An experimental study on distributed damage detection algorithms

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An experimental study on distributed damagedetection algorithms for structural healthmonitoringTo cite this article Madhuka Jayawardhana et al 2011 J Phys Conf Ser 305 012068

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An experimental study on distributed damage

detection algorithms for structural health monitoring

Madhuka Jayawardhana Xinqun Zhu and Ranjith LiyanapathiranaSchool of Engineering University of Western Sydney Penrith South DC NSW 1797 Australia

E-mail mjayawardhanauwseduau xinqunzhuuwseduau ranjithieeeorg

Abstract Distributed structural damage detection has become the subject of many recentstudies in Structural Health Monitoring (SHM) Development of smart sensor nodes hasfacilitated the growth of this concept enabling decentralized data processing capabilities ofnodes whose sole responsibility once was acquisition of data An experimental study has beencarried out on a two span reinforced concrete slab in this paper Different crack damages arecreated by the static loads and the impact tests that are carried out on the slab Two damagedetection and localization methods one based on Auto Correlation Function-Cross CorrelationFunction (ACF-CCF) and the other on Auto Regressive (AR) time series model are used todetect damage from measured responses The results from the two methods are compared inorder to determine which method has been more effective and reliable in determining the damageto the concrete structure

1 IntroductionWith the advancements of wireless communication technologies and smart devices structuralhealth monitoring is no longer a concept limited only to theory and research WirelessSensor Networks (WSNs) have made the deployment of SHM systems practically realisable andmanageable These actual applications have brought the attention of engineers and researchersto many new areas and issues related to SHM Distributed structural damage detection is onesuch new area with high potential for development In the light of development of sensor nodes asintelligent devices distributed computing strategy for structural damage detection has proved tosignificantly reduce the power consumption of the system while giving more robust and accurateresults with increased efficiency

Several Time-Series based methods are available in the literature for SHM Many of these areprimarily based on the Auto Regressive (AR) model AR (Sohn et al 2000 Fugate et al 2001)AR-ARX (Auto Regressive with exogenous input) (Sohn and Farrar 2001 Lynch et al 2003Lynch et al 2004 Lei et al 2003) and ARMA (Auto Regressive Moving Average) (Nair et al2005) are some The main concept behind these methods is that if the structure is damagedthe prediction model developed from the undamaged response data time series will not be ableto reproduce the new data series obtained from the unknown state of the structure Time-seriescomputations can be time consuming and complex in implementation

The Damage Location Assurance Criterion (DLAC) (Messina et al 1998 Clayton et al2005) is a correlation based method which uses modal frequencies It correlates modal frequencychange caused by possible structural damages between the actual structural response data andthose synthesized from an analytical model of the structure to identify and localize damage

9th International Conference on Damage Assessment of Structures (DAMAS 2011) IOP PublishingJournal of Physics Conference Series 305 (2011) 012068 doi1010881742-65963051012068

Published under licence by IOP Publishing Ltd 1

Although it is energy efficient relying on structural model is an undesirable property in thismethod as accurate models of actual complex structures can be extremely difficult to produce

In this study a correlation based method and a statistical time-series method have beentested on actual structural response data obtained by a series of tests carried out on a two-spanreinforced slab structure The correlation based approach called ACF-CCF method (Liu et al2009) is a recently developed method The AR-ARX time-series approach (Sohn and Farrar2001 Lynch et al 2003 Lynch et al 2004 Lei et al 2003) has been used for detecting damageand localizing for some time now In the remainder of this paper we will first be discussingthe implementation of the two algorithms in detail and the experimental set up used to obtainthe structural data We will then present the damage detection results obtained through theimplementation of both algorithms and compare their accuracy

2 Damage detection algorithms21 ACF-CCF methodThis damage detection and identification method uses the autocorrelation function (ACF) ofthe measured signal of each node to detect damage and the cross-correlation function (CCF)of node pairs to locate damage It is based on the premise that if the structure is damagedthere would be a difference in the ACFCCF coefficients of reference and damaged structuresThe choice of ACFCCF has been due to its sensitivity to damage and its robustness to inputand environmental changes The functionality of this strategy has two levels In the first levelthe damage detection takes place This is carried out in each sensor node independently Thesecond level is carried out only if damage is detected In this level the sensor nodes work in pairsto perform damage localization To determine if the ACFCCF coefficients calculated from newdata are statistically different from reference ACFCCF data the X-bar control chart method(Montgomery 1996) is used in this algorithm The implementation of the ACF-CCF method isdone in two stages The Offline (Initialization) stage and the Online stage

Offline stage This stage initializes the algorithm by setting up references to which the onlinedata can be compared with The data for this stage has to be obtained when the structure is ina healthy state

(i) Data collected from the healthy structure subjected to various environmental conditions is

standardized as xi =ximinusmicroxiσxi

where microxi and σxi are the mean and the standard deviation of

the ith sample of reference data respectivelyHereafter xi will be represented by xi for convenience

