effectiveness of the combined fore-casting models +e calculation results are shown inTable 5
In Table 5 it is found that the first four indexes of thecombined forecasting method based on the IOWA oper-ator are significantly lower than those of others AlthoughMSPE of the combined forecasting method based on theIOWA operator is not the least it is close to MSPE ofcombined forecasting methods based on the IOWGAoperator and IOWHA operator +erefore the combinedforecasting model based on the IOWA operator has thebest effect Meanwhile by normalizing the above fiveindexes the expression of the comprehensive evaluationindex C is obtained as follows
Ci 1n
1113944
n
j1
min Ej1113872 1113873
Eij
(12)
Best 011231 mean 0497158
Best fitness Mean fitness
Fitn
ess v
alue
0 5 10 15 20 25 30 35 40 45 50Generation
180
160
140
120
100
80
60
40
20
0
Figure 9 Best fitness value and mean fitness value
10 Advances in Civil Engineering
where Ci is the comprehensive evaluation index of the i-thmethod i 1 2 M Eij is the j-th index of the i-thmethod j 1 2 n and min(Ej) is the minimum valueamong the j-th indexes of m methods +e higher the C isthe better the corresponding combined forecasting model is+e index C of each method is developed by bringing the fiveindex values in Table 5 into equation (12)
Figure 11 shows that the comprehensive evaluationindex of each combined forecasting model is significantlyhigher than that of the two single detection methods in-dicating that the combined forecasting model can improvethe forecasting precision of the internal defects of the timber
components Furthermore the C of the combined fore-casting model based on the IOWA operator is 972 higherthan others All the analysis shows that the combinedforecasting model based on the IOWA operator is the op-timal model followed by the combined forecasting modelsbased on the IOWGA operator and IOWHA operator
5 Applicability Assessment
An applicability assessment is performed for the combinedforecasting models based on the IOWA operator IOWGAoperator and IOWHA operator
51 Cross-Validation 9eory Since there are a total of 18working conditions in this test each working conditionhas a corresponding set of actual values and detectedvalues obtained by stress wave and drilling resistance tests(see Table 2) Because of the small number of data samplesand each combined forecasting model is tested only oncethe randomness is large which does not prove that theabove optimal models have good universality In order tomake full use of the data samples a cross-validationmethod is applied to carry out the test +e researchprocess is shown in Figure 12
Firstly by setting random samples we randomlyextracted N (N 5 6 17) working conditions from 18working conditions as a training set (IN) and then thecorresponding remaining 18minusN working conditions areconsidered as a testing set (IN) For the number (N) ofrandomly selected samples there are CN
18 subsets for both thetraining set and the testing set (see Table 6) For example ifN 5 both the training set (I5) and the testing set (I5) willhave 8568 subsets
Table 3 Results of each combined forecasting model
If I5 working condition 1 working condition 2working condition 3 working condition 4 working con-dition 5 then I5 working condition 6 working condi-tion 7 working condition 8 working condition 9 workingcondition 10 working condition 11 working condition 12working condition 13 working condition 14 workingcondition 15 working condition 16 working condition17
By analogy we can get 8568 subsets for the training set(I5) and the testing set (I5)
Secondly based on random sample data in each trainingset (IN) three combined forecasting models based on theIOWA operator IOWGA operator and IOWHA operatorare established to solve three sets of corresponding optimalweights Based on the cross-validation method three sets ofweights are substituted into the corresponding testing set(IN) For the training set and testing set we can get thecomprehensive evaluation index C corresponding to eachcombined forecasting model using equation (12)
Finally we calculate the mean value (EC) and variance(VC) of the comprehensive evaluation index C +rough thestatistical analysis of the change law of the mean value (EC)and variance (VC) the universality of the optimal combinedforecasting model is judged
52 Cross-Validation Result Analysis +e mean value (EC)and the variance (VC) of the comprehensive evaluationindexes are evaluated by each combined forecasting modelin the training sets (see Table 7)
In Table 7 we find that EC-IOWA of each training set has asignificantly higher value compared to EC-IOWGA and EC-IOWHA+e higher the EC is the better the overall forecasting precisionis +e alignment of the variance of the comprehensive evalu-ation indexes is VC-IOWAltVC-IOWGAltVC-IOWHA +e smallerthe VC is the smaller the dispersion of the C value is and themore stable the data change is+is indicates that the combinedforecasting model based on the IOWA operator is wellapplicable
In Figure 13 the distribution maps of EC and VC corre-sponding to each training set show a roughly linear changingtrend When the sample data in the training set (IN) increaseEC-IOWA and EC-IOWH increase and EC-IOWGA decreases Withthe increase of the number of sample data in the training setsthe VC of the three combined forecasting models decreasesBut the change of VC-IOWA is smallest indicating that the Cdoes not fluctuate much and the data are very stable
Based on the cross-validation theory the optimalweights obtained by each training set are brought into thecorresponding testing set EC and VC of the testing sets arelisted in Table 8 and the distribution maps of EC and VCcalculated by each testing set are shown in Figure 14
In Table 8 EC-IOWA of testing sets is significantlyhigher than EC-IOWGA and EC-IOWHA while VC-IOWA issignificantly lower than VC-IOWGA and VC-IOWHA How-ever it is noted the values of EC-IOWGA and EC-IOWHA orVC-IOWGA and VC-IOWHA are very close to each otherMeanwhile it is found from Figure 14 that EC corre-sponding to each testing set decreases with the decrease ofthe sample number in the testing sets Contrarily VCincreases with the decrease of the sample number in thetesting sets +e distribution map of VC-IOWA has littlechange in slope meaning the corresponding C value ismore stable +e results show that the combined fore-casting model based on the IOWA operator has thehighest overall forecasting precision and best level ofapplicability among the three models
6 Nondestructive Tests for Double-CiroldLongevity Pavilion
Double-Cirold Longevity Pavilion is located in the BeijingTiantan Park It was built in the Middle Qing Dynasty andhas a history of 277 years Double-Cirold Longevity Pavilionis a combination of two round pavilions with double eavesand spires Its structure is peculiar and precise and its shapeis novel and well proportioned +is kind of pavilion hashigh scientific artistic and cultural value in the Chinesetimber structure Affected by the natural environment andhuman factors all year round timber components aredamaged Eventually it leads to the loss of the externalprotective layer for timber components and the accelerationof the internal and external damage of timber components
Nondestructive tests of timber components of thedouble-ring marsupial pavilion were performed by stresswave and drilling resistance (see Figure 15) It was found thatthe beams and the columns had internal defects +e B2column of Double-Cirold Longevity Pavilion is an examplewith a moisture content of 98 +e perimeter of thewooden column is 1099 cm and the detected section area is96163 cm2 According to the two-dimensional image ob-tained by the stress wave tests the internal defects werelocated Drilling resistance tests were conducted pertinently+ere were two detected paths in drilling resistance tests andeach path passed through the location of defects
+rough nondestructive tests it was found that there wasan uncompacted sound when knocking the position of theB2 column 400mm from the ground A certain degree ofdefect is found in the interior wood by the stress wave tests(see Figure 16) +e damaged area detected by the stresswave tests accounts for 18 of the detected section and thedamaged area is 17309 cm2 +e drilling resistance testsshow the damaged area is 49 cm2 +e damaged area of theB2 column calculated by the combined forecasting model
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
Chemical EngineeringInternational Journal of Antennas and
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International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
(1) 10 Sensors were placed around the specimen con-necting to the wood with steel nails
(2) Sensors were connected to amplifier boxes(3) Bluetooth connection is established to PC(4) Each sensor is tapped 3 times by a hammer(5) +e data are transmitted to a laptop to calculate the
two-dimensional image
25 Drilling Resistance Tests Drilling resistance tests arebased on microdrilling of wood at a constant velocity by astandard drill IML-RESI PD500 has a small needle driven bya motor to penetrate into the wood at a constant speedWhen the drilling needle enters the interior of the wood it
encounters relative resistance in both directions which arethe forward direction and the direction of rotation +erelative resistance value varies with the density of each treespecies and the instrument records the relative resistanceduring the test +e resistance image processing software(PD-Tools Pro) is applied to export the data information toExcel which can be used to draw two-dimensional images ofrelative resistance In the figure the abscissa represents thepath length and the ordinate represents the relative re-sistance that the drilling needle encounters Based on themeasured impedance curve the width of the damaged areacan be determined according to the changes in the peaks andtroughs in the curve (see Figures 6(b) and 6(d)) +e decayinside the wood can be judged [48 49] and the test steps areas follows
Figure 3 Shape of the simulated defective area
(a) (b) (c) (d)
Figure 4 Specimen and test equipment (a) Fakopp (b) IML-RESI PD500 (c) GANN-HT85T (d) BOSCH
(a) (b) (c) (d)
Figure 2 Fabrication of test specimens (a) sawing (b) damage ratio (c) manual digging (d) manual drilling
4 Advances in Civil Engineering
Table 1 Parameters of test specimens
Working condition Damagedproportion
Simulationtype Tree species Radius (mm) Height (mm) Moisture
(1) +ree paths are selected for the test specimen(2) +e bit should be perpendicular to the direction of
the rings (see Figures 6(a) and 6(c))(3) +e drilling needle rotation rate and advance rate
parameters of the test equipment are set re-spectively +e stability of the drilling resistance testequipment should be ensured
3 Discussion and Analysis of Test Results
31 Two-Dimensional Images For example in specimen 2the tree species is elm and the simulated defect type ishollow Because of limited pages Figure 7 only shows therelative impedance curve in one path direction
When there is no internal damage in the specimen (seeFigure 7(a)) the two-dimensional image detected by stresswave tests is green and the relative impedance curve de-tected by drilling resistance tests is continuous Two de-tection methods indicate that the specimen is healthy woodWhile the internal hollow is small (when the damagedproportion is less than 18) pale yellow (see Figure 7(b)) andred (see Figure 7(c)) colors are presented in the center of thetwo-dimensional image detected by stress wave testsHowever the relative impedance curve image detected bythe drilling resistance tests starts to appear ldquoblankrdquo reflectingthe approximate width of the hollow area With the ex-pansion of the internal hollow area the center part of thetwo-dimensional image detected by stress wave tests shows abright blue color +e stress wave tests are more accurate inidentifying the size and location of internal hollow (seeFigures 7(d)ndash7(f)) +e stress wave tests visually express thelocation and size of internal hollow through colors but the
boundary of the hollow is relatively fuzzy For drilling re-sistance tests the length of the ldquoblankrdquo on the relative im-pedance curve increases with the expansion of the internalhollow area which is basically similar to the test resultsdetected by stress wave tests
To sum up the stress wave tests can quickly make anintuitive judgment on the general position and degree ofdamage but the judgment on the damage type is weak andthe boundary division of internal defects is fuzzy Howeverthe drilling resistance tests only reflect the internal damageof the wooden components under one path according to therelative impedance curve It is not possible to detect everyposition of a cross section and there is no great referencevalue when used alone If enough information is neededmore drilling resistance paths should be provided +roughanalysis it is found that the stress wave image and the re-sistance curve have a good correspondence relationship inthis test Putting the results of the two together for com-parative analysis can make up for their respectiveshortcomings
32DetectionData +edetection data listed in Table 2 showthat the detected precision of the same detection method isdifferent while it is working in various working conditions+e mean error and mean precision obtained by stress wavetests are 1113 cm2 and 729 respectively while the meanerror and mean precision obtained by drilling resistancetests are 847 cm2 and 876 respectively +e correlationcoefficients between the detected data obtained by stresswave and drilling resistance tests and the actual value are09894 and 09989 +e overall detection effect of drilling
(a)
100
Am
plitu
de (
) 80
60
40
20
00 2 4 6 8 10
Drilling depth (cm)
Hollow
12 14 16 18 20 22
(b)
(c)
100
Am
plitu
de (
) 80
60
40
20
00 2 4 6 8 10
Drilling depth (cm)
Insect attacks
12 14 16 18 20 22
(d)
Figure 6 Drilling resistance tests (a) hollow and (b) its two-dimensional image (c) insect attacks and (d) their two-dimensional image
6 Advances in Civil Engineering
resistance tests is more precise compared to that of stresswave tests
Although the correlation coefficients between the twosets of test data and the real value are very high the de-tected precision is still low under some conditions es-pecially when the stress wave detection is used We findthat the detected precision of the stress wave tests underworking condition 1 working condition 4 workingcondition 9 working condition 14 and working condition15 is relatively low +e proportion of damage simulatedunder the five working conditions is also small +ereforeit is of great engineering value to study the precision ofstress wave detection with such a small internal damagedproportion
When we examined the curves of detected precision underdifferent working conditions (see Figure 8) we found that thedetected precision obtained by stress wave tests increases withthe increase of the internal damaged area in the wood
As far as drilling resistance tests are concerned thedetected precision increases with the increase of the internaldefects in the wood when the internal damage type is hollow(see Figures 8(a) and 8(b))While the internal damage type isinsect attacks the detected precision of specimen 3 does notchange much with the increase of insect attack area (seeFigures 8(c) and 8(d))
In addition when the internal defects are small thedetected precision of drilling resistance tests is higher thanthat of stress wave tests With the further increase of
simulated damaged area the detected precision of bothdetection methods tends to be close to each other When theinternal damaged proportion of wood exceeds 14 thedetected precision of stress wave tests is higher than that ofdrilling resistance tests (see Figures 8(b)ndash8(d))
To sum up comprehensive use of stress wave and drillingresistance tests can screen the type position and size ofinternal damage of timber components However the de-tection results of the two detectionmethods are quite differentwith low detected precision In order to comprehensively usethe information provided by the two detection methods thispaper introduces several new combined forecasting modelswhich are different from the literature [24] in order to im-prove the prediction precision of the internal damage inancient building wood components
4 Combined Forecasting Model
41 Model Building Based on the OWA operator [50]OWGAoperator [51] andOWHAoperator [38] great deals ofextensions have been developed +ese extensions are theIOWA operator IOWGA operator and IOWHA operator Inthis study we reordered the arguments by an inducing variable
If there arem feasible single detection methods to detectinternal defects of the timber components in ancientbuildings under a certain working condition the detectionvalue of the i-th detection method in the t-th workingcondition is xit where i 1 2 m and t 1 2 N
If lm is the weight of the m-th single detection in thecombined forecasting model the weight satisfy the nor-malization and nonnegativity such that
116 18 1455
60
65
70
75
80
85
90
95D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(a)
132 116 18 14 1230
40
50
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(b)
132 116 18 14 12
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(c)
132 116 18 14 1230
40
50
60
70
80
90
100D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(d)
Figure 8 Curves of detected precision under different working conditions (a) Specimen 1 (b) Specimen 2 (c) Specimen 3 (d) Specimen 4
where ait represents the detected precision of the i-th de-tection method under the t-th working condition ait isin [0 1]When ait is regarded as the inducement value of xit it canformm two-dimensional arrays which are (a1t x1t) (a2t x2t) (amt xmt) +e detected precision sequence (a1t a2t amt) of m detection methods under the t-th working con-dition is arranged from high to low Let us hypothesize thata-index(it) is a subscript of the i-th largest value among thedetection sequence
(1) Model based on the IOWA operator [34] the squaresum of error is taken as the criterion to establish thecombined forecasting model According to the de-tected precision sequence the combined forecastingvalue based on the IOWA operator can be obtainedby
IL a1t x1t( 1113857 a2t x2t( 1113857 amt xmt( 11138571113858 1113859
1113944m
i1lixaminusindex(it)
(2)
+e optimal combined forecasting model based onthe IOWA operator with the square sum of error asthe criterion can be expressed as follows
SIOWA 1113944N
t1xt minus 1113944
m
i1lixaminusindex(it)
⎛⎝ ⎞⎠
2
(3)
(2) Model based on the IOWGA operator [36] thesquare sum of logarithmic error is taken as thecriterion to establish the combined forecastingmodel According to the detected precision se-quence the combined forecasting value based on theIOWGA operator can be obtained by
+eoptimal combined forecastingmodel based on theIOWGA operator with the square sum of logarithmicerror as the criterion can be expressed as follows
SIOWGA 1113944N
t1lnxt minus ln1113945
m
i1x
liaminusindex(it)
⎞⎠
2
⎛⎝ (5)
(3) Model based on the IOWHA operator [38] thesquare sum of reciprocal error is taken as the cri-terion to establish the combined forecasting modelAccording to the detected precision sequence thecombined forecasting value based on the IOWHAoperator can be obtained by
+e optimal combined forecasting model based onthe IOWHA operator with the square sum of re-ciprocal error as the criterion can be expressed asfollows
SIOWHA 1113944N
t11113944
m
i1li
1xt
minus1
xaminusindex(it)
1113888 1113889⎛⎝ ⎞⎠
2
(7)
42 Solving Model Taking the simulated hollow test ofspecimen 1 as an example we can list the two-dimensionalarray of detection values and its detected precision under thet-th working condition as follows
(0576 3722) (0817 2134)
(0650 7059) (0844 4412)
(0808 12464) (0909 9502)
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (8)
+e prediction value based on the IOWA operator iscalculated according to equation (2) +e solving process isshown as follows
By substituting them into equation (3) the optimalcombined forecasting model based on the IOWA operator isarranged as follows
min SIOWA l1 l2( 1113857 2613minus 2134l1 minus 3722l2( 11138572
+ 5227minus 4412l1 minus 7059l2( 11138572
+ 10454minus 9502l1 minus 12464l2( 11138572
stl1 + l2 1
l1 ge 0 l2 ge 01113896
(10)
Advances in Civil Engineering 9
+e MATLAB software is used to solve the optimalweight (li) Some parameters of the genetic algorithm are setas follows
Generations 50StallGenLimi 100PopInitRange [zeros(1 m) ones(1 m)]PopulationSize 10000
After 50 genetic iterations the MATLAB softwareshows that (l1 l2) is (069 031) respectively +e black andblue points in Figure 9 are the best fitness value and themean fitness value respectively It is found that the meanfitness value of the population represents a smoothdownward trend with the increase of the number of iter-ations and gradually moves towards the best fitness value(see Figure 9)
Similarly the solving processes of the models basedon the IOWGA operator and IOWHA operator are thesame as that of the model based on the IOWA operator Inorder to select the optimal model the traditional com-bined forecasting models based on the entropy valueand Shapley value are introduced in this paper forcomparison
43 Analyzing Precision of Different Combined ForecastingModels In Table 3 the mean precision from large to small isP1 P2 P3 P4 and P5 Compared to detected precision ofstress wave tests the precision is improved by 258 254252 215 and 176 respectively While compared todetected precision of drilling resistance tests the precision isimproved by 47 43 42 11 and 22 respectivelyAdditionally the mean absolute error from small to large ise1 e2 e3 e5 and e4 So we find that the models based on theIOWA operator IOWGA operator and IOWHA operatorhave better forecasting effects compared to others (seeFigure 10)
Other than that through statistical analysis of workingcondition 1 working condition 4 working condition 9working condition 14 and working condition 15 (seeTable 4) we also find that the combined forecasting modelsbased on the IOWA operator IOWGA operator andIOWHA operator are more effective compared to thecombined forecasting models based on the entropy valueand Shapley value in improving the detected precision ofstress wave tests in the case of small defects inside thewood
44 Forecasting Effect Evaluation According to the eval-uation principle of the forecasting effect SSE MSEMAE MAPE and MSPE are selected as evaluation in-dexes to reflect the effectiveness of the combined fore-casting models +e calculation results are shown inTable 5
In Table 5 it is found that the first four indexes of thecombined forecasting method based on the IOWA oper-ator are significantly lower than those of others AlthoughMSPE of the combined forecasting method based on theIOWA operator is not the least it is close to MSPE ofcombined forecasting methods based on the IOWGAoperator and IOWHA operator +erefore the combinedforecasting model based on the IOWA operator has thebest effect Meanwhile by normalizing the above fiveindexes the expression of the comprehensive evaluationindex C is obtained as follows
Ci 1n
1113944
n
j1
min Ej1113872 1113873
Eij
(12)
Best 011231 mean 0497158
Best fitness Mean fitness
Fitn
ess v
alue
0 5 10 15 20 25 30 35 40 45 50Generation
180
160
140
120
100
80
60
40
20
0
Figure 9 Best fitness value and mean fitness value
10 Advances in Civil Engineering
where Ci is the comprehensive evaluation index of the i-thmethod i 1 2 M Eij is the j-th index of the i-thmethod j 1 2 n and min(Ej) is the minimum valueamong the j-th indexes of m methods +e higher the C isthe better the corresponding combined forecasting model is+e index C of each method is developed by bringing the fiveindex values in Table 5 into equation (12)
Figure 11 shows that the comprehensive evaluationindex of each combined forecasting model is significantlyhigher than that of the two single detection methods in-dicating that the combined forecasting model can improvethe forecasting precision of the internal defects of the timber
components Furthermore the C of the combined fore-casting model based on the IOWA operator is 972 higherthan others All the analysis shows that the combinedforecasting model based on the IOWA operator is the op-timal model followed by the combined forecasting modelsbased on the IOWGA operator and IOWHA operator
5 Applicability Assessment
An applicability assessment is performed for the combinedforecasting models based on the IOWA operator IOWGAoperator and IOWHA operator
51 Cross-Validation 9eory Since there are a total of 18working conditions in this test each working conditionhas a corresponding set of actual values and detectedvalues obtained by stress wave and drilling resistance tests(see Table 2) Because of the small number of data samplesand each combined forecasting model is tested only oncethe randomness is large which does not prove that theabove optimal models have good universality In order tomake full use of the data samples a cross-validationmethod is applied to carry out the test +e researchprocess is shown in Figure 12
Firstly by setting random samples we randomlyextracted N (N 5 6 17) working conditions from 18working conditions as a training set (IN) and then thecorresponding remaining 18minusN working conditions areconsidered as a testing set (IN) For the number (N) ofrandomly selected samples there are CN
18 subsets for both thetraining set and the testing set (see Table 6) For example ifN 5 both the training set (I5) and the testing set (I5) willhave 8568 subsets
Table 3 Results of each combined forecasting model
If I5 working condition 1 working condition 2working condition 3 working condition 4 working con-dition 5 then I5 working condition 6 working condi-tion 7 working condition 8 working condition 9 workingcondition 10 working condition 11 working condition 12working condition 13 working condition 14 workingcondition 15 working condition 16 working condition17
By analogy we can get 8568 subsets for the training set(I5) and the testing set (I5)
Secondly based on random sample data in each trainingset (IN) three combined forecasting models based on theIOWA operator IOWGA operator and IOWHA operatorare established to solve three sets of corresponding optimalweights Based on the cross-validation method three sets ofweights are substituted into the corresponding testing set(IN) For the training set and testing set we can get thecomprehensive evaluation index C corresponding to eachcombined forecasting model using equation (12)
Finally we calculate the mean value (EC) and variance(VC) of the comprehensive evaluation index C +rough thestatistical analysis of the change law of the mean value (EC)and variance (VC) the universality of the optimal combinedforecasting model is judged
52 Cross-Validation Result Analysis +e mean value (EC)and the variance (VC) of the comprehensive evaluationindexes are evaluated by each combined forecasting modelin the training sets (see Table 7)
In Table 7 we find that EC-IOWA of each training set has asignificantly higher value compared to EC-IOWGA and EC-IOWHA+e higher the EC is the better the overall forecasting precisionis +e alignment of the variance of the comprehensive evalu-ation indexes is VC-IOWAltVC-IOWGAltVC-IOWHA +e smallerthe VC is the smaller the dispersion of the C value is and themore stable the data change is+is indicates that the combinedforecasting model based on the IOWA operator is wellapplicable
In Figure 13 the distribution maps of EC and VC corre-sponding to each training set show a roughly linear changingtrend When the sample data in the training set (IN) increaseEC-IOWA and EC-IOWH increase and EC-IOWGA decreases Withthe increase of the number of sample data in the training setsthe VC of the three combined forecasting models decreasesBut the change of VC-IOWA is smallest indicating that the Cdoes not fluctuate much and the data are very stable
Based on the cross-validation theory the optimalweights obtained by each training set are brought into thecorresponding testing set EC and VC of the testing sets arelisted in Table 8 and the distribution maps of EC and VCcalculated by each testing set are shown in Figure 14
In Table 8 EC-IOWA of testing sets is significantlyhigher than EC-IOWGA and EC-IOWHA while VC-IOWA issignificantly lower than VC-IOWGA and VC-IOWHA How-ever it is noted the values of EC-IOWGA and EC-IOWHA orVC-IOWGA and VC-IOWHA are very close to each otherMeanwhile it is found from Figure 14 that EC corre-sponding to each testing set decreases with the decrease ofthe sample number in the testing sets Contrarily VCincreases with the decrease of the sample number in thetesting sets +e distribution map of VC-IOWA has littlechange in slope meaning the corresponding C value ismore stable +e results show that the combined fore-casting model based on the IOWA operator has thehighest overall forecasting precision and best level ofapplicability among the three models
6 Nondestructive Tests for Double-CiroldLongevity Pavilion
Double-Cirold Longevity Pavilion is located in the BeijingTiantan Park It was built in the Middle Qing Dynasty andhas a history of 277 years Double-Cirold Longevity Pavilionis a combination of two round pavilions with double eavesand spires Its structure is peculiar and precise and its shapeis novel and well proportioned +is kind of pavilion hashigh scientific artistic and cultural value in the Chinesetimber structure Affected by the natural environment andhuman factors all year round timber components aredamaged Eventually it leads to the loss of the externalprotective layer for timber components and the accelerationof the internal and external damage of timber components
Nondestructive tests of timber components of thedouble-ring marsupial pavilion were performed by stresswave and drilling resistance (see Figure 15) It was found thatthe beams and the columns had internal defects +e B2column of Double-Cirold Longevity Pavilion is an examplewith a moisture content of 98 +e perimeter of thewooden column is 1099 cm and the detected section area is96163 cm2 According to the two-dimensional image ob-tained by the stress wave tests the internal defects werelocated Drilling resistance tests were conducted pertinently+ere were two detected paths in drilling resistance tests andeach path passed through the location of defects
+rough nondestructive tests it was found that there wasan uncompacted sound when knocking the position of theB2 column 400mm from the ground A certain degree ofdefect is found in the interior wood by the stress wave tests(see Figure 16) +e damaged area detected by the stresswave tests accounts for 18 of the detected section and thedamaged area is 17309 cm2 +e drilling resistance testsshow the damaged area is 49 cm2 +e damaged area of theB2 column calculated by the combined forecasting model
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
(1) +ree paths are selected for the test specimen(2) +e bit should be perpendicular to the direction of
the rings (see Figures 6(a) and 6(c))(3) +e drilling needle rotation rate and advance rate
parameters of the test equipment are set re-spectively +e stability of the drilling resistance testequipment should be ensured
3 Discussion and Analysis of Test Results
31 Two-Dimensional Images For example in specimen 2the tree species is elm and the simulated defect type ishollow Because of limited pages Figure 7 only shows therelative impedance curve in one path direction
When there is no internal damage in the specimen (seeFigure 7(a)) the two-dimensional image detected by stresswave tests is green and the relative impedance curve de-tected by drilling resistance tests is continuous Two de-tection methods indicate that the specimen is healthy woodWhile the internal hollow is small (when the damagedproportion is less than 18) pale yellow (see Figure 7(b)) andred (see Figure 7(c)) colors are presented in the center of thetwo-dimensional image detected by stress wave testsHowever the relative impedance curve image detected bythe drilling resistance tests starts to appear ldquoblankrdquo reflectingthe approximate width of the hollow area With the ex-pansion of the internal hollow area the center part of thetwo-dimensional image detected by stress wave tests shows abright blue color +e stress wave tests are more accurate inidentifying the size and location of internal hollow (seeFigures 7(d)ndash7(f)) +e stress wave tests visually express thelocation and size of internal hollow through colors but the
boundary of the hollow is relatively fuzzy For drilling re-sistance tests the length of the ldquoblankrdquo on the relative im-pedance curve increases with the expansion of the internalhollow area which is basically similar to the test resultsdetected by stress wave tests
To sum up the stress wave tests can quickly make anintuitive judgment on the general position and degree ofdamage but the judgment on the damage type is weak andthe boundary division of internal defects is fuzzy Howeverthe drilling resistance tests only reflect the internal damageof the wooden components under one path according to therelative impedance curve It is not possible to detect everyposition of a cross section and there is no great referencevalue when used alone If enough information is neededmore drilling resistance paths should be provided +roughanalysis it is found that the stress wave image and the re-sistance curve have a good correspondence relationship inthis test Putting the results of the two together for com-parative analysis can make up for their respectiveshortcomings
32DetectionData +edetection data listed in Table 2 showthat the detected precision of the same detection method isdifferent while it is working in various working conditions+e mean error and mean precision obtained by stress wavetests are 1113 cm2 and 729 respectively while the meanerror and mean precision obtained by drilling resistancetests are 847 cm2 and 876 respectively +e correlationcoefficients between the detected data obtained by stresswave and drilling resistance tests and the actual value are09894 and 09989 +e overall detection effect of drilling
(a)
100
Am
plitu
de (
) 80
60
40
20
00 2 4 6 8 10
Drilling depth (cm)
Hollow
12 14 16 18 20 22
(b)
(c)
100
Am
plitu
de (
) 80
60
40
20
00 2 4 6 8 10
Drilling depth (cm)
Insect attacks
12 14 16 18 20 22
(d)
Figure 6 Drilling resistance tests (a) hollow and (b) its two-dimensional image (c) insect attacks and (d) their two-dimensional image
6 Advances in Civil Engineering
resistance tests is more precise compared to that of stresswave tests
Although the correlation coefficients between the twosets of test data and the real value are very high the de-tected precision is still low under some conditions es-pecially when the stress wave detection is used We findthat the detected precision of the stress wave tests underworking condition 1 working condition 4 workingcondition 9 working condition 14 and working condition15 is relatively low +e proportion of damage simulatedunder the five working conditions is also small +ereforeit is of great engineering value to study the precision ofstress wave detection with such a small internal damagedproportion
When we examined the curves of detected precision underdifferent working conditions (see Figure 8) we found that thedetected precision obtained by stress wave tests increases withthe increase of the internal damaged area in the wood
As far as drilling resistance tests are concerned thedetected precision increases with the increase of the internaldefects in the wood when the internal damage type is hollow(see Figures 8(a) and 8(b))While the internal damage type isinsect attacks the detected precision of specimen 3 does notchange much with the increase of insect attack area (seeFigures 8(c) and 8(d))
In addition when the internal defects are small thedetected precision of drilling resistance tests is higher thanthat of stress wave tests With the further increase of
simulated damaged area the detected precision of bothdetection methods tends to be close to each other When theinternal damaged proportion of wood exceeds 14 thedetected precision of stress wave tests is higher than that ofdrilling resistance tests (see Figures 8(b)ndash8(d))
To sum up comprehensive use of stress wave and drillingresistance tests can screen the type position and size ofinternal damage of timber components However the de-tection results of the two detectionmethods are quite differentwith low detected precision In order to comprehensively usethe information provided by the two detection methods thispaper introduces several new combined forecasting modelswhich are different from the literature [24] in order to im-prove the prediction precision of the internal damage inancient building wood components
4 Combined Forecasting Model
41 Model Building Based on the OWA operator [50]OWGAoperator [51] andOWHAoperator [38] great deals ofextensions have been developed +ese extensions are theIOWA operator IOWGA operator and IOWHA operator Inthis study we reordered the arguments by an inducing variable
If there arem feasible single detection methods to detectinternal defects of the timber components in ancientbuildings under a certain working condition the detectionvalue of the i-th detection method in the t-th workingcondition is xit where i 1 2 m and t 1 2 N
If lm is the weight of the m-th single detection in thecombined forecasting model the weight satisfy the nor-malization and nonnegativity such that
116 18 1455
60
65
70
75
80
85
90
95D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(a)
132 116 18 14 1230
40
50
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(b)
132 116 18 14 12
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(c)
132 116 18 14 1230
40
50
60
70
80
90
100D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(d)
Figure 8 Curves of detected precision under different working conditions (a) Specimen 1 (b) Specimen 2 (c) Specimen 3 (d) Specimen 4
where ait represents the detected precision of the i-th de-tection method under the t-th working condition ait isin [0 1]When ait is regarded as the inducement value of xit it canformm two-dimensional arrays which are (a1t x1t) (a2t x2t) (amt xmt) +e detected precision sequence (a1t a2t amt) of m detection methods under the t-th working con-dition is arranged from high to low Let us hypothesize thata-index(it) is a subscript of the i-th largest value among thedetection sequence
(1) Model based on the IOWA operator [34] the squaresum of error is taken as the criterion to establish thecombined forecasting model According to the de-tected precision sequence the combined forecastingvalue based on the IOWA operator can be obtainedby
IL a1t x1t( 1113857 a2t x2t( 1113857 amt xmt( 11138571113858 1113859
1113944m
i1lixaminusindex(it)
(2)
+e optimal combined forecasting model based onthe IOWA operator with the square sum of error asthe criterion can be expressed as follows
SIOWA 1113944N
t1xt minus 1113944
m
i1lixaminusindex(it)
⎛⎝ ⎞⎠
2
(3)
(2) Model based on the IOWGA operator [36] thesquare sum of logarithmic error is taken as thecriterion to establish the combined forecastingmodel According to the detected precision se-quence the combined forecasting value based on theIOWGA operator can be obtained by
+eoptimal combined forecastingmodel based on theIOWGA operator with the square sum of logarithmicerror as the criterion can be expressed as follows
SIOWGA 1113944N
t1lnxt minus ln1113945
m
i1x
liaminusindex(it)
⎞⎠
2
⎛⎝ (5)
(3) Model based on the IOWHA operator [38] thesquare sum of reciprocal error is taken as the cri-terion to establish the combined forecasting modelAccording to the detected precision sequence thecombined forecasting value based on the IOWHAoperator can be obtained by
+e optimal combined forecasting model based onthe IOWHA operator with the square sum of re-ciprocal error as the criterion can be expressed asfollows
SIOWHA 1113944N
t11113944
m
i1li
1xt
minus1
xaminusindex(it)
1113888 1113889⎛⎝ ⎞⎠
2
(7)
42 Solving Model Taking the simulated hollow test ofspecimen 1 as an example we can list the two-dimensionalarray of detection values and its detected precision under thet-th working condition as follows