(ii) Reference ACF is calculated with standardized data

ACF xi (m) =Mminusmsumn=1

xi(n) lowast xi(n+m) (1)

where M is the length of xi and m = 0 1 M minus 1

(iii) Novelty Index (NIx) is calculated using ACF xi and its mean macrACFx

NIxi = 1minus corrcoef(ACF xi macrACF

x) (2)

where corrcoef(x y) =

sumM

k=1(x(k)minusmicrox)(y(k)minusmicroy)xminusmicroxyminusmicroy

(iv) Upper-Control-Limit (UCLx) and Lower-Control-Limit (LCLx)are calculated

UCLx = microNIx + γσNIx amp LCLx = microNIx minus γσNIx (3)

where microNIx σNIx are the mean and standard deviation of NIx and γ = 3 is chosencorresponding to an interval of 997 confidence in a normal distribution


2

(v) X-bar control chart (Montgomery 1996) of Novelty Index with UCLx and LCLx is drawn

The above reference database is established for each sensor node initialization This can becalculated offline and stored in each node

Similarly reference CCF database is calculated for each node pair but using the two setsof measured reference data from the two nodes in the pair The two nodes in each pair aredesignated one as master node and the other as slave nodeOnline stage In this stage the current data (Y ) of the structures that are in use are measuredand the Novelty Index (NIy) is calculated similar to the reference stage but with current dataUsing UCLx and LCLx it is determined if the ACF y is different from ACF x That is if NIy

exceeds UCLx it is called an outlier and damage is detected To decrease the rate of false alarmsit is defined that unless three consecutive data sets indicate damage as per above damage is notdetected

In the case of damage the CCF y is calculated between the node pair on which the damageindication is givenThe master node of the pair is in charge of this calculation Synchronizationbetween the nodes of a pair has to be carried out prior to calculating the CCF y The statisticaldifference between the CCF x and CCF y is determined similarly as the ACF comparison Withthese results the master node is able to determine in which area the damage has occurred (Liuet al 2009)

22 AR-ARX MethodAuto Regressive-Auto-Regressive with exogenous input(AR-ARX) is a statistical time seriesapproach for detection and localization of damage It is based on the premise that the statisticalprediction model developed from the time series measurement data of the undamaged (reference)data would not be able to reproduce or predict the newly obtained time series if the currentstructure is damaged The prediction model used here is the Auto Regressive (AR) model Inthe second part of the algorithm the same model is used with an exogenous input for reasonsthat will be discussed subsequently The algorithm is described as follows

(i) The collected undamaged structural response data is normalized at each node Assumingthat this response is stationary an AR model is fitted to these data

xk =psumi=1

φxi xkminusi + exk (4)

where p is the order of the model and xkminusi stands for the p previous responses φxi are theAR coefficients of the previous responses and exk is the residual error which is the DamageSensitive Feature (DSF) in this caseThe residual error of an AR model is influenced by the operational variability of thestructure causing inaccuracies in damage detection Therefore in order to avoid the effect ofoperational variability and to obtain the residual error resulting from the structural damagean AR model with exogenous input (ARX) is introduced

(ii) In ARX the relationship between the measured response xk and the AR model residualerror exk is computed

xk =asumi=1

αixkminusi +bsum

j=1

βjexkminusj + εxk (5)

where a and b are model orders and εxk is the residual error after fitting the ARX(ab)which is the new DSF unaffected by operational state αi and βj are the coefficients ofpast measurements and the residual error of past measurements respectively The AR andARX model orders p a and b are determined by exploring the autocorrelation function ofthe model residual errors (Sohn et al 2001 Lynch et al 2003)


3

(iii) The structural response data in the unknown state is collected normalized and fit to anAR model with order p similarly as above

yk =psumi=1

φyi ykminusi + eyk (6)

(iv) The signal segment xk from the reference database which is closest to the new signal yk ischosen by minimizing the following difference of AR coefficients

Difference =psumi=1

(φxi minus φyi )

2 (7)

This is performed in order to select the reference signal which is recorded under operationalconditions closest to the newly obtained signal If there is no damage to the structureand the operational conditions are close the selected reference AR model will closelyapproximate the measured signal If there is damage even the closest AR model of thedatabase will not approximate the measured response

(v) Equation (5) is used to determine the residual error εyk of the ARX model of the new responseyk by substituting yk and the corresponding residual error eyk as follows

εyk = yk minusasumi=1

αiykminusi minusbsum

j=1

βjeykminusj (8)

(vi) The ratio of standard deviations of the residual errors of undamaged and unknown state ofthe structure is defined as the DSF This ratio is monitored for structural anomalies

DSF =σ(εy)

σ(εx)(9)