(0576 3722) (0817 2134)
(0650 7059) (0844 4412)
(0808 12464) (0909 9502)
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (8)
+e prediction value based on the IOWA operator iscalculated according to equation (2) +e solving process isshown as follows
By substituting them into equation (3) the optimalcombined forecasting model based on the IOWA operator isarranged as follows
min SIOWA l1 l2( 1113857 2613minus 2134l1 minus 3722l2( 11138572
+ 5227minus 4412l1 minus 7059l2( 11138572
+ 10454minus 9502l1 minus 12464l2( 11138572
stl1 + l2 1
l1 ge 0 l2 ge 01113896
(10)
Advances in Civil Engineering 9
+e MATLAB software is used to solve the optimalweight (li) Some parameters of the genetic algorithm are setas follows
Generations 50StallGenLimi 100PopInitRange [zeros(1 m) ones(1 m)]PopulationSize 10000
After 50 genetic iterations the MATLAB softwareshows that (l1 l2) is (069 031) respectively +e black andblue points in Figure 9 are the best fitness value and themean fitness value respectively It is found that the meanfitness value of the population represents a smoothdownward trend with the increase of the number of iter-ations and gradually moves towards the best fitness value(see Figure 9)
Similarly the solving processes of the models basedon the IOWGA operator and IOWHA operator are thesame as that of the model based on the IOWA operator Inorder to select the optimal model the traditional com-bined forecasting models based on the entropy valueand Shapley value are introduced in this paper forcomparison
43 Analyzing Precision of Different Combined ForecastingModels In Table 3 the mean precision from large to small isP1 P2 P3 P4 and P5 Compared to detected precision ofstress wave tests the precision is improved by 258 254252 215 and 176 respectively While compared todetected precision of drilling resistance tests the precision isimproved by 47 43 42 11 and 22 respectivelyAdditionally the mean absolute error from small to large ise1 e2 e3 e5 and e4 So we find that the models based on theIOWA operator IOWGA operator and IOWHA operatorhave better forecasting effects compared to others (seeFigure 10)
Other than that through statistical analysis of workingcondition 1 working condition 4 working condition 9working condition 14 and working condition 15 (seeTable 4) we also find that the combined forecasting modelsbased on the IOWA operator IOWGA operator andIOWHA operator are more effective compared to thecombined forecasting models based on the entropy valueand Shapley value in improving the detected precision ofstress wave tests in the case of small defects inside thewood
44 Forecasting Effect Evaluation According to the eval-uation principle of the forecasting effect SSE MSEMAE MAPE and MSPE are selected as evaluation in-dexes to reflect the effectiveness of the combined fore-casting models +e calculation results are shown inTable 5
In Table 5 it is found that the first four indexes of thecombined forecasting method based on the IOWA oper-ator are significantly lower than those of others AlthoughMSPE of the combined forecasting method based on theIOWA operator is not the least it is close to MSPE ofcombined forecasting methods based on the IOWGAoperator and IOWHA operator +erefore the combinedforecasting model based on the IOWA operator has thebest effect Meanwhile by normalizing the above fiveindexes the expression of the comprehensive evaluationindex C is obtained as follows
Ci 1n
1113944
n
j1
min Ej1113872 1113873
Eij
(12)
Best 011231 mean 0497158
Best fitness Mean fitness
Fitn
ess v
alue
0 5 10 15 20 25 30 35 40 45 50Generation
180
160
140
120
100
80
60
40
20
0
Figure 9 Best fitness value and mean fitness value
10 Advances in Civil Engineering
where Ci is the comprehensive evaluation index of the i-thmethod i 1 2 M Eij is the j-th index of the i-thmethod j 1 2 n and min(Ej) is the minimum valueamong the j-th indexes of m methods +e higher the C isthe better the corresponding combined forecasting model is+e index C of each method is developed by bringing the fiveindex values in Table 5 into equation (12)
Figure 11 shows that the comprehensive evaluationindex of each combined forecasting model is significantlyhigher than that of the two single detection methods in-dicating that the combined forecasting model can improvethe forecasting precision of the internal defects of the timber
components Furthermore the C of the combined fore-casting model based on the IOWA operator is 972 higherthan others All the analysis shows that the combinedforecasting model based on the IOWA operator is the op-timal model followed by the combined forecasting modelsbased on the IOWGA operator and IOWHA operator
5 Applicability Assessment
An applicability assessment is performed for the combinedforecasting models based on the IOWA operator IOWGAoperator and IOWHA operator
51 Cross-Validation 9eory Since there are a total of 18working conditions in this test each working conditionhas a corresponding set of actual values and detectedvalues obtained by stress wave and drilling resistance tests(see Table 2) Because of the small number of data samplesand each combined forecasting model is tested only oncethe randomness is large which does not prove that theabove optimal models have good universality In order tomake full use of the data samples a cross-validationmethod is applied to carry out the test +e researchprocess is shown in Figure 12
Firstly by setting random samples we randomlyextracted N (N 5 6 17) working conditions from 18working conditions as a training set (IN) and then thecorresponding remaining 18minusN working conditions areconsidered as a testing set (IN) For the number (N) ofrandomly selected samples there are CN
18 subsets for both thetraining set and the testing set (see Table 6) For example ifN 5 both the training set (I5) and the testing set (I5) willhave 8568 subsets
Table 3 Results of each combined forecasting model
If I5 working condition 1 working condition 2working condition 3 working condition 4 working con-dition 5 then I5 working condition 6 working condi-tion 7 working condition 8 working condition 9 workingcondition 10 working condition 11 working condition 12working condition 13 working condition 14 workingcondition 15 working condition 16 working condition17
By analogy we can get 8568 subsets for the training set(I5) and the testing set (I5)
Secondly based on random sample data in each trainingset (IN) three combined forecasting models based on theIOWA operator IOWGA operator and IOWHA operatorare established to solve three sets of corresponding optimalweights Based on the cross-validation method three sets ofweights are substituted into the corresponding testing set(IN) For the training set and testing set we can get thecomprehensive evaluation index C corresponding to eachcombined forecasting model using equation (12)
Finally we calculate the mean value (EC) and variance(VC) of the comprehensive evaluation index C +rough thestatistical analysis of the change law of the mean value (EC)and variance (VC) the universality of the optimal combinedforecasting model is judged
52 Cross-Validation Result Analysis +e mean value (EC)and the variance (VC) of the comprehensive evaluationindexes are evaluated by each combined forecasting modelin the training sets (see Table 7)
In Table 7 we find that EC-IOWA of each training set has asignificantly higher value compared to EC-IOWGA and EC-IOWHA+e higher the EC is the better the overall forecasting precisionis +e alignment of the variance of the comprehensive evalu-ation indexes is VC-IOWAltVC-IOWGAltVC-IOWHA +e smallerthe VC is the smaller the dispersion of the C value is and themore stable the data change is+is indicates that the combinedforecasting model based on the IOWA operator is wellapplicable
In Figure 13 the distribution maps of EC and VC corre-sponding to each training set show a roughly linear changingtrend When the sample data in the training set (IN) increaseEC-IOWA and EC-IOWH increase and EC-IOWGA decreases Withthe increase of the number of sample data in the training setsthe VC of the three combined forecasting models decreasesBut the change of VC-IOWA is smallest indicating that the Cdoes not fluctuate much and the data are very stable
Based on the cross-validation theory the optimalweights obtained by each training set are brought into thecorresponding testing set EC and VC of the testing sets arelisted in Table 8 and the distribution maps of EC and VCcalculated by each testing set are shown in Figure 14
In Table 8 EC-IOWA of testing sets is significantlyhigher than EC-IOWGA and EC-IOWHA while VC-IOWA issignificantly lower than VC-IOWGA and VC-IOWHA How-ever it is noted the values of EC-IOWGA and EC-IOWHA orVC-IOWGA and VC-IOWHA are very close to each otherMeanwhile it is found from Figure 14 that EC corre-sponding to each testing set decreases with the decrease ofthe sample number in the testing sets Contrarily VCincreases with the decrease of the sample number in thetesting sets +e distribution map of VC-IOWA has littlechange in slope meaning the corresponding C value ismore stable +e results show that the combined fore-casting model based on the IOWA operator has thehighest overall forecasting precision and best level ofapplicability among the three models
6 Nondestructive Tests for Double-CiroldLongevity Pavilion
Double-Cirold Longevity Pavilion is located in the BeijingTiantan Park It was built in the Middle Qing Dynasty andhas a history of 277 years Double-Cirold Longevity Pavilionis a combination of two round pavilions with double eavesand spires Its structure is peculiar and precise and its shapeis novel and well proportioned +is kind of pavilion hashigh scientific artistic and cultural value in the Chinesetimber structure Affected by the natural environment andhuman factors all year round timber components aredamaged Eventually it leads to the loss of the externalprotective layer for timber components and the accelerationof the internal and external damage of timber components
Nondestructive tests of timber components of thedouble-ring marsupial pavilion were performed by stresswave and drilling resistance (see Figure 15) It was found thatthe beams and the columns had internal defects +e B2column of Double-Cirold Longevity Pavilion is an examplewith a moisture content of 98 +e perimeter of thewooden column is 1099 cm and the detected section area is96163 cm2 According to the two-dimensional image ob-tained by the stress wave tests the internal defects werelocated Drilling resistance tests were conducted pertinently+ere were two detected paths in drilling resistance tests andeach path passed through the location of defects
+rough nondestructive tests it was found that there wasan uncompacted sound when knocking the position of theB2 column 400mm from the ground A certain degree ofdefect is found in the interior wood by the stress wave tests(see Figure 16) +e damaged area detected by the stresswave tests accounts for 18 of the detected section and thedamaged area is 17309 cm2 +e drilling resistance testsshow the damaged area is 49 cm2 +e damaged area of theB2 column calculated by the combined forecasting model
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
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Multimedia
Submit your manuscripts atwwwhindawicom
(1) +ree paths are selected for the test specimen(2) +e bit should be perpendicular to the direction of
the rings (see Figures 6(a) and 6(c))(3) +e drilling needle rotation rate and advance rate
parameters of the test equipment are set re-spectively +e stability of the drilling resistance testequipment should be ensured
3 Discussion and Analysis of Test Results
31 Two-Dimensional Images For example in specimen 2the tree species is elm and the simulated defect type ishollow Because of limited pages Figure 7 only shows therelative impedance curve in one path direction
When there is no internal damage in the specimen (seeFigure 7(a)) the two-dimensional image detected by stresswave tests is green and the relative impedance curve de-tected by drilling resistance tests is continuous Two de-tection methods indicate that the specimen is healthy woodWhile the internal hollow is small (when the damagedproportion is less than 18) pale yellow (see Figure 7(b)) andred (see Figure 7(c)) colors are presented in the center of thetwo-dimensional image detected by stress wave testsHowever the relative impedance curve image detected bythe drilling resistance tests starts to appear ldquoblankrdquo reflectingthe approximate width of the hollow area With the ex-pansion of the internal hollow area the center part of thetwo-dimensional image detected by stress wave tests shows abright blue color +e stress wave tests are more accurate inidentifying the size and location of internal hollow (seeFigures 7(d)ndash7(f)) +e stress wave tests visually express thelocation and size of internal hollow through colors but the
boundary of the hollow is relatively fuzzy For drilling re-sistance tests the length of the ldquoblankrdquo on the relative im-pedance curve increases with the expansion of the internalhollow area which is basically similar to the test resultsdetected by stress wave tests
To sum up the stress wave tests can quickly make anintuitive judgment on the general position and degree ofdamage but the judgment on the damage type is weak andthe boundary division of internal defects is fuzzy Howeverthe drilling resistance tests only reflect the internal damageof the wooden components under one path according to therelative impedance curve It is not possible to detect everyposition of a cross section and there is no great referencevalue when used alone If enough information is neededmore drilling resistance paths should be provided +roughanalysis it is found that the stress wave image and the re-sistance curve have a good correspondence relationship inthis test Putting the results of the two together for com-parative analysis can make up for their respectiveshortcomings
32DetectionData +edetection data listed in Table 2 showthat the detected precision of the same detection method isdifferent while it is working in various working conditions+e mean error and mean precision obtained by stress wavetests are 1113 cm2 and 729 respectively while the meanerror and mean precision obtained by drilling resistancetests are 847 cm2 and 876 respectively +e correlationcoefficients between the detected data obtained by stresswave and drilling resistance tests and the actual value are09894 and 09989 +e overall detection effect of drilling
(a)
100
Am
plitu
de (
) 80
60
40
20
00 2 4 6 8 10
Drilling depth (cm)
Hollow
12 14 16 18 20 22
(b)
(c)
100
Am
plitu
de (
) 80
60
40
20
00 2 4 6 8 10
Drilling depth (cm)
Insect attacks
12 14 16 18 20 22
(d)
Figure 6 Drilling resistance tests (a) hollow and (b) its two-dimensional image (c) insect attacks and (d) their two-dimensional image
6 Advances in Civil Engineering
resistance tests is more precise compared to that of stresswave tests
Although the correlation coefficients between the twosets of test data and the real value are very high the de-tected precision is still low under some conditions es-pecially when the stress wave detection is used We findthat the detected precision of the stress wave tests underworking condition 1 working condition 4 workingcondition 9 working condition 14 and working condition15 is relatively low +e proportion of damage simulatedunder the five working conditions is also small +ereforeit is of great engineering value to study the precision ofstress wave detection with such a small internal damagedproportion
When we examined the curves of detected precision underdifferent working conditions (see Figure 8) we found that thedetected precision obtained by stress wave tests increases withthe increase of the internal damaged area in the wood
As far as drilling resistance tests are concerned thedetected precision increases with the increase of the internaldefects in the wood when the internal damage type is hollow(see Figures 8(a) and 8(b))While the internal damage type isinsect attacks the detected precision of specimen 3 does notchange much with the increase of insect attack area (seeFigures 8(c) and 8(d))
In addition when the internal defects are small thedetected precision of drilling resistance tests is higher thanthat of stress wave tests With the further increase of
simulated damaged area the detected precision of bothdetection methods tends to be close to each other When theinternal damaged proportion of wood exceeds 14 thedetected precision of stress wave tests is higher than that ofdrilling resistance tests (see Figures 8(b)ndash8(d))
To sum up comprehensive use of stress wave and drillingresistance tests can screen the type position and size ofinternal damage of timber components However the de-tection results of the two detectionmethods are quite differentwith low detected precision In order to comprehensively usethe information provided by the two detection methods thispaper introduces several new combined forecasting modelswhich are different from the literature [24] in order to im-prove the prediction precision of the internal damage inancient building wood components
4 Combined Forecasting Model
41 Model Building Based on the OWA operator [50]OWGAoperator [51] andOWHAoperator [38] great deals ofextensions have been developed +ese extensions are theIOWA operator IOWGA operator and IOWHA operator Inthis study we reordered the arguments by an inducing variable
If there arem feasible single detection methods to detectinternal defects of the timber components in ancientbuildings under a certain working condition the detectionvalue of the i-th detection method in the t-th workingcondition is xit where i 1 2 m and t 1 2 N
If lm is the weight of the m-th single detection in thecombined forecasting model the weight satisfy the nor-malization and nonnegativity such that
116 18 1455
60
65
70
75
80
85
90
95D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(a)
132 116 18 14 1230
40
50
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(b)
132 116 18 14 12
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(c)
132 116 18 14 1230
40
50
60
70
80
90
100D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(d)
Figure 8 Curves of detected precision under different working conditions (a) Specimen 1 (b) Specimen 2 (c) Specimen 3 (d) Specimen 4
where ait represents the detected precision of the i-th de-tection method under the t-th working condition ait isin [0 1]When ait is regarded as the inducement value of xit it canformm two-dimensional arrays which are (a1t x1t) (a2t x2t) (amt xmt) +e detected precision sequence (a1t a2t amt) of m detection methods under the t-th working con-dition is arranged from high to low Let us hypothesize thata-index(it) is a subscript of the i-th largest value among thedetection sequence
(1) Model based on the IOWA operator [34] the squaresum of error is taken as the criterion to establish thecombined forecasting model According to the de-tected precision sequence the combined forecastingvalue based on the IOWA operator can be obtainedby
IL a1t x1t( 1113857 a2t x2t( 1113857 amt xmt( 11138571113858 1113859
1113944m
i1lixaminusindex(it)
(2)
+e optimal combined forecasting model based onthe IOWA operator with the square sum of error asthe criterion can be expressed as follows
SIOWA 1113944N
t1xt minus 1113944
m
i1lixaminusindex(it)
⎛⎝ ⎞⎠
2
(3)
(2) Model based on the IOWGA operator [36] thesquare sum of logarithmic error is taken as thecriterion to establish the combined forecastingmodel According to the detected precision se-quence the combined forecasting value based on theIOWGA operator can be obtained by
+eoptimal combined forecastingmodel based on theIOWGA operator with the square sum of logarithmicerror as the criterion can be expressed as follows
SIOWGA 1113944N
t1lnxt minus ln1113945
m
i1x
liaminusindex(it)
⎞⎠
2
⎛⎝ (5)
(3) Model based on the IOWHA operator [38] thesquare sum of reciprocal error is taken as the cri-terion to establish the combined forecasting modelAccording to the detected precision sequence thecombined forecasting value based on the IOWHAoperator can be obtained by
+e optimal combined forecasting model based onthe IOWHA operator with the square sum of re-ciprocal error as the criterion can be expressed asfollows
SIOWHA 1113944N
t11113944
m
i1li
1xt
minus1
xaminusindex(it)
1113888 1113889⎛⎝ ⎞⎠
2
(7)
42 Solving Model Taking the simulated hollow test ofspecimen 1 as an example we can list the two-dimensionalarray of detection values and its detected precision under thet-th working condition as follows
(0576 3722) (0817 2134)
(0650 7059) (0844 4412)
(0808 12464) (0909 9502)
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (8)
+e prediction value based on the IOWA operator iscalculated according to equation (2) +e solving process isshown as follows
By substituting them into equation (3) the optimalcombined forecasting model based on the IOWA operator isarranged as follows
min SIOWA l1 l2( 1113857 2613minus 2134l1 minus 3722l2( 11138572
+ 5227minus 4412l1 minus 7059l2( 11138572
+ 10454minus 9502l1 minus 12464l2( 11138572
stl1 + l2 1
l1 ge 0 l2 ge 01113896
(10)
Advances in Civil Engineering 9
+e MATLAB software is used to solve the optimalweight (li) Some parameters of the genetic algorithm are setas follows
Generations 50StallGenLimi 100PopInitRange [zeros(1 m) ones(1 m)]PopulationSize 10000
After 50 genetic iterations the MATLAB softwareshows that (l1 l2) is (069 031) respectively +e black andblue points in Figure 9 are the best fitness value and themean fitness value respectively It is found that the meanfitness value of the population represents a smoothdownward trend with the increase of the number of iter-ations and gradually moves towards the best fitness value(see Figure 9)
Similarly the solving processes of the models basedon the IOWGA operator and IOWHA operator are thesame as that of the model based on the IOWA operator Inorder to select the optimal model the traditional com-bined forecasting models based on the entropy valueand Shapley value are introduced in this paper forcomparison
43 Analyzing Precision of Different Combined ForecastingModels In Table 3 the mean precision from large to small isP1 P2 P3 P4 and P5 Compared to detected precision ofstress wave tests the precision is improved by 258 254252 215 and 176 respectively While compared todetected precision of drilling resistance tests the precision isimproved by 47 43 42 11 and 22 respectivelyAdditionally the mean absolute error from small to large ise1 e2 e3 e5 and e4 So we find that the models based on theIOWA operator IOWGA operator and IOWHA operatorhave better forecasting effects compared to others (seeFigure 10)
Other than that through statistical analysis of workingcondition 1 working condition 4 working condition 9working condition 14 and working condition 15 (seeTable 4) we also find that the combined forecasting modelsbased on the IOWA operator IOWGA operator andIOWHA operator are more effective compared to thecombined forecasting models based on the entropy valueand Shapley value in improving the detected precision ofstress wave tests in the case of small defects inside thewood
44 Forecasting Effect Evaluation According to the eval-uation principle of the forecasting effect SSE MSEMAE MAPE and MSPE are selected as evaluation in-dexes to reflect the effectiveness of the combined fore-casting models +e calculation results are shown inTable 5
In Table 5 it is found that the first four indexes of thecombined forecasting method based on the IOWA oper-ator are significantly lower than those of others AlthoughMSPE of the combined forecasting method based on theIOWA operator is not the least it is close to MSPE ofcombined forecasting methods based on the IOWGAoperator and IOWHA operator +erefore the combinedforecasting model based on the IOWA operator has thebest effect Meanwhile by normalizing the above fiveindexes the expression of the comprehensive evaluationindex C is obtained as follows
Ci 1n
1113944
n
j1
min Ej1113872 1113873
Eij
(12)
Best 011231 mean 0497158
Best fitness Mean fitness
Fitn
ess v
alue
0 5 10 15 20 25 30 35 40 45 50Generation
180
160
140
120
100
80
60
40
20
0
Figure 9 Best fitness value and mean fitness value
10 Advances in Civil Engineering
where Ci is the comprehensive evaluation index of the i-thmethod i 1 2 M Eij is the j-th index of the i-thmethod j 1 2 n and min(Ej) is the minimum valueamong the j-th indexes of m methods +e higher the C isthe better the corresponding combined forecasting model is+e index C of each method is developed by bringing the fiveindex values in Table 5 into equation (12)
Figure 11 shows that the comprehensive evaluationindex of each combined forecasting model is significantlyhigher than that of the two single detection methods in-dicating that the combined forecasting model can improvethe forecasting precision of the internal defects of the timber
components Furthermore the C of the combined fore-casting model based on the IOWA operator is 972 higherthan others All the analysis shows that the combinedforecasting model based on the IOWA operator is the op-timal model followed by the combined forecasting modelsbased on the IOWGA operator and IOWHA operator
5 Applicability Assessment
An applicability assessment is performed for the combinedforecasting models based on the IOWA operator IOWGAoperator and IOWHA operator
51 Cross-Validation 9eory Since there are a total of 18working conditions in this test each working conditionhas a corresponding set of actual values and detectedvalues obtained by stress wave and drilling resistance tests(see Table 2) Because of the small number of data samplesand each combined forecasting model is tested only oncethe randomness is large which does not prove that theabove optimal models have good universality In order tomake full use of the data samples a cross-validationmethod is applied to carry out the test +e researchprocess is shown in Figure 12
Firstly by setting random samples we randomlyextracted N (N 5 6 17) working conditions from 18working conditions as a training set (IN) and then thecorresponding remaining 18minusN working conditions areconsidered as a testing set (IN) For the number (N) ofrandomly selected samples there are CN
18 subsets for both thetraining set and the testing set (see Table 6) For example ifN 5 both the training set (I5) and the testing set (I5) willhave 8568 subsets
Table 3 Results of each combined forecasting model
If I5 working condition 1 working condition 2working condition 3 working condition 4 working con-dition 5 then I5 working condition 6 working condi-tion 7 working condition 8 working condition 9 workingcondition 10 working condition 11 working condition 12working condition 13 working condition 14 workingcondition 15 working condition 16 working condition17
By analogy we can get 8568 subsets for the training set(I5) and the testing set (I5)
Secondly based on random sample data in each trainingset (IN) three combined forecasting models based on theIOWA operator IOWGA operator and IOWHA operatorare established to solve three sets of corresponding optimalweights Based on the cross-validation method three sets ofweights are substituted into the corresponding testing set(IN) For the training set and testing set we can get thecomprehensive evaluation index C corresponding to eachcombined forecasting model using equation (12)
Finally we calculate the mean value (EC) and variance(VC) of the comprehensive evaluation index C +rough thestatistical analysis of the change law of the mean value (EC)and variance (VC) the universality of the optimal combinedforecasting model is judged
52 Cross-Validation Result Analysis +e mean value (EC)and the variance (VC) of the comprehensive evaluationindexes are evaluated by each combined forecasting modelin the training sets (see Table 7)
In Table 7 we find that EC-IOWA of each training set has asignificantly higher value compared to EC-IOWGA and EC-IOWHA+e higher the EC is the better the overall forecasting precisionis +e alignment of the variance of the comprehensive evalu-ation indexes is VC-IOWAltVC-IOWGAltVC-IOWHA +e smallerthe VC is the smaller the dispersion of the C value is and themore stable the data change is+is indicates that the combinedforecasting model based on the IOWA operator is wellapplicable
In Figure 13 the distribution maps of EC and VC corre-sponding to each training set show a roughly linear changingtrend When the sample data in the training set (IN) increaseEC-IOWA and EC-IOWH increase and EC-IOWGA decreases Withthe increase of the number of sample data in the training setsthe VC of the three combined forecasting models decreasesBut the change of VC-IOWA is smallest indicating that the Cdoes not fluctuate much and the data are very stable
Based on the cross-validation theory the optimalweights obtained by each training set are brought into thecorresponding testing set EC and VC of the testing sets arelisted in Table 8 and the distribution maps of EC and VCcalculated by each testing set are shown in Figure 14
In Table 8 EC-IOWA of testing sets is significantlyhigher than EC-IOWGA and EC-IOWHA while VC-IOWA issignificantly lower than VC-IOWGA and VC-IOWHA How-ever it is noted the values of EC-IOWGA and EC-IOWHA orVC-IOWGA and VC-IOWHA are very close to each otherMeanwhile it is found from Figure 14 that EC corre-sponding to each testing set decreases with the decrease ofthe sample number in the testing sets Contrarily VCincreases with the decrease of the sample number in thetesting sets +e distribution map of VC-IOWA has littlechange in slope meaning the corresponding C value ismore stable +e results show that the combined fore-casting model based on the IOWA operator has thehighest overall forecasting precision and best level ofapplicability among the three models
6 Nondestructive Tests for Double-CiroldLongevity Pavilion
Double-Cirold Longevity Pavilion is located in the BeijingTiantan Park It was built in the Middle Qing Dynasty andhas a history of 277 years Double-Cirold Longevity Pavilionis a combination of two round pavilions with double eavesand spires Its structure is peculiar and precise and its shapeis novel and well proportioned +is kind of pavilion hashigh scientific artistic and cultural value in the Chinesetimber structure Affected by the natural environment andhuman factors all year round timber components aredamaged Eventually it leads to the loss of the externalprotective layer for timber components and the accelerationof the internal and external damage of timber components
Nondestructive tests of timber components of thedouble-ring marsupial pavilion were performed by stresswave and drilling resistance (see Figure 15) It was found thatthe beams and the columns had internal defects +e B2column of Double-Cirold Longevity Pavilion is an examplewith a moisture content of 98 +e perimeter of thewooden column is 1099 cm and the detected section area is96163 cm2 According to the two-dimensional image ob-tained by the stress wave tests the internal defects werelocated Drilling resistance tests were conducted pertinently+ere were two detected paths in drilling resistance tests andeach path passed through the location of defects
+rough nondestructive tests it was found that there wasan uncompacted sound when knocking the position of theB2 column 400mm from the ground A certain degree ofdefect is found in the interior wood by the stress wave tests(see Figure 16) +e damaged area detected by the stresswave tests accounts for 18 of the detected section and thedamaged area is 17309 cm2 +e drilling resistance testsshow the damaged area is 49 cm2 +e damaged area of theB2 column calculated by the combined forecasting model
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
Chemical EngineeringInternational Journal of Antennas and
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International Journal of
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resistance tests is more precise compared to that of stresswave tests
Although the correlation coefficients between the twosets of test data and the real value are very high the de-tected precision is still low under some conditions es-pecially when the stress wave detection is used We findthat the detected precision of the stress wave tests underworking condition 1 working condition 4 workingcondition 9 working condition 14 and working condition15 is relatively low +e proportion of damage simulatedunder the five working conditions is also small +ereforeit is of great engineering value to study the precision ofstress wave detection with such a small internal damagedproportion
When we examined the curves of detected precision underdifferent working conditions (see Figure 8) we found that thedetected precision obtained by stress wave tests increases withthe increase of the internal damaged area in the wood
As far as drilling resistance tests are concerned thedetected precision increases with the increase of the internaldefects in the wood when the internal damage type is hollow(see Figures 8(a) and 8(b))While the internal damage type isinsect attacks the detected precision of specimen 3 does notchange much with the increase of insect attack area (seeFigures 8(c) and 8(d))
In addition when the internal defects are small thedetected precision of drilling resistance tests is higher thanthat of stress wave tests With the further increase of
simulated damaged area the detected precision of bothdetection methods tends to be close to each other When theinternal damaged proportion of wood exceeds 14 thedetected precision of stress wave tests is higher than that ofdrilling resistance tests (see Figures 8(b)ndash8(d))
To sum up comprehensive use of stress wave and drillingresistance tests can screen the type position and size ofinternal damage of timber components However the de-tection results of the two detectionmethods are quite differentwith low detected precision In order to comprehensively usethe information provided by the two detection methods thispaper introduces several new combined forecasting modelswhich are different from the literature [24] in order to im-prove the prediction precision of the internal damage inancient building wood components
4 Combined Forecasting Model
41 Model Building Based on the OWA operator [50]OWGAoperator [51] andOWHAoperator [38] great deals ofextensions have been developed +ese extensions are theIOWA operator IOWGA operator and IOWHA operator Inthis study we reordered the arguments by an inducing variable
If there arem feasible single detection methods to detectinternal defects of the timber components in ancientbuildings under a certain working condition the detectionvalue of the i-th detection method in the t-th workingcondition is xit where i 1 2 m and t 1 2 N
If lm is the weight of the m-th single detection in thecombined forecasting model the weight satisfy the nor-malization and nonnegativity such that
116 18 1455
60
65
70
75
80
85
90
95D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(a)
132 116 18 14 1230
40
50
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(b)
132 116 18 14 12
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(c)
132 116 18 14 1230
40
50
60
70
80
90
100D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(d)
Figure 8 Curves of detected precision under different working conditions (a) Specimen 1 (b) Specimen 2 (c) Specimen 3 (d) Specimen 4
where ait represents the detected precision of the i-th de-tection method under the t-th working condition ait isin [0 1]When ait is regarded as the inducement value of xit it canformm two-dimensional arrays which are (a1t x1t) (a2t x2t) (amt xmt) +e detected precision sequence (a1t a2t amt) of m detection methods under the t-th working con-dition is arranged from high to low Let us hypothesize thata-index(it) is a subscript of the i-th largest value among thedetection sequence
(1) Model based on the IOWA operator [34] the squaresum of error is taken as the criterion to establish thecombined forecasting model According to the de-tected precision sequence the combined forecastingvalue based on the IOWA operator can be obtainedby
IL a1t x1t( 1113857 a2t x2t( 1113857 amt xmt( 11138571113858 1113859
1113944m
i1lixaminusindex(it)
(2)
+e optimal combined forecasting model based onthe IOWA operator with the square sum of error asthe criterion can be expressed as follows
SIOWA 1113944N
t1xt minus 1113944
m
i1lixaminusindex(it)
⎛⎝ ⎞⎠
2
(3)
(2) Model based on the IOWGA operator [36] thesquare sum of logarithmic error is taken as thecriterion to establish the combined forecastingmodel According to the detected precision se-quence the combined forecasting value based on theIOWGA operator can be obtained by
+eoptimal combined forecastingmodel based on theIOWGA operator with the square sum of logarithmicerror as the criterion can be expressed as follows
SIOWGA 1113944N
t1lnxt minus ln1113945
m
i1x
liaminusindex(it)
⎞⎠
2
⎛⎝ (5)
(3) Model based on the IOWHA operator [38] thesquare sum of reciprocal error is taken as the cri-terion to establish the combined forecasting modelAccording to the detected precision sequence thecombined forecasting value based on the IOWHAoperator can be obtained by
+e optimal combined forecasting model based onthe IOWHA operator with the square sum of re-ciprocal error as the criterion can be expressed asfollows
SIOWHA 1113944N
t11113944
m
i1li
1xt
minus1
xaminusindex(it)
1113888 1113889⎛⎝ ⎞⎠
2
(7)
42 Solving Model Taking the simulated hollow test ofspecimen 1 as an example we can list the two-dimensionalarray of detection values and its detected precision under thet-th working condition as follows
(0576 3722) (0817 2134)
(0650 7059) (0844 4412)
(0808 12464) (0909 9502)
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (8)
+e prediction value based on the IOWA operator iscalculated according to equation (2) +e solving process isshown as follows
By substituting them into equation (3) the optimalcombined forecasting model based on the IOWA operator isarranged as follows
min SIOWA l1 l2( 1113857 2613minus 2134l1 minus 3722l2( 11138572
+ 5227minus 4412l1 minus 7059l2( 11138572
+ 10454minus 9502l1 minus 12464l2( 11138572
stl1 + l2 1
l1 ge 0 l2 ge 01113896
(10)
Advances in Civil Engineering 9
+e MATLAB software is used to solve the optimalweight (li) Some parameters of the genetic algorithm are setas follows
Generations 50StallGenLimi 100PopInitRange [zeros(1 m) ones(1 m)]PopulationSize 10000
After 50 genetic iterations the MATLAB softwareshows that (l1 l2) is (069 031) respectively +e black andblue points in Figure 9 are the best fitness value and themean fitness value respectively It is found that the meanfitness value of the population represents a smoothdownward trend with the increase of the number of iter-ations and gradually moves towards the best fitness value(see Figure 9)
Similarly the solving processes of the models basedon the IOWGA operator and IOWHA operator are thesame as that of the model based on the IOWA operator Inorder to select the optimal model the traditional com-bined forecasting models based on the entropy valueand Shapley value are introduced in this paper forcomparison
43 Analyzing Precision of Different Combined ForecastingModels In Table 3 the mean precision from large to small isP1 P2 P3 P4 and P5 Compared to detected precision ofstress wave tests the precision is improved by 258 254252 215 and 176 respectively While compared todetected precision of drilling resistance tests the precision isimproved by 47 43 42 11 and 22 respectivelyAdditionally the mean absolute error from small to large ise1 e2 e3 e5 and e4 So we find that the models based on theIOWA operator IOWGA operator and IOWHA operatorhave better forecasting effects compared to others (seeFigure 10)
Other than that through statistical analysis of workingcondition 1 working condition 4 working condition 9working condition 14 and working condition 15 (seeTable 4) we also find that the combined forecasting modelsbased on the IOWA operator IOWGA operator andIOWHA operator are more effective compared to thecombined forecasting models based on the entropy valueand Shapley value in improving the detected precision ofstress wave tests in the case of small defects inside thewood