Another technique of detecting damage with the AR-ARX method is by testing the nullhypothesis H0 σ2(εx) = σ2(εy) against the one sided alternative H1 σ2(εx) lt σ2(εy) ofthe variance ratio σ2(εy)σ2(εx) which follows the F-distribution (Sohn and Farrar 2001)

F =σ2(εy)

σ2(εx)(10)

The Degree of Freedom (DOF) of this F-distribution are nxminus1 and nyminus1 where nx and nyare the numbers of samples of εx and εy respectivelyThe null hypothesis H0 is rejected whenthe F-statistic in equation (14) exceed the upper 100 lowast α percentile of the F-distribution

In standard deviation ratio DSF the ratio value reaches a maximum near the actual damagelocalization In the F-statistic technique the number of rejections of the null hypothesis is at amaximum near the damage location (Sohn and Farrar 2001 Lynch et al 2003 Lynch et al2004 Lei et al 2003)

3 Experimental set-upThese tests have been conducted on a two-span reinforced concrete slab of dimensions 6400 mm800 mm 100 mm The spans are 3000 mm with a 200 mm overhang at each end (Figure 1) Itwas supported by wooden planks placed over three steel UB sections

In the experiment the slab has been continuously loaded with an incremental load with thegoal of creating crack damage A four-point loading was used at the middle of each span as


4

Figure 1 Static load test carried out on the RC slab structure

Figure 2 Experimental set-up and sensor locations

shown in Figure 1 The loading system is also connected to the slab supports in order to reducethe effect of the system on the supports Twelve loading levels were performed on the structurewhile increasing the maximum loading level Table 1 gives the static loads on the two spansrecorded using two load cells while measuring the displacements and monitoring crack locationsand lengths The deflection under the static load was measured by four displacement transducerslocated at the middle of each span The dynamic loading test was conducted using a 54 kgimpact hammer and three sets of measurements with the nine accelerometers evenly distributedalong the slab in each set were obtained as dynamic responses The sensor and impact locationsare shown in Figure 2 Data of length 4096 has been acquired at a sampling rate of 500 Hz fromall the channels including the impulse load using a data acquisition system

Table 1 Loading stages and damage scenarios

Loading stage 1 2 3 4 5 6 7 8 9 10 11 12 13

P1(kN) 0 3 6 12 18 18 18 18 18 25 32 35 38P2(kN) 0 0 0 0 0 3 6 12 18 25 25 35 38

Damage No One Two Threescenario damage damage damage damage

zone zone zone zone


5

Figure 3 Damage detection of Set 2 sensors loading stage 3

4 Results and discussionThe ACF-CCF algorithm and the AR-ARX algorithm as described in section 2 were implementedin Matlab Actual structural response data obtained from the above set of tests was used asinput For convenience of illustration we present here the output resulting from only one set ofsensors from the above experimental set-up We have chosen the sensor set 2 which consists ofresponses from the nine sensors located in the center row of the structure (Figure 2) For eachcase the test is repeated six times resulting in six data sample sets

41 ACF-CCFFigure 3 shows the plots of NIs of each sensor in set 2 the undamaged structural data (referencedata) given in a continuous line and the unknown state of the structure-given in a dashed lineThe two horizontal dashed lines are the Upper Control Limit (UCL) and Lower Control Limit(LCL) computed from the reference NI data This plot is obtained from data of loading stage3 (Table 1) which is from the One damage zone In Figure 3 the NI values of Sensors 7 and 8are above the UCL which indicates potential damage in the structure Sensors being numberedfrom right to left along the length of the slab Sensors 7 and 8 are located in the middle areaof the left span From Figure 4 which shows the experimental records of crack patterns in thestructure it is apparent that the first damage zone is in the middle of left span which carriedthe only load at this stage

Figure 5 shows the localization results of the above damage scenario Although damagelocalization is performed only in the sensor pairs where at least one sensor has detected damagewe have displayed the data of all the sensor pairs for comparison purposes Since the sensorset is short of one to pair-off perfectly the eighth sensor is paired with both seventh and ninthsensors separately making 5 pairs of sensors Similar to Figure 3 the NIs of undamaged state ofall the sensor pairs in Figure 5 are quite similar to that of the reference state except for sensors7 and 8 Therefore we can conclude that the damage location is between sensors 7 and 8

The same applies to Figure 6 where damage is detected in sensors 2 6 7 and 8 This plot


6

Figure 4 Crack patterns for different damage zones from experimental records

Figure 5 Damage localization of Set 2 sensor pairs loading stage 3

resulted from loading stage 8 of Set 2 sensors Comparing with experimental records of Figure 4it can be explained that since stage 8 is in the Three damage zone damage occurs in the middleof both left and right spans as well as at the mid support of slab Damage indicated sensorsin the simulated results are in these areas of damage showing that the algorithm was able to