44 Forecasting Effect Evaluation According to the eval-uation principle of the forecasting effect SSE MSEMAE MAPE and MSPE are selected as evaluation in-dexes to reflect the effectiveness of the combined fore-casting models +e calculation results are shown inTable 5
In Table 5 it is found that the first four indexes of thecombined forecasting method based on the IOWA oper-ator are significantly lower than those of others AlthoughMSPE of the combined forecasting method based on theIOWA operator is not the least it is close to MSPE ofcombined forecasting methods based on the IOWGAoperator and IOWHA operator +erefore the combinedforecasting model based on the IOWA operator has thebest effect Meanwhile by normalizing the above fiveindexes the expression of the comprehensive evaluationindex C is obtained as follows
Ci 1n
1113944
n
j1
min Ej1113872 1113873
Eij
(12)
Best 011231 mean 0497158
Best fitness Mean fitness
Fitn
ess v
alue
0 5 10 15 20 25 30 35 40 45 50Generation
180
160
140
120
100
80
60
40
20
0
Figure 9 Best fitness value and mean fitness value
10 Advances in Civil Engineering
where Ci is the comprehensive evaluation index of the i-thmethod i 1 2 M Eij is the j-th index of the i-thmethod j 1 2 n and min(Ej) is the minimum valueamong the j-th indexes of m methods +e higher the C isthe better the corresponding combined forecasting model is+e index C of each method is developed by bringing the fiveindex values in Table 5 into equation (12)
Figure 11 shows that the comprehensive evaluationindex of each combined forecasting model is significantlyhigher than that of the two single detection methods in-dicating that the combined forecasting model can improvethe forecasting precision of the internal defects of the timber
components Furthermore the C of the combined fore-casting model based on the IOWA operator is 972 higherthan others All the analysis shows that the combinedforecasting model based on the IOWA operator is the op-timal model followed by the combined forecasting modelsbased on the IOWGA operator and IOWHA operator
5 Applicability Assessment
An applicability assessment is performed for the combinedforecasting models based on the IOWA operator IOWGAoperator and IOWHA operator
51 Cross-Validation 9eory Since there are a total of 18working conditions in this test each working conditionhas a corresponding set of actual values and detectedvalues obtained by stress wave and drilling resistance tests(see Table 2) Because of the small number of data samplesand each combined forecasting model is tested only oncethe randomness is large which does not prove that theabove optimal models have good universality In order tomake full use of the data samples a cross-validationmethod is applied to carry out the test +e researchprocess is shown in Figure 12
Firstly by setting random samples we randomlyextracted N (N 5 6 17) working conditions from 18working conditions as a training set (IN) and then thecorresponding remaining 18minusN working conditions areconsidered as a testing set (IN) For the number (N) ofrandomly selected samples there are CN
18 subsets for both thetraining set and the testing set (see Table 6) For example ifN 5 both the training set (I5) and the testing set (I5) willhave 8568 subsets
Table 3 Results of each combined forecasting model
If I5 working condition 1 working condition 2working condition 3 working condition 4 working con-dition 5 then I5 working condition 6 working condi-tion 7 working condition 8 working condition 9 workingcondition 10 working condition 11 working condition 12working condition 13 working condition 14 workingcondition 15 working condition 16 working condition17
By analogy we can get 8568 subsets for the training set(I5) and the testing set (I5)
Secondly based on random sample data in each trainingset (IN) three combined forecasting models based on theIOWA operator IOWGA operator and IOWHA operatorare established to solve three sets of corresponding optimalweights Based on the cross-validation method three sets ofweights are substituted into the corresponding testing set(IN) For the training set and testing set we can get thecomprehensive evaluation index C corresponding to eachcombined forecasting model using equation (12)
Finally we calculate the mean value (EC) and variance(VC) of the comprehensive evaluation index C +rough thestatistical analysis of the change law of the mean value (EC)and variance (VC) the universality of the optimal combinedforecasting model is judged
52 Cross-Validation Result Analysis +e mean value (EC)and the variance (VC) of the comprehensive evaluationindexes are evaluated by each combined forecasting modelin the training sets (see Table 7)
In Table 7 we find that EC-IOWA of each training set has asignificantly higher value compared to EC-IOWGA and EC-IOWHA+e higher the EC is the better the overall forecasting precisionis +e alignment of the variance of the comprehensive evalu-ation indexes is VC-IOWAltVC-IOWGAltVC-IOWHA +e smallerthe VC is the smaller the dispersion of the C value is and themore stable the data change is+is indicates that the combinedforecasting model based on the IOWA operator is wellapplicable
In Figure 13 the distribution maps of EC and VC corre-sponding to each training set show a roughly linear changingtrend When the sample data in the training set (IN) increaseEC-IOWA and EC-IOWH increase and EC-IOWGA decreases Withthe increase of the number of sample data in the training setsthe VC of the three combined forecasting models decreasesBut the change of VC-IOWA is smallest indicating that the Cdoes not fluctuate much and the data are very stable
Based on the cross-validation theory the optimalweights obtained by each training set are brought into thecorresponding testing set EC and VC of the testing sets arelisted in Table 8 and the distribution maps of EC and VCcalculated by each testing set are shown in Figure 14
In Table 8 EC-IOWA of testing sets is significantlyhigher than EC-IOWGA and EC-IOWHA while VC-IOWA issignificantly lower than VC-IOWGA and VC-IOWHA How-ever it is noted the values of EC-IOWGA and EC-IOWHA orVC-IOWGA and VC-IOWHA are very close to each otherMeanwhile it is found from Figure 14 that EC corre-sponding to each testing set decreases with the decrease ofthe sample number in the testing sets Contrarily VCincreases with the decrease of the sample number in thetesting sets +e distribution map of VC-IOWA has littlechange in slope meaning the corresponding C value ismore stable +e results show that the combined fore-casting model based on the IOWA operator has thehighest overall forecasting precision and best level ofapplicability among the three models
6 Nondestructive Tests for Double-CiroldLongevity Pavilion
Double-Cirold Longevity Pavilion is located in the BeijingTiantan Park It was built in the Middle Qing Dynasty andhas a history of 277 years Double-Cirold Longevity Pavilionis a combination of two round pavilions with double eavesand spires Its structure is peculiar and precise and its shapeis novel and well proportioned +is kind of pavilion hashigh scientific artistic and cultural value in the Chinesetimber structure Affected by the natural environment andhuman factors all year round timber components aredamaged Eventually it leads to the loss of the externalprotective layer for timber components and the accelerationof the internal and external damage of timber components
Nondestructive tests of timber components of thedouble-ring marsupial pavilion were performed by stresswave and drilling resistance (see Figure 15) It was found thatthe beams and the columns had internal defects +e B2column of Double-Cirold Longevity Pavilion is an examplewith a moisture content of 98 +e perimeter of thewooden column is 1099 cm and the detected section area is96163 cm2 According to the two-dimensional image ob-tained by the stress wave tests the internal defects werelocated Drilling resistance tests were conducted pertinently+ere were two detected paths in drilling resistance tests andeach path passed through the location of defects
+rough nondestructive tests it was found that there wasan uncompacted sound when knocking the position of theB2 column 400mm from the ground A certain degree ofdefect is found in the interior wood by the stress wave tests(see Figure 16) +e damaged area detected by the stresswave tests accounts for 18 of the detected section and thedamaged area is 17309 cm2 +e drilling resistance testsshow the damaged area is 49 cm2 +e damaged area of theB2 column calculated by the combined forecasting model
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
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Navigation and Observation
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Hindawi
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Submit your manuscripts atwwwhindawicom
simulated damaged area the detected precision of bothdetection methods tends to be close to each other When theinternal damaged proportion of wood exceeds 14 thedetected precision of stress wave tests is higher than that ofdrilling resistance tests (see Figures 8(b)ndash8(d))
To sum up comprehensive use of stress wave and drillingresistance tests can screen the type position and size ofinternal damage of timber components However the de-tection results of the two detectionmethods are quite differentwith low detected precision In order to comprehensively usethe information provided by the two detection methods thispaper introduces several new combined forecasting modelswhich are different from the literature [24] in order to im-prove the prediction precision of the internal damage inancient building wood components
4 Combined Forecasting Model
41 Model Building Based on the OWA operator [50]OWGAoperator [51] andOWHAoperator [38] great deals ofextensions have been developed +ese extensions are theIOWA operator IOWGA operator and IOWHA operator Inthis study we reordered the arguments by an inducing variable
If there arem feasible single detection methods to detectinternal defects of the timber components in ancientbuildings under a certain working condition the detectionvalue of the i-th detection method in the t-th workingcondition is xit where i 1 2 m and t 1 2 N
If lm is the weight of the m-th single detection in thecombined forecasting model the weight satisfy the nor-malization and nonnegativity such that
116 18 1455
60
65
70
75
80
85
90
95D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(a)
132 116 18 14 1230
40
50
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(b)
132 116 18 14 12
60
70
80
90
100
Det
ecte
d pr
ecisi
on (
)
Damaged proportion
Stress waveDrilling resistance
(c)
132 116 18 14 1230
40
50
60
70
80
90
100D
etec
ted
prec
ision
()
Damaged proportion
Stress waveDrilling resistance
(d)
Figure 8 Curves of detected precision under different working conditions (a) Specimen 1 (b) Specimen 2 (c) Specimen 3 (d) Specimen 4
where ait represents the detected precision of the i-th de-tection method under the t-th working condition ait isin [0 1]When ait is regarded as the inducement value of xit it canformm two-dimensional arrays which are (a1t x1t) (a2t x2t) (amt xmt) +e detected precision sequence (a1t a2t amt) of m detection methods under the t-th working con-dition is arranged from high to low Let us hypothesize thata-index(it) is a subscript of the i-th largest value among thedetection sequence
(1) Model based on the IOWA operator [34] the squaresum of error is taken as the criterion to establish thecombined forecasting model According to the de-tected precision sequence the combined forecastingvalue based on the IOWA operator can be obtainedby
IL a1t x1t( 1113857 a2t x2t( 1113857 amt xmt( 11138571113858 1113859
1113944m
i1lixaminusindex(it)
(2)
+e optimal combined forecasting model based onthe IOWA operator with the square sum of error asthe criterion can be expressed as follows
SIOWA 1113944N
t1xt minus 1113944
m
i1lixaminusindex(it)
⎛⎝ ⎞⎠
2
(3)
(2) Model based on the IOWGA operator [36] thesquare sum of logarithmic error is taken as thecriterion to establish the combined forecastingmodel According to the detected precision se-quence the combined forecasting value based on theIOWGA operator can be obtained by
+eoptimal combined forecastingmodel based on theIOWGA operator with the square sum of logarithmicerror as the criterion can be expressed as follows
SIOWGA 1113944N
t1lnxt minus ln1113945
m
i1x
liaminusindex(it)
⎞⎠
2
⎛⎝ (5)
(3) Model based on the IOWHA operator [38] thesquare sum of reciprocal error is taken as the cri-terion to establish the combined forecasting modelAccording to the detected precision sequence thecombined forecasting value based on the IOWHAoperator can be obtained by
+e optimal combined forecasting model based onthe IOWHA operator with the square sum of re-ciprocal error as the criterion can be expressed asfollows
SIOWHA 1113944N
t11113944
m
i1li
1xt
minus1
xaminusindex(it)
1113888 1113889⎛⎝ ⎞⎠
2
(7)
42 Solving Model Taking the simulated hollow test ofspecimen 1 as an example we can list the two-dimensionalarray of detection values and its detected precision under thet-th working condition as follows
(0576 3722) (0817 2134)
(0650 7059) (0844 4412)
(0808 12464) (0909 9502)
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (8)
+e prediction value based on the IOWA operator iscalculated according to equation (2) +e solving process isshown as follows
By substituting them into equation (3) the optimalcombined forecasting model based on the IOWA operator isarranged as follows
min SIOWA l1 l2( 1113857 2613minus 2134l1 minus 3722l2( 11138572
+ 5227minus 4412l1 minus 7059l2( 11138572
+ 10454minus 9502l1 minus 12464l2( 11138572
stl1 + l2 1
l1 ge 0 l2 ge 01113896
(10)
Advances in Civil Engineering 9
+e MATLAB software is used to solve the optimalweight (li) Some parameters of the genetic algorithm are setas follows
Generations 50StallGenLimi 100PopInitRange [zeros(1 m) ones(1 m)]PopulationSize 10000
After 50 genetic iterations the MATLAB softwareshows that (l1 l2) is (069 031) respectively +e black andblue points in Figure 9 are the best fitness value and themean fitness value respectively It is found that the meanfitness value of the population represents a smoothdownward trend with the increase of the number of iter-ations and gradually moves towards the best fitness value(see Figure 9)
Similarly the solving processes of the models basedon the IOWGA operator and IOWHA operator are thesame as that of the model based on the IOWA operator Inorder to select the optimal model the traditional com-bined forecasting models based on the entropy valueand Shapley value are introduced in this paper forcomparison
43 Analyzing Precision of Different Combined ForecastingModels In Table 3 the mean precision from large to small isP1 P2 P3 P4 and P5 Compared to detected precision ofstress wave tests the precision is improved by 258 254252 215 and 176 respectively While compared todetected precision of drilling resistance tests the precision isimproved by 47 43 42 11 and 22 respectivelyAdditionally the mean absolute error from small to large ise1 e2 e3 e5 and e4 So we find that the models based on theIOWA operator IOWGA operator and IOWHA operatorhave better forecasting effects compared to others (seeFigure 10)
Other than that through statistical analysis of workingcondition 1 working condition 4 working condition 9working condition 14 and working condition 15 (seeTable 4) we also find that the combined forecasting modelsbased on the IOWA operator IOWGA operator andIOWHA operator are more effective compared to thecombined forecasting models based on the entropy valueand Shapley value in improving the detected precision ofstress wave tests in the case of small defects inside thewood
44 Forecasting Effect Evaluation According to the eval-uation principle of the forecasting effect SSE MSEMAE MAPE and MSPE are selected as evaluation in-dexes to reflect the effectiveness of the combined fore-casting models +e calculation results are shown inTable 5
In Table 5 it is found that the first four indexes of thecombined forecasting method based on the IOWA oper-ator are significantly lower than those of others AlthoughMSPE of the combined forecasting method based on theIOWA operator is not the least it is close to MSPE ofcombined forecasting methods based on the IOWGAoperator and IOWHA operator +erefore the combinedforecasting model based on the IOWA operator has thebest effect Meanwhile by normalizing the above fiveindexes the expression of the comprehensive evaluationindex C is obtained as follows
Ci 1n
1113944
n
j1
min Ej1113872 1113873
Eij
(12)
Best 011231 mean 0497158
Best fitness Mean fitness
Fitn
ess v
alue
0 5 10 15 20 25 30 35 40 45 50Generation
180
160
140
120
100
80
60
40
20
0
Figure 9 Best fitness value and mean fitness value
10 Advances in Civil Engineering
where Ci is the comprehensive evaluation index of the i-thmethod i 1 2 M Eij is the j-th index of the i-thmethod j 1 2 n and min(Ej) is the minimum valueamong the j-th indexes of m methods +e higher the C isthe better the corresponding combined forecasting model is+e index C of each method is developed by bringing the fiveindex values in Table 5 into equation (12)
Figure 11 shows that the comprehensive evaluationindex of each combined forecasting model is significantlyhigher than that of the two single detection methods in-dicating that the combined forecasting model can improvethe forecasting precision of the internal defects of the timber
components Furthermore the C of the combined fore-casting model based on the IOWA operator is 972 higherthan others All the analysis shows that the combinedforecasting model based on the IOWA operator is the op-timal model followed by the combined forecasting modelsbased on the IOWGA operator and IOWHA operator
5 Applicability Assessment
An applicability assessment is performed for the combinedforecasting models based on the IOWA operator IOWGAoperator and IOWHA operator
51 Cross-Validation 9eory Since there are a total of 18working conditions in this test each working conditionhas a corresponding set of actual values and detectedvalues obtained by stress wave and drilling resistance tests(see Table 2) Because of the small number of data samplesand each combined forecasting model is tested only oncethe randomness is large which does not prove that theabove optimal models have good universality In order tomake full use of the data samples a cross-validationmethod is applied to carry out the test +e researchprocess is shown in Figure 12
Firstly by setting random samples we randomlyextracted N (N 5 6 17) working conditions from 18working conditions as a training set (IN) and then thecorresponding remaining 18minusN working conditions areconsidered as a testing set (IN) For the number (N) ofrandomly selected samples there are CN
18 subsets for both thetraining set and the testing set (see Table 6) For example ifN 5 both the training set (I5) and the testing set (I5) willhave 8568 subsets
Table 3 Results of each combined forecasting model
If I5 working condition 1 working condition 2working condition 3 working condition 4 working con-dition 5 then I5 working condition 6 working condi-tion 7 working condition 8 working condition 9 workingcondition 10 working condition 11 working condition 12working condition 13 working condition 14 workingcondition 15 working condition 16 working condition17
By analogy we can get 8568 subsets for the training set(I5) and the testing set (I5)
Secondly based on random sample data in each trainingset (IN) three combined forecasting models based on theIOWA operator IOWGA operator and IOWHA operatorare established to solve three sets of corresponding optimalweights Based on the cross-validation method three sets ofweights are substituted into the corresponding testing set(IN) For the training set and testing set we can get thecomprehensive evaluation index C corresponding to eachcombined forecasting model using equation (12)
Finally we calculate the mean value (EC) and variance(VC) of the comprehensive evaluation index C +rough thestatistical analysis of the change law of the mean value (EC)and variance (VC) the universality of the optimal combinedforecasting model is judged
52 Cross-Validation Result Analysis +e mean value (EC)and the variance (VC) of the comprehensive evaluationindexes are evaluated by each combined forecasting modelin the training sets (see Table 7)
In Table 7 we find that EC-IOWA of each training set has asignificantly higher value compared to EC-IOWGA and EC-IOWHA+e higher the EC is the better the overall forecasting precisionis +e alignment of the variance of the comprehensive evalu-ation indexes is VC-IOWAltVC-IOWGAltVC-IOWHA +e smallerthe VC is the smaller the dispersion of the C value is and themore stable the data change is+is indicates that the combinedforecasting model based on the IOWA operator is wellapplicable
In Figure 13 the distribution maps of EC and VC corre-sponding to each training set show a roughly linear changingtrend When the sample data in the training set (IN) increaseEC-IOWA and EC-IOWH increase and EC-IOWGA decreases Withthe increase of the number of sample data in the training setsthe VC of the three combined forecasting models decreasesBut the change of VC-IOWA is smallest indicating that the Cdoes not fluctuate much and the data are very stable
Based on the cross-validation theory the optimalweights obtained by each training set are brought into thecorresponding testing set EC and VC of the testing sets arelisted in Table 8 and the distribution maps of EC and VCcalculated by each testing set are shown in Figure 14
In Table 8 EC-IOWA of testing sets is significantlyhigher than EC-IOWGA and EC-IOWHA while VC-IOWA issignificantly lower than VC-IOWGA and VC-IOWHA How-ever it is noted the values of EC-IOWGA and EC-IOWHA orVC-IOWGA and VC-IOWHA are very close to each otherMeanwhile it is found from Figure 14 that EC corre-sponding to each testing set decreases with the decrease ofthe sample number in the testing sets Contrarily VCincreases with the decrease of the sample number in thetesting sets +e distribution map of VC-IOWA has littlechange in slope meaning the corresponding C value ismore stable +e results show that the combined fore-casting model based on the IOWA operator has thehighest overall forecasting precision and best level ofapplicability among the three models
6 Nondestructive Tests for Double-CiroldLongevity Pavilion
Double-Cirold Longevity Pavilion is located in the BeijingTiantan Park It was built in the Middle Qing Dynasty andhas a history of 277 years Double-Cirold Longevity Pavilionis a combination of two round pavilions with double eavesand spires Its structure is peculiar and precise and its shapeis novel and well proportioned +is kind of pavilion hashigh scientific artistic and cultural value in the Chinesetimber structure Affected by the natural environment andhuman factors all year round timber components aredamaged Eventually it leads to the loss of the externalprotective layer for timber components and the accelerationof the internal and external damage of timber components
Nondestructive tests of timber components of thedouble-ring marsupial pavilion were performed by stresswave and drilling resistance (see Figure 15) It was found thatthe beams and the columns had internal defects +e B2column of Double-Cirold Longevity Pavilion is an examplewith a moisture content of 98 +e perimeter of thewooden column is 1099 cm and the detected section area is96163 cm2 According to the two-dimensional image ob-tained by the stress wave tests the internal defects werelocated Drilling resistance tests were conducted pertinently+ere were two detected paths in drilling resistance tests andeach path passed through the location of defects
+rough nondestructive tests it was found that there wasan uncompacted sound when knocking the position of theB2 column 400mm from the ground A certain degree ofdefect is found in the interior wood by the stress wave tests(see Figure 16) +e damaged area detected by the stresswave tests accounts for 18 of the detected section and thedamaged area is 17309 cm2 +e drilling resistance testsshow the damaged area is 49 cm2 +e damaged area of theB2 column calculated by the combined forecasting model
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
where ait represents the detected precision of the i-th de-tection method under the t-th working condition ait isin [0 1]When ait is regarded as the inducement value of xit it canformm two-dimensional arrays which are (a1t x1t) (a2t x2t) (amt xmt) +e detected precision sequence (a1t a2t amt) of m detection methods under the t-th working con-dition is arranged from high to low Let us hypothesize thata-index(it) is a subscript of the i-th largest value among thedetection sequence
(1) Model based on the IOWA operator [34] the squaresum of error is taken as the criterion to establish thecombined forecasting model According to the de-tected precision sequence the combined forecastingvalue based on the IOWA operator can be obtainedby
IL a1t x1t( 1113857 a2t x2t( 1113857 amt xmt( 11138571113858 1113859
1113944m
i1lixaminusindex(it)
(2)
+e optimal combined forecasting model based onthe IOWA operator with the square sum of error asthe criterion can be expressed as follows
SIOWA 1113944N
t1xt minus 1113944
m
i1lixaminusindex(it)
⎛⎝ ⎞⎠
2
(3)
(2) Model based on the IOWGA operator [36] thesquare sum of logarithmic error is taken as thecriterion to establish the combined forecastingmodel According to the detected precision se-quence the combined forecasting value based on theIOWGA operator can be obtained by
+eoptimal combined forecastingmodel based on theIOWGA operator with the square sum of logarithmicerror as the criterion can be expressed as follows
SIOWGA 1113944N
t1lnxt minus ln1113945
m
i1x
liaminusindex(it)
⎞⎠
2
⎛⎝ (5)
(3) Model based on the IOWHA operator [38] thesquare sum of reciprocal error is taken as the cri-terion to establish the combined forecasting modelAccording to the detected precision sequence thecombined forecasting value based on the IOWHAoperator can be obtained by
+e optimal combined forecasting model based onthe IOWHA operator with the square sum of re-ciprocal error as the criterion can be expressed asfollows
SIOWHA 1113944N
t11113944
m
i1li
1xt
minus1
xaminusindex(it)
1113888 1113889⎛⎝ ⎞⎠
2
(7)
42 Solving Model Taking the simulated hollow test ofspecimen 1 as an example we can list the two-dimensionalarray of detection values and its detected precision under thet-th working condition as follows
(0576 3722) (0817 2134)
(0650 7059) (0844 4412)
(0808 12464) (0909 9502)
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (8)
+e prediction value based on the IOWA operator iscalculated according to equation (2) +e solving process isshown as follows
By substituting them into equation (3) the optimalcombined forecasting model based on the IOWA operator isarranged as follows
min SIOWA l1 l2( 1113857 2613minus 2134l1 minus 3722l2( 11138572
+ 5227minus 4412l1 minus 7059l2( 11138572
+ 10454minus 9502l1 minus 12464l2( 11138572
stl1 + l2 1
l1 ge 0 l2 ge 01113896
(10)
Advances in Civil Engineering 9
+e MATLAB software is used to solve the optimalweight (li) Some parameters of the genetic algorithm are setas follows
Generations 50StallGenLimi 100PopInitRange [zeros(1 m) ones(1 m)]PopulationSize 10000
After 50 genetic iterations the MATLAB softwareshows that (l1 l2) is (069 031) respectively +e black andblue points in Figure 9 are the best fitness value and themean fitness value respectively It is found that the meanfitness value of the population represents a smoothdownward trend with the increase of the number of iter-ations and gradually moves towards the best fitness value(see Figure 9)
Similarly the solving processes of the models basedon the IOWGA operator and IOWHA operator are thesame as that of the model based on the IOWA operator Inorder to select the optimal model the traditional com-bined forecasting models based on the entropy valueand Shapley value are introduced in this paper forcomparison
43 Analyzing Precision of Different Combined ForecastingModels In Table 3 the mean precision from large to small isP1 P2 P3 P4 and P5 Compared to detected precision ofstress wave tests the precision is improved by 258 254252 215 and 176 respectively While compared todetected precision of drilling resistance tests the precision isimproved by 47 43 42 11 and 22 respectivelyAdditionally the mean absolute error from small to large ise1 e2 e3 e5 and e4 So we find that the models based on theIOWA operator IOWGA operator and IOWHA operatorhave better forecasting effects compared to others (seeFigure 10)
Other than that through statistical analysis of workingcondition 1 working condition 4 working condition 9working condition 14 and working condition 15 (seeTable 4) we also find that the combined forecasting modelsbased on the IOWA operator IOWGA operator andIOWHA operator are more effective compared to thecombined forecasting models based on the entropy valueand Shapley value in improving the detected precision ofstress wave tests in the case of small defects inside thewood
44 Forecasting Effect Evaluation According to the eval-uation principle of the forecasting effect SSE MSEMAE MAPE and MSPE are selected as evaluation in-dexes to reflect the effectiveness of the combined fore-casting models +e calculation results are shown inTable 5
In Table 5 it is found that the first four indexes of thecombined forecasting method based on the IOWA oper-ator are significantly lower than those of others AlthoughMSPE of the combined forecasting method based on theIOWA operator is not the least it is close to MSPE ofcombined forecasting methods based on the IOWGAoperator and IOWHA operator +erefore the combinedforecasting model based on the IOWA operator has thebest effect Meanwhile by normalizing the above fiveindexes the expression of the comprehensive evaluationindex C is obtained as follows
Ci 1n
1113944
n
j1
min Ej1113872 1113873
Eij
(12)
Best 011231 mean 0497158
Best fitness Mean fitness
Fitn
ess v
alue
0 5 10 15 20 25 30 35 40 45 50Generation
180
160
140
120
100
80
60
40
20
0
Figure 9 Best fitness value and mean fitness value
10 Advances in Civil Engineering
where Ci is the comprehensive evaluation index of the i-thmethod i 1 2 M Eij is the j-th index of the i-thmethod j 1 2 n and min(Ej) is the minimum valueamong the j-th indexes of m methods +e higher the C isthe better the corresponding combined forecasting model is+e index C of each method is developed by bringing the fiveindex values in Table 5 into equation (12)
Figure 11 shows that the comprehensive evaluationindex of each combined forecasting model is significantlyhigher than that of the two single detection methods in-dicating that the combined forecasting model can improvethe forecasting precision of the internal defects of the timber
components Furthermore the C of the combined fore-casting model based on the IOWA operator is 972 higherthan others All the analysis shows that the combinedforecasting model based on the IOWA operator is the op-timal model followed by the combined forecasting modelsbased on the IOWGA operator and IOWHA operator
5 Applicability Assessment
An applicability assessment is performed for the combinedforecasting models based on the IOWA operator IOWGAoperator and IOWHA operator
51 Cross-Validation 9eory Since there are a total of 18working conditions in this test each working conditionhas a corresponding set of actual values and detectedvalues obtained by stress wave and drilling resistance tests(see Table 2) Because of the small number of data samplesand each combined forecasting model is tested only oncethe randomness is large which does not prove that theabove optimal models have good universality In order tomake full use of the data samples a cross-validationmethod is applied to carry out the test +e researchprocess is shown in Figure 12
Firstly by setting random samples we randomlyextracted N (N 5 6 17) working conditions from 18working conditions as a training set (IN) and then thecorresponding remaining 18minusN working conditions areconsidered as a testing set (IN) For the number (N) ofrandomly selected samples there are CN
18 subsets for both thetraining set and the testing set (see Table 6) For example ifN 5 both the training set (I5) and the testing set (I5) willhave 8568 subsets
Table 3 Results of each combined forecasting model
If I5 working condition 1 working condition 2working condition 3 working condition 4 working con-dition 5 then I5 working condition 6 working condi-tion 7 working condition 8 working condition 9 workingcondition 10 working condition 11 working condition 12working condition 13 working condition 14 workingcondition 15 working condition 16 working condition17
By analogy we can get 8568 subsets for the training set(I5) and the testing set (I5)
Secondly based on random sample data in each trainingset (IN) three combined forecasting models based on theIOWA operator IOWGA operator and IOWHA operatorare established to solve three sets of corresponding optimalweights Based on the cross-validation method three sets ofweights are substituted into the corresponding testing set(IN) For the training set and testing set we can get thecomprehensive evaluation index C corresponding to eachcombined forecasting model using equation (12)
Finally we calculate the mean value (EC) and variance(VC) of the comprehensive evaluation index C +rough thestatistical analysis of the change law of the mean value (EC)and variance (VC) the universality of the optimal combinedforecasting model is judged
52 Cross-Validation Result Analysis +e mean value (EC)and the variance (VC) of the comprehensive evaluationindexes are evaluated by each combined forecasting modelin the training sets (see Table 7)
In Table 7 we find that EC-IOWA of each training set has asignificantly higher value compared to EC-IOWGA and EC-IOWHA+e higher the EC is the better the overall forecasting precisionis +e alignment of the variance of the comprehensive evalu-ation indexes is VC-IOWAltVC-IOWGAltVC-IOWHA +e smallerthe VC is the smaller the dispersion of the C value is and themore stable the data change is+is indicates that the combinedforecasting model based on the IOWA operator is wellapplicable
In Figure 13 the distribution maps of EC and VC corre-sponding to each training set show a roughly linear changingtrend When the sample data in the training set (IN) increaseEC-IOWA and EC-IOWH increase and EC-IOWGA decreases Withthe increase of the number of sample data in the training setsthe VC of the three combined forecasting models decreasesBut the change of VC-IOWA is smallest indicating that the Cdoes not fluctuate much and the data are very stable
Based on the cross-validation theory the optimalweights obtained by each training set are brought into thecorresponding testing set EC and VC of the testing sets arelisted in Table 8 and the distribution maps of EC and VCcalculated by each testing set are shown in Figure 14
In Table 8 EC-IOWA of testing sets is significantlyhigher than EC-IOWGA and EC-IOWHA while VC-IOWA issignificantly lower than VC-IOWGA and VC-IOWHA How-ever it is noted the values of EC-IOWGA and EC-IOWHA orVC-IOWGA and VC-IOWHA are very close to each otherMeanwhile it is found from Figure 14 that EC corre-sponding to each testing set decreases with the decrease ofthe sample number in the testing sets Contrarily VCincreases with the decrease of the sample number in thetesting sets +e distribution map of VC-IOWA has littlechange in slope meaning the corresponding C value ismore stable +e results show that the combined fore-casting model based on the IOWA operator has thehighest overall forecasting precision and best level ofapplicability among the three models
6 Nondestructive Tests for Double-CiroldLongevity Pavilion
Double-Cirold Longevity Pavilion is located in the BeijingTiantan Park It was built in the Middle Qing Dynasty andhas a history of 277 years Double-Cirold Longevity Pavilionis a combination of two round pavilions with double eavesand spires Its structure is peculiar and precise and its shapeis novel and well proportioned +is kind of pavilion hashigh scientific artistic and cultural value in the Chinesetimber structure Affected by the natural environment andhuman factors all year round timber components aredamaged Eventually it leads to the loss of the externalprotective layer for timber components and the accelerationof the internal and external damage of timber components
Nondestructive tests of timber components of thedouble-ring marsupial pavilion were performed by stresswave and drilling resistance (see Figure 15) It was found thatthe beams and the columns had internal defects +e B2column of Double-Cirold Longevity Pavilion is an examplewith a moisture content of 98 +e perimeter of thewooden column is 1099 cm and the detected section area is96163 cm2 According to the two-dimensional image ob-tained by the stress wave tests the internal defects werelocated Drilling resistance tests were conducted pertinently+ere were two detected paths in drilling resistance tests andeach path passed through the location of defects
+rough nondestructive tests it was found that there wasan uncompacted sound when knocking the position of theB2 column 400mm from the ground A certain degree ofdefect is found in the interior wood by the stress wave tests(see Figure 16) +e damaged area detected by the stresswave tests accounts for 18 of the detected section and thedamaged area is 17309 cm2 +e drilling resistance testsshow the damaged area is 49 cm2 +e damaged area of theB2 column calculated by the combined forecasting model
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
+e MATLAB software is used to solve the optimalweight (li) Some parameters of the genetic algorithm are setas follows
Generations 50StallGenLimi 100PopInitRange [zeros(1 m) ones(1 m)]PopulationSize 10000
After 50 genetic iterations the MATLAB softwareshows that (l1 l2) is (069 031) respectively +e black andblue points in Figure 9 are the best fitness value and themean fitness value respectively It is found that the meanfitness value of the population represents a smoothdownward trend with the increase of the number of iter-ations and gradually moves towards the best fitness value(see Figure 9)
Similarly the solving processes of the models basedon the IOWGA operator and IOWHA operator are thesame as that of the model based on the IOWA operator Inorder to select the optimal model the traditional com-bined forecasting models based on the entropy valueand Shapley value are introduced in this paper forcomparison
43 Analyzing Precision of Different Combined ForecastingModels In Table 3 the mean precision from large to small isP1 P2 P3 P4 and P5 Compared to detected precision ofstress wave tests the precision is improved by 258 254252 215 and 176 respectively While compared todetected precision of drilling resistance tests the precision isimproved by 47 43 42 11 and 22 respectivelyAdditionally the mean absolute error from small to large ise1 e2 e3 e5 and e4 So we find that the models based on theIOWA operator IOWGA operator and IOWHA operatorhave better forecasting effects compared to others (seeFigure 10)
Other than that through statistical analysis of workingcondition 1 working condition 4 working condition 9working condition 14 and working condition 15 (seeTable 4) we also find that the combined forecasting modelsbased on the IOWA operator IOWGA operator andIOWHA operator are more effective compared to thecombined forecasting models based on the entropy valueand Shapley value in improving the detected precision ofstress wave tests in the case of small defects inside thewood
44 Forecasting Effect Evaluation According to the eval-uation principle of the forecasting effect SSE MSEMAE MAPE and MSPE are selected as evaluation in-dexes to reflect the effectiveness of the combined fore-casting models +e calculation results are shown inTable 5