7


identify the three damages of the structureThe next online stage of the algorithm for loading stage 8 gives the damage localization plot

given in Figure 7 This plot shows that the online NIs of sensor pairs 1 and 2 3 and 4 7 and8 9 and 8 are above the UCL We can conclude from these results that damages exist betweensensors 1 and 2 3 and 4 7 8 and 9 According to the experimental records in Figure 4 we canverify that the results obtained above are quite accurate ACF-CCF results will be comparedwith AR-ARX results in section 43

42 AR-ARXTables 2 and 3 show the damage detection and localization results of the AR-ARX method Forillustration purposes only the results of 4 loading stages are presented The loading stages arechosen from each of the three damage zones and the undamaged case

The results in Table 2 do not show significant increases of the DSF except in the case ofThree damage zone That is according to experimental records as per Figure 4 the structureis damaged from One damage zone through to Three damage zone near sensors 7 8 and 9 Butin AR-ARX results of Table 2 no significant increase of the DSF can be noticed in either ofthose 3 sensors in One and Two damage zones In Three damage zone a noticeable increase hasoccurred In fact in the Three damage zone significant increases of DSF can be seen in sensors1 35 6 8 and 9 which correspond to the experimental records of three damage locations Butsuch an increase does not appear in other sensors

In Table 3 null hypothesis rejections out of the hypothesis tests performed illustrated Sincesix tests were performed in each loading case the number of hypothesis tests performed hereis also six Therefore in order to reject the null hypothesis in the final result at least threetests out of six has to be rejected In Table 3 the Three damage zone gives successful resultsrejecting null hypothesis in sensors 1 5 6 8 and 9 which matches with the experimental recordsgiving damage indication and location In Two damage zone of the table sensor 4 indicates


8


Table 2 Ratio of standard deviations (σ(εy)σ(εx))

Damage zones S1 S2 S3 S4 S5 S6 S7 S8 S9

None 09952 11143 11025 10859 10122 10473 10605 10616 10667One damage 07984 10217 09136 10803 1071 12543 09216 08936 08956Two damages 0814 09914 09573 1174 09159 11211 08778 08697 09059

Three damages 14728 1026 1234 07779 13457 14011 11664 12676 14437

damage matching the experimental records of middle damage area of the RC structure but failsto indicate the damage in sensors 7 8 or 9 There is a false indication of potential damage insensor 6 in One damage done From the results of Tables 2 and 3 we can conclude that thesecond DSF - the F-statistic has been more successful in detecting damage than the standarddeviation ratio used in our study

43 ACF-CCF vs AR-ARXIn our implementation of the two methods with the use of experimental data from the RCstructure the ACF-CCF method was successful in identifying and locating damage Identifyingand localizing of one damage and three damages were illustrated in the previous sections Evenin the Three damage zone case ACF-CCF was able to distinctly identify and localize damageBut in the AR-ARX implementation the results showed only some damage occurrences Inone occasion a false damage indication was given These shortcomings of the AR-ARX methodcould be a result of the low number of samples that we have used in this implementation asthe availability of samples in each test case was limited to six AR-ARX method has been used


9

Table 3 Null hypothesis test H0 σ2(εx) = σ2(εy) against H1 σ2(εx) lt σ2(εy)



Three damages 6 0 2 0 5 5 0 4 6

successfully in literature to detect and locate damage Nevertheless this proves a limitation ofthe AR-ARX method as it requires more data to detect and locate damage as opposed to theACF-CCF method

The descriptions of the two damage detection algorithms differentiates the two in numerousways Firstly in the AR-ARX method each sensor node gathers and processes its sensor dataindependently without sharing with the neighbouring nodes whereas in the ACF-CCF methodthe second half of the method communicates within node pairs The ability of AR-ARX toprovide accurate damage location is limited because of its inability to incorporate the availablespatial information Even though this method does not share sensor information betweenneighbours much energy is spent on the transmission of AR coefficients to the base station inorder to retrieve the corresponding ARX coefficients However the inter-nodal communicationin ACF-CCF can be justified because it occurs only after a damage has been detected in thestructure The computation of the AR and ARX models in AR-ARX method is quite complexcompared with the ACF and CCF functions of the ACF-CCF method and also it is timeconsuming This was observed during the implementation of the algorithms where the executionof the AR-ARX method in the matlab code took more than four times the time taken by ACF-CCF Both algorithms do not rely on the structural model which is a desirable feature and bothuse time series sensor data directly to compute the DSF of the method

5 ConclusionIn this paper a comparison between a correlation based distributed damage detection methodand a statistical damage detection method based on time series models has been presentedMeasurement data from an experimental study carried out on a two-span concrete slab has beenused to verify these algorithms The results show that in this study the ACF-CCF methodproves to be a better damage detection and localization method than the AR-ARX methodThe NI value of the ACF-CCF method could be a good indicator of the damage