In Table 5 it is found that the first four indexes of thecombined forecasting method based on the IOWA oper-ator are significantly lower than those of others AlthoughMSPE of the combined forecasting method based on theIOWA operator is not the least it is close to MSPE ofcombined forecasting methods based on the IOWGAoperator and IOWHA operator +erefore the combinedforecasting model based on the IOWA operator has thebest effect Meanwhile by normalizing the above fiveindexes the expression of the comprehensive evaluationindex C is obtained as follows
Ci 1n
1113944
n
j1
min Ej1113872 1113873
Eij
(12)
Best 011231 mean 0497158
Best fitness Mean fitness
Fitn
ess v
alue
0 5 10 15 20 25 30 35 40 45 50Generation
180
160
140
120
100
80
60
40
20
0
Figure 9 Best fitness value and mean fitness value
10 Advances in Civil Engineering
where Ci is the comprehensive evaluation index of the i-thmethod i 1 2 M Eij is the j-th index of the i-thmethod j 1 2 n and min(Ej) is the minimum valueamong the j-th indexes of m methods +e higher the C isthe better the corresponding combined forecasting model is+e index C of each method is developed by bringing the fiveindex values in Table 5 into equation (12)
Figure 11 shows that the comprehensive evaluationindex of each combined forecasting model is significantlyhigher than that of the two single detection methods in-dicating that the combined forecasting model can improvethe forecasting precision of the internal defects of the timber
components Furthermore the C of the combined fore-casting model based on the IOWA operator is 972 higherthan others All the analysis shows that the combinedforecasting model based on the IOWA operator is the op-timal model followed by the combined forecasting modelsbased on the IOWGA operator and IOWHA operator
5 Applicability Assessment
An applicability assessment is performed for the combinedforecasting models based on the IOWA operator IOWGAoperator and IOWHA operator
51 Cross-Validation 9eory Since there are a total of 18working conditions in this test each working conditionhas a corresponding set of actual values and detectedvalues obtained by stress wave and drilling resistance tests(see Table 2) Because of the small number of data samplesand each combined forecasting model is tested only oncethe randomness is large which does not prove that theabove optimal models have good universality In order tomake full use of the data samples a cross-validationmethod is applied to carry out the test +e researchprocess is shown in Figure 12
Firstly by setting random samples we randomlyextracted N (N 5 6 17) working conditions from 18working conditions as a training set (IN) and then thecorresponding remaining 18minusN working conditions areconsidered as a testing set (IN) For the number (N) ofrandomly selected samples there are CN
18 subsets for both thetraining set and the testing set (see Table 6) For example ifN 5 both the training set (I5) and the testing set (I5) willhave 8568 subsets
Table 3 Results of each combined forecasting model
If I5 working condition 1 working condition 2working condition 3 working condition 4 working con-dition 5 then I5 working condition 6 working condi-tion 7 working condition 8 working condition 9 workingcondition 10 working condition 11 working condition 12working condition 13 working condition 14 workingcondition 15 working condition 16 working condition17
By analogy we can get 8568 subsets for the training set(I5) and the testing set (I5)
Secondly based on random sample data in each trainingset (IN) three combined forecasting models based on theIOWA operator IOWGA operator and IOWHA operatorare established to solve three sets of corresponding optimalweights Based on the cross-validation method three sets ofweights are substituted into the corresponding testing set(IN) For the training set and testing set we can get thecomprehensive evaluation index C corresponding to eachcombined forecasting model using equation (12)
Finally we calculate the mean value (EC) and variance(VC) of the comprehensive evaluation index C +rough thestatistical analysis of the change law of the mean value (EC)and variance (VC) the universality of the optimal combinedforecasting model is judged
52 Cross-Validation Result Analysis +e mean value (EC)and the variance (VC) of the comprehensive evaluationindexes are evaluated by each combined forecasting modelin the training sets (see Table 7)
In Table 7 we find that EC-IOWA of each training set has asignificantly higher value compared to EC-IOWGA and EC-IOWHA+e higher the EC is the better the overall forecasting precisionis +e alignment of the variance of the comprehensive evalu-ation indexes is VC-IOWAltVC-IOWGAltVC-IOWHA +e smallerthe VC is the smaller the dispersion of the C value is and themore stable the data change is+is indicates that the combinedforecasting model based on the IOWA operator is wellapplicable
In Figure 13 the distribution maps of EC and VC corre-sponding to each training set show a roughly linear changingtrend When the sample data in the training set (IN) increaseEC-IOWA and EC-IOWH increase and EC-IOWGA decreases Withthe increase of the number of sample data in the training setsthe VC of the three combined forecasting models decreasesBut the change of VC-IOWA is smallest indicating that the Cdoes not fluctuate much and the data are very stable
Based on the cross-validation theory the optimalweights obtained by each training set are brought into thecorresponding testing set EC and VC of the testing sets arelisted in Table 8 and the distribution maps of EC and VCcalculated by each testing set are shown in Figure 14
In Table 8 EC-IOWA of testing sets is significantlyhigher than EC-IOWGA and EC-IOWHA while VC-IOWA issignificantly lower than VC-IOWGA and VC-IOWHA How-ever it is noted the values of EC-IOWGA and EC-IOWHA orVC-IOWGA and VC-IOWHA are very close to each otherMeanwhile it is found from Figure 14 that EC corre-sponding to each testing set decreases with the decrease ofthe sample number in the testing sets Contrarily VCincreases with the decrease of the sample number in thetesting sets +e distribution map of VC-IOWA has littlechange in slope meaning the corresponding C value ismore stable +e results show that the combined fore-casting model based on the IOWA operator has thehighest overall forecasting precision and best level ofapplicability among the three models
6 Nondestructive Tests for Double-CiroldLongevity Pavilion
Double-Cirold Longevity Pavilion is located in the BeijingTiantan Park It was built in the Middle Qing Dynasty andhas a history of 277 years Double-Cirold Longevity Pavilionis a combination of two round pavilions with double eavesand spires Its structure is peculiar and precise and its shapeis novel and well proportioned +is kind of pavilion hashigh scientific artistic and cultural value in the Chinesetimber structure Affected by the natural environment andhuman factors all year round timber components aredamaged Eventually it leads to the loss of the externalprotective layer for timber components and the accelerationof the internal and external damage of timber components
Nondestructive tests of timber components of thedouble-ring marsupial pavilion were performed by stresswave and drilling resistance (see Figure 15) It was found thatthe beams and the columns had internal defects +e B2column of Double-Cirold Longevity Pavilion is an examplewith a moisture content of 98 +e perimeter of thewooden column is 1099 cm and the detected section area is96163 cm2 According to the two-dimensional image ob-tained by the stress wave tests the internal defects werelocated Drilling resistance tests were conducted pertinently+ere were two detected paths in drilling resistance tests andeach path passed through the location of defects
+rough nondestructive tests it was found that there wasan uncompacted sound when knocking the position of theB2 column 400mm from the ground A certain degree ofdefect is found in the interior wood by the stress wave tests(see Figure 16) +e damaged area detected by the stresswave tests accounts for 18 of the detected section and thedamaged area is 17309 cm2 +e drilling resistance testsshow the damaged area is 49 cm2 +e damaged area of theB2 column calculated by the combined forecasting model
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
where Ci is the comprehensive evaluation index of the i-thmethod i 1 2 M Eij is the j-th index of the i-thmethod j 1 2 n and min(Ej) is the minimum valueamong the j-th indexes of m methods +e higher the C isthe better the corresponding combined forecasting model is+e index C of each method is developed by bringing the fiveindex values in Table 5 into equation (12)
Figure 11 shows that the comprehensive evaluationindex of each combined forecasting model is significantlyhigher than that of the two single detection methods in-dicating that the combined forecasting model can improvethe forecasting precision of the internal defects of the timber
components Furthermore the C of the combined fore-casting model based on the IOWA operator is 972 higherthan others All the analysis shows that the combinedforecasting model based on the IOWA operator is the op-timal model followed by the combined forecasting modelsbased on the IOWGA operator and IOWHA operator
5 Applicability Assessment
An applicability assessment is performed for the combinedforecasting models based on the IOWA operator IOWGAoperator and IOWHA operator
51 Cross-Validation 9eory Since there are a total of 18working conditions in this test each working conditionhas a corresponding set of actual values and detectedvalues obtained by stress wave and drilling resistance tests(see Table 2) Because of the small number of data samplesand each combined forecasting model is tested only oncethe randomness is large which does not prove that theabove optimal models have good universality In order tomake full use of the data samples a cross-validationmethod is applied to carry out the test +e researchprocess is shown in Figure 12
Firstly by setting random samples we randomlyextracted N (N 5 6 17) working conditions from 18working conditions as a training set (IN) and then thecorresponding remaining 18minusN working conditions areconsidered as a testing set (IN) For the number (N) ofrandomly selected samples there are CN
18 subsets for both thetraining set and the testing set (see Table 6) For example ifN 5 both the training set (I5) and the testing set (I5) willhave 8568 subsets
Table 3 Results of each combined forecasting model
If I5 working condition 1 working condition 2working condition 3 working condition 4 working con-dition 5 then I5 working condition 6 working condi-tion 7 working condition 8 working condition 9 workingcondition 10 working condition 11 working condition 12working condition 13 working condition 14 workingcondition 15 working condition 16 working condition17
By analogy we can get 8568 subsets for the training set(I5) and the testing set (I5)
Secondly based on random sample data in each trainingset (IN) three combined forecasting models based on theIOWA operator IOWGA operator and IOWHA operatorare established to solve three sets of corresponding optimalweights Based on the cross-validation method three sets ofweights are substituted into the corresponding testing set(IN) For the training set and testing set we can get thecomprehensive evaluation index C corresponding to eachcombined forecasting model using equation (12)
Finally we calculate the mean value (EC) and variance(VC) of the comprehensive evaluation index C +rough thestatistical analysis of the change law of the mean value (EC)and variance (VC) the universality of the optimal combinedforecasting model is judged
52 Cross-Validation Result Analysis +e mean value (EC)and the variance (VC) of the comprehensive evaluationindexes are evaluated by each combined forecasting modelin the training sets (see Table 7)
In Table 7 we find that EC-IOWA of each training set has asignificantly higher value compared to EC-IOWGA and EC-IOWHA+e higher the EC is the better the overall forecasting precisionis +e alignment of the variance of the comprehensive evalu-ation indexes is VC-IOWAltVC-IOWGAltVC-IOWHA +e smallerthe VC is the smaller the dispersion of the C value is and themore stable the data change is+is indicates that the combinedforecasting model based on the IOWA operator is wellapplicable
In Figure 13 the distribution maps of EC and VC corre-sponding to each training set show a roughly linear changingtrend When the sample data in the training set (IN) increaseEC-IOWA and EC-IOWH increase and EC-IOWGA decreases Withthe increase of the number of sample data in the training setsthe VC of the three combined forecasting models decreasesBut the change of VC-IOWA is smallest indicating that the Cdoes not fluctuate much and the data are very stable
Based on the cross-validation theory the optimalweights obtained by each training set are brought into thecorresponding testing set EC and VC of the testing sets arelisted in Table 8 and the distribution maps of EC and VCcalculated by each testing set are shown in Figure 14
In Table 8 EC-IOWA of testing sets is significantlyhigher than EC-IOWGA and EC-IOWHA while VC-IOWA issignificantly lower than VC-IOWGA and VC-IOWHA How-ever it is noted the values of EC-IOWGA and EC-IOWHA orVC-IOWGA and VC-IOWHA are very close to each otherMeanwhile it is found from Figure 14 that EC corre-sponding to each testing set decreases with the decrease ofthe sample number in the testing sets Contrarily VCincreases with the decrease of the sample number in thetesting sets +e distribution map of VC-IOWA has littlechange in slope meaning the corresponding C value ismore stable +e results show that the combined fore-casting model based on the IOWA operator has thehighest overall forecasting precision and best level ofapplicability among the three models
6 Nondestructive Tests for Double-CiroldLongevity Pavilion
Double-Cirold Longevity Pavilion is located in the BeijingTiantan Park It was built in the Middle Qing Dynasty andhas a history of 277 years Double-Cirold Longevity Pavilionis a combination of two round pavilions with double eavesand spires Its structure is peculiar and precise and its shapeis novel and well proportioned +is kind of pavilion hashigh scientific artistic and cultural value in the Chinesetimber structure Affected by the natural environment andhuman factors all year round timber components aredamaged Eventually it leads to the loss of the externalprotective layer for timber components and the accelerationof the internal and external damage of timber components
Nondestructive tests of timber components of thedouble-ring marsupial pavilion were performed by stresswave and drilling resistance (see Figure 15) It was found thatthe beams and the columns had internal defects +e B2column of Double-Cirold Longevity Pavilion is an examplewith a moisture content of 98 +e perimeter of thewooden column is 1099 cm and the detected section area is96163 cm2 According to the two-dimensional image ob-tained by the stress wave tests the internal defects werelocated Drilling resistance tests were conducted pertinently+ere were two detected paths in drilling resistance tests andeach path passed through the location of defects
+rough nondestructive tests it was found that there wasan uncompacted sound when knocking the position of theB2 column 400mm from the ground A certain degree ofdefect is found in the interior wood by the stress wave tests(see Figure 16) +e damaged area detected by the stresswave tests accounts for 18 of the detected section and thedamaged area is 17309 cm2 +e drilling resistance testsshow the damaged area is 49 cm2 +e damaged area of theB2 column calculated by the combined forecasting model
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
If I5 working condition 1 working condition 2working condition 3 working condition 4 working con-dition 5 then I5 working condition 6 working condi-tion 7 working condition 8 working condition 9 workingcondition 10 working condition 11 working condition 12working condition 13 working condition 14 workingcondition 15 working condition 16 working condition17
By analogy we can get 8568 subsets for the training set(I5) and the testing set (I5)
Secondly based on random sample data in each trainingset (IN) three combined forecasting models based on theIOWA operator IOWGA operator and IOWHA operatorare established to solve three sets of corresponding optimalweights Based on the cross-validation method three sets ofweights are substituted into the corresponding testing set(IN) For the training set and testing set we can get thecomprehensive evaluation index C corresponding to eachcombined forecasting model using equation (12)
Finally we calculate the mean value (EC) and variance(VC) of the comprehensive evaluation index C +rough thestatistical analysis of the change law of the mean value (EC)and variance (VC) the universality of the optimal combinedforecasting model is judged
52 Cross-Validation Result Analysis +e mean value (EC)and the variance (VC) of the comprehensive evaluationindexes are evaluated by each combined forecasting modelin the training sets (see Table 7)
In Table 7 we find that EC-IOWA of each training set has asignificantly higher value compared to EC-IOWGA and EC-IOWHA+e higher the EC is the better the overall forecasting precisionis +e alignment of the variance of the comprehensive evalu-ation indexes is VC-IOWAltVC-IOWGAltVC-IOWHA +e smallerthe VC is the smaller the dispersion of the C value is and themore stable the data change is+is indicates that the combinedforecasting model based on the IOWA operator is wellapplicable
In Figure 13 the distribution maps of EC and VC corre-sponding to each training set show a roughly linear changingtrend When the sample data in the training set (IN) increaseEC-IOWA and EC-IOWH increase and EC-IOWGA decreases Withthe increase of the number of sample data in the training setsthe VC of the three combined forecasting models decreasesBut the change of VC-IOWA is smallest indicating that the Cdoes not fluctuate much and the data are very stable
Based on the cross-validation theory the optimalweights obtained by each training set are brought into thecorresponding testing set EC and VC of the testing sets arelisted in Table 8 and the distribution maps of EC and VCcalculated by each testing set are shown in Figure 14
In Table 8 EC-IOWA of testing sets is significantlyhigher than EC-IOWGA and EC-IOWHA while VC-IOWA issignificantly lower than VC-IOWGA and VC-IOWHA How-ever it is noted the values of EC-IOWGA and EC-IOWHA orVC-IOWGA and VC-IOWHA are very close to each otherMeanwhile it is found from Figure 14 that EC corre-sponding to each testing set decreases with the decrease ofthe sample number in the testing sets Contrarily VCincreases with the decrease of the sample number in thetesting sets +e distribution map of VC-IOWA has littlechange in slope meaning the corresponding C value ismore stable +e results show that the combined fore-casting model based on the IOWA operator has thehighest overall forecasting precision and best level ofapplicability among the three models
6 Nondestructive Tests for Double-CiroldLongevity Pavilion
Double-Cirold Longevity Pavilion is located in the BeijingTiantan Park It was built in the Middle Qing Dynasty andhas a history of 277 years Double-Cirold Longevity Pavilionis a combination of two round pavilions with double eavesand spires Its structure is peculiar and precise and its shapeis novel and well proportioned +is kind of pavilion hashigh scientific artistic and cultural value in the Chinesetimber structure Affected by the natural environment andhuman factors all year round timber components aredamaged Eventually it leads to the loss of the externalprotective layer for timber components and the accelerationof the internal and external damage of timber components
Nondestructive tests of timber components of thedouble-ring marsupial pavilion were performed by stresswave and drilling resistance (see Figure 15) It was found thatthe beams and the columns had internal defects +e B2column of Double-Cirold Longevity Pavilion is an examplewith a moisture content of 98 +e perimeter of thewooden column is 1099 cm and the detected section area is96163 cm2 According to the two-dimensional image ob-tained by the stress wave tests the internal defects werelocated Drilling resistance tests were conducted pertinently+ere were two detected paths in drilling resistance tests andeach path passed through the location of defects
+rough nondestructive tests it was found that there wasan uncompacted sound when knocking the position of theB2 column 400mm from the ground A certain degree ofdefect is found in the interior wood by the stress wave tests(see Figure 16) +e damaged area detected by the stresswave tests accounts for 18 of the detected section and thedamaged area is 17309 cm2 +e drilling resistance testsshow the damaged area is 49 cm2 +e damaged area of theB2 column calculated by the combined forecasting model
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
If I5 working condition 1 working condition 2working condition 3 working condition 4 working con-dition 5 then I5 working condition 6 working condi-tion 7 working condition 8 working condition 9 workingcondition 10 working condition 11 working condition 12working condition 13 working condition 14 workingcondition 15 working condition 16 working condition17
By analogy we can get 8568 subsets for the training set(I5) and the testing set (I5)
Secondly based on random sample data in each trainingset (IN) three combined forecasting models based on theIOWA operator IOWGA operator and IOWHA operatorare established to solve three sets of corresponding optimalweights Based on the cross-validation method three sets ofweights are substituted into the corresponding testing set(IN) For the training set and testing set we can get thecomprehensive evaluation index C corresponding to eachcombined forecasting model using equation (12)
Finally we calculate the mean value (EC) and variance(VC) of the comprehensive evaluation index C +rough thestatistical analysis of the change law of the mean value (EC)and variance (VC) the universality of the optimal combinedforecasting model is judged
52 Cross-Validation Result Analysis +e mean value (EC)and the variance (VC) of the comprehensive evaluationindexes are evaluated by each combined forecasting modelin the training sets (see Table 7)
In Table 7 we find that EC-IOWA of each training set has asignificantly higher value compared to EC-IOWGA and EC-IOWHA+e higher the EC is the better the overall forecasting precisionis +e alignment of the variance of the comprehensive evalu-ation indexes is VC-IOWAltVC-IOWGAltVC-IOWHA +e smallerthe VC is the smaller the dispersion of the C value is and themore stable the data change is+is indicates that the combinedforecasting model based on the IOWA operator is wellapplicable
In Figure 13 the distribution maps of EC and VC corre-sponding to each training set show a roughly linear changingtrend When the sample data in the training set (IN) increaseEC-IOWA and EC-IOWH increase and EC-IOWGA decreases Withthe increase of the number of sample data in the training setsthe VC of the three combined forecasting models decreasesBut the change of VC-IOWA is smallest indicating that the Cdoes not fluctuate much and the data are very stable
Based on the cross-validation theory the optimalweights obtained by each training set are brought into thecorresponding testing set EC and VC of the testing sets arelisted in Table 8 and the distribution maps of EC and VCcalculated by each testing set are shown in Figure 14
In Table 8 EC-IOWA of testing sets is significantlyhigher than EC-IOWGA and EC-IOWHA while VC-IOWA issignificantly lower than VC-IOWGA and VC-IOWHA How-ever it is noted the values of EC-IOWGA and EC-IOWHA orVC-IOWGA and VC-IOWHA are very close to each otherMeanwhile it is found from Figure 14 that EC corre-sponding to each testing set decreases with the decrease ofthe sample number in the testing sets Contrarily VCincreases with the decrease of the sample number in thetesting sets +e distribution map of VC-IOWA has littlechange in slope meaning the corresponding C value ismore stable +e results show that the combined fore-casting model based on the IOWA operator has thehighest overall forecasting precision and best level ofapplicability among the three models
6 Nondestructive Tests for Double-CiroldLongevity Pavilion
Double-Cirold Longevity Pavilion is located in the BeijingTiantan Park It was built in the Middle Qing Dynasty andhas a history of 277 years Double-Cirold Longevity Pavilionis a combination of two round pavilions with double eavesand spires Its structure is peculiar and precise and its shapeis novel and well proportioned +is kind of pavilion hashigh scientific artistic and cultural value in the Chinesetimber structure Affected by the natural environment andhuman factors all year round timber components aredamaged Eventually it leads to the loss of the externalprotective layer for timber components and the accelerationof the internal and external damage of timber components
Nondestructive tests of timber components of thedouble-ring marsupial pavilion were performed by stresswave and drilling resistance (see Figure 15) It was found thatthe beams and the columns had internal defects +e B2column of Double-Cirold Longevity Pavilion is an examplewith a moisture content of 98 +e perimeter of thewooden column is 1099 cm and the detected section area is96163 cm2 According to the two-dimensional image ob-tained by the stress wave tests the internal defects werelocated Drilling resistance tests were conducted pertinently+ere were two detected paths in drilling resistance tests andeach path passed through the location of defects
+rough nondestructive tests it was found that there wasan uncompacted sound when knocking the position of theB2 column 400mm from the ground A certain degree ofdefect is found in the interior wood by the stress wave tests(see Figure 16) +e damaged area detected by the stresswave tests accounts for 18 of the detected section and thedamaged area is 17309 cm2 +e drilling resistance testsshow the damaged area is 49 cm2 +e damaged area of theB2 column calculated by the combined forecasting model
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
70
75
80
85
90
95
100
EC-IOWA VC-IOWAEC-IOWGA VC-IOWGAEC-IOWHA VC-IOWHA
E C (
)
Testing set
000
002
004
006
008
010
V C
ndashI5ndashI6
ndashI7ndashI8
ndashI9ndashI10
ndashI11ndashI12
ndashI13ndashI14
ndashI15ndashI16
ndashI17
Figure 14 Curves of EC and VC of testing sets
(a) (b) (c)
Figure 15 Nondestructive tests of the B2 column (a) Double-Cirold Longevity Pavilion (b) stress wave (c) drilling resistance
Decayed
Intact
Hollow
30
20
10
0
30
30
20
20
10
100
0
3020100
(cm
)
(cm)
(cm)
(cm
)
1
2
3
4
5
6
7
8
9
10
(a)
Figure 16 Continued
Advances in Civil Engineering 15
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
based on the IOWA operator is 8747 cm2 It is found thatthe B2 column is defective and the wooden column needs tobe repaired
7 Conclusion
(1) When used alone both the stress wave and drillingresistance tests have their own advantages and dis-advantages +rough analysis it is found that thestress wave image and the resistance curve have goodcorrespondence in this test which can make up fortheir respective shortcomings Stress wave anddrilling resistance tests can be used together toqualitatively analyze the internal damage of the woodstructure
(2) Weighing test results of the stress wave and drillingresistance and establishing a combined forecastingmodel can quantify the test results Comparedwith thecombined forecasting models based on the entropyvalue and Shapley value the combined forecastingmodels based on the IOWA operator IOWGA op-erator and IOWHA operator have better forecastingeffects according to the idea of variable weight notonly greatly reducing the sensitivity of the results topoor detection methods but also effectively improvingthe forecasting precision of internal damage of timbercomponents in ancient buildings When the internaldamage of the wood specimen is small the methodproposed in this paper is more effective in improvingthe precision of stress wave detection
(3) +e mean precision and mean absolute error calcu-lated by the combined forecasting model based on theIOWA operator are 917 and 342 cm2 +e meanprecision is improved by 258 and 47 compared tothe stress wave and drilling resistance tests In additionCIOWA is 972 and the overall forecasting effect of thecombined forecasting model based on the IOWAoperator is the best of all +e analysis results based onthe cross-validation theory show that the combinedforecastingmodel based on the IOWAoperator has theoptimal performance and good applicability +e
model can quickly and accurately analyze and judgethe internal damage of timber components in ancientbuildings qualitatively and quantitatively
Data Availability
+e data used to support the findings of this study areavailable from the corresponding author upon request
Conflicts of Interest
+e authors declare that they have no conflicts of interest
Acknowledgments
+is study was financially supported by the National KeyRampD Program of China (grant no 2018YFD1100902-01)the National Natural Science Foundation of China (grantnos 51678017 and 51678005) Beijing Municipal EducationCommission Science and Technology General Project (grantno KM201810005021) Beijing Natural Science FoundationProject (8182008) and the Open Fund of Shanghai KeyLaboratory of Engineering Structure Safety (no 2017-KF03)
References
[1] C Calderoni G De Matteis C Giubileo andF M Mazzolani ldquoExperimental correlations between de-structive and non-destructive tests on ancient timber ele-mentsrdquo Engineering Structures vol 32 no 2 pp 442ndash4482010
[2] M Riggio RW Anthony F Augelli et al ldquoIn situ assessmentof structural timber using non-destructive techniquesrdquo Ma-terials and Structures vol 47 no 5 pp 749ndash766 2014
[3] S Rust and L Gocke ldquoA new tomographic device for the non-destructive testing of standing treerdquo in Proceedings of the 12thInternational Symposium on Nondestructive Testing of WoodUniversity of Western Hungary Sopron Hungary September2000
[4] X Li J DaiW Qian and L-H Chang ldquoPrediction of internaldefect area in wooden components by stress wave velocityanalysisrdquo Bioresources vol 10 no 3 pp 4167ndash4177 2015
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
[5] U Dackermann K Crews B Kasal et al ldquoIn situ assessmentof structural timber using stress-wave measurementsrdquo Ma-terials and Structures vol 47 no 5 pp 787ndash803 2014
[6] T Lechner Y Sandin and R Kliger ldquoAssessment of densityin timber using X-Ray equipmentrdquo International Journal ofArchitectural Heritage vol 7 no 4 pp 416ndash433 2013
[7] S Franke B Franke and F Scharmacher ldquoAssessment oftimber structures using the X-ray technologyrdquo in Procedingsof the 2nd International Conference on Structural HealthAssessment of Timber Structures (SHATIS 2013) Trento ItalySeptember 2013
[8] M Riggio J Sandak and S Franke ldquoApplication of imagingtechniques for detection of defects damage and decay intimber structures on-siterdquo Construction and Building Mate-rials vol 101 no 2 pp 1241ndash1252 2015
[9] F Isik and B Li ldquoRapid assessment of wood density of livetrees using the resistograph for selection in tree improvementprogramsrdquo Canadian Journal of Forest Research vol 33no 12 pp 2426ndash2435 2003
[10] B Kasal and RW Anthony ldquoAdvances inin situ evaluation oftimber structuresrdquo Progress in Structural Engineering andMaterials vol 6 no 2 pp 94ndash103 2004
[11] T P Nowak J Jasienko and K Hamrol-Bielecka ldquoIn situassessment of structural timber using the resistance drillingmethodmdashevaluation of usefulnessrdquo Construction and Build-ing Materials vol 102 no 1 pp 403ndash415 2016
[12] L Espinosa F Prieto L Brancheriau and P LasayguesldquoEffect of wood anisotropy in ultrasonic wave propagation aray-tracing approachrdquo Ultrasonics vol 91 pp 242ndash251 2019
[13] D A Gatto M R F Goncalves B D Mattos L Calegari andD M Stangerlin ldquoEstimativa da deterioraccedilatildeo da madeira deassoalho de predio historico por meio de ondas ultrassonicasrdquoCerne vol 18 no 4 pp 651ndash656 2012
[14] K J Vossing M Gaal and E Niederleithinger ldquoAir-coupledferroelectret ultrasonic transducers for nondestructive testingof wood-based materialsrdquo Wood Science and Technologyvol 52 no 6 pp 1527ndash1538 2018
[15] X Q Yue L H Wang A P Wacker and Z M Zhu ldquoElectricresistance tomography and stress wave tomography for decaydetection in trees-a comparison studyrdquo PeerJ vol 7 articlee6444 2019
[16] Z X Liu X H Di L H Wang and T Y Sun ldquoEffect ofdifferent detection angle on propagation velocity of stresswave in health standing treesrdquo Journal of North-East ForestryUniversity vol 42 no 4 pp 105ndash108 2014
[17] X Guan M-C Zhao Z Wang W-L Sha and Z-R ZhouldquoStudy of stress wave speed and elastic modulus measurementof poplar log base on longitudinal resonancerdquo Journal of WestChina Forestry Science vol 42 no 2 pp 14ndash19 2013
[18] G Li X Weng X Du X Wang and H Feng ldquoStress wavevelocity patterns in the longitudinal-radial plane of trees fordefect diagnosisrdquo Computers and Electronics in Agriculturevol 124 pp 23ndash28 2016
[19] E Guntekin Z G Emiroglu and T Yilmaz ldquoPrediction ofbending properties for Turkish red pine (Pinus brutia Ten)lumber using stress wave methodrdquo Bioresources vol 8 no 1pp 231ndash237 2013
[20] T Y Sun and L H Wang ldquoNon-destructive testing of loginternal decay based on two-dimensional CT images of stresswave and X-ray testingrdquo Forest Engineering vol 27 no 6pp 26ndash29 2011
[21] Q Wei B Leblon and A La Rocque ldquoOn the use of X-raycomputed tomography for determining wood properties areview1+is article is a contribution to the series the role of
sensors in the new forest products industry and bioeconomyrdquoCanadian Journal of Forest Research vol 41 no 11pp 2120ndash2140 2011
[22] L P Perlin A D Valle and R C de Andrade Pinto ldquoNewmethod to locate the pith position in a wood cross-sectionbased on ultrasonic measurementsrdquo Construction andBuilding Materials vol 169 pp 733ndash739 2018
[23] T-Y Yu B Boyaci and H F Wu ldquoSimulated transientelectromagnetic response for the inspection of GFRP-wrap-ped concrete cylinders using radar NDErdquo Research in Non-destructive Evaluation vol 24 no 3 pp 125ndash153 2013
[24] L H Chang W Qian and J Dai ldquoCombination forecastingresearch on timber building internal defectsrdquo Journal ofSimulation Systems Science and Technology vol 17 no 25pp 1473ndash8031 2016
[25] Y An Y F Yin X M Jiang and Y C Zhou ldquoInspection ofdecay distribution in wood column by stress wave andresistograph techniquesrdquo Journal of Building Materialsvol 11 no 4 pp 457ndash463 2008
[26] L H Chang X H Chang H Chnag W Qian L T Chengand X L Han ldquoNondestructive testing on ancient woodencomponents based on Shapley valuerdquo Advances in MaterialsScience and Engineering vol 2019 Article ID 803973411 pages 2019
[27] W Qian J Dai X Li and L H Chang ldquo+e systematicapplication of non-destructive testing techniques for ancientwood buildingsrdquo in Proceedings of the 4th InternationalConference on Civil Engineering and Building Materials(CEBM) Hong Kong China November 2014
[28] X W Ge L H Wang T Y Sun et al ldquoQuantitative detectionof salix matsudana inner decay based on stress wave andresistograph techniquesrdquo China Forestry Science and Tech-nology vol 28 no 5 pp 87ndash91 2014
[29] X P Wang and R B Allison ldquoDecay detection in red oaktrees using a combination of visual inspection acoustictesting and resistance microdrillingrdquo Arboriculture amp UrbanForestry vol 34 no 1 pp 1ndash4 2008
[30] S-T Chuang and S-Y Wang ldquoEvaluation of standing treequality of Japanese cedar grown with different spacing usingstress-wave and ultrasonic-wave methodsrdquo Journal of WoodScience vol 47 no 4 pp 245ndash253 2001
[31] C Rabe D Ferner S Fink and F W M R SchwarzeldquoDetection of decay in trees with stress waves and in-terpretation of acoustic tomogramsrdquo Arboricultural Journalvol 28 no 1-2 pp 3ndash19 2004
[32] J M Bates and C W J Granger ldquo+e combination offorecastsrdquo OR vol 20 no 4 pp 451ndash468 1969
[33] R R Yager ldquoInduced aggregation operatorsrdquo Fuzzy Sets andSystems vol 137 no 1 pp 59ndash69 2003
[34] H Y Chen and C L Liu ldquoA kind of combination forecastingmethod baesd on induced ordered weighted averaging(IOWA) operatorsrdquo Forecasting vol 22 no 6 pp 61ndash652003
[35] M Aggarwal ldquoA new family of induced OWA operatorsrdquoInternational Journal of Intelligent Systems vol 30 no 2pp 170ndash205 2015
[36] H Y Chen and Z H Sheng ldquoA kind of new combinationforecasting method based on induced ordered weightedgeometric averaging (IOWGA) operatorrdquo Journal of In-dustrial Engineering and Engineering Management vol 19no 4 pp 36ndash39 2005
[37] J W Yang D S Shao Z M Wang et al ldquoA new method ofvariable weight combination forecasting based on entropy
Advances in Civil Engineering 17
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
weight and IOWGA operatorrdquo Journal of Geodesy andGeodynamics vol 37 no 12 pp 1243ndash1247 2017
[38] H Y Chen C L Liu and Z H Sheng ldquoInduced orderedweighted harmonic averaging (IOWHA) operator and itsapplication to combination forecasting methodrdquo ChineseJournal of Management Science vol 12 no 5 pp 35ndash40 2004
[39] J Z Zhao T X Xu H J Li and W Ye ldquoConsumptionforecast of missile spare parts based on improved theil co-efficientrdquo Systems Engineering amp Electronics vol 35 no 8pp 1681ndash1686 2013
[40] H Li D Chen E Arzaghi et al ldquoSafety assessment of hydro-generating units using experiments and grey-entropy corre-lation analysisrdquo Energy vol 165 pp 222ndash234 2018
[41] S Huang B Ming Q Huang G Leng and B Hou ldquoA casestudy on a combination NDVI forecasting model based on theentropy weight methodrdquo Water Resources Managementvol 31 no 11 pp 3667ndash3681 2017
[42] L H Chang J Dai and W Qian ldquoNondestructive testing ofinternal defect of ancient architecture wood members basedon Shapley valuerdquo Journal of Beijing University of Technologyvol 42 no 6 pp 886ndash892 2016
[43] Y Tang Q Xu B Ke et al ldquoStudy on optimization of SVMmodel of rock blasting fragmentation based on cross-vali-dationrdquo Blasting vol 35 no 3 pp 74ndash79 2018
[44] F G R de Oliveira M Candian F F Lucchette J LuisSalgon and A Sales ldquoA technical note on the relationshipbetween ultrasonic velocity and moisture content of Brazilianhardwood (Goupia glabra)rdquo Building and Environmentvol 40 no 2 pp 297ndash300 2005
[45] H Liu and J M Gao ldquoEffects of moisture content and densityon the stress wave velocity in woodrdquo Journal of BeijingForestry University vol 36 no 6 pp 154ndash158 2014
[46] MOHURD GBT50329-2012 ldquoStandard for design of timberstructuresrdquo Tech Rep China Architecture Building PressBeijing China 2017
[47] MOHURD GBT50329-2012 ldquoStandard for test methods oftimber structuresrdquo Tech Rep China Architecture BuildingPress Beijing China 2012
[48] J Jasienko T Nowak and K Hamrol ldquoSelected methods ofdiagnosis of historic timber structures-principles and possi-bilities of assessmentrdquo in Proceedings of the 2nd InternationalConference on Structural Health Assessment of TimberStructures (SHATIS) Trento Italy September 2014
[49] J M Branco M Piazza and P J S Cruz ldquoStructural analysisof two king-post timber trusses non-destructive evaluationand load-carrying testsrdquo Construction and Building Materialsvol 24 no 3 pp 371ndash383 2010
[50] R R Yager ldquoFamily of OWA operatorsrdquo Fuzzy Sets andSystems vol 59 no 2 pp 125ndash148 1993
[51] Z S Xu and Q L Da ldquo+e ordered weighted geometricaveraging operatorsrdquo International Journal of IntelligentSystems vol 17 no 7 pp 709ndash716 2002
![Prediction of impact damage in composite plates · The Chang–Chang failure criteria [1] and DYNA3D are widely used for the prediction of impact damage in composites [2–5]. Hallett](https://static.documents.pub/doc/80x56/5e95c9720f078278e263fb0c/prediction-of-impact-damage-in-composite-plates-the-changachang-failure-criteria.jpg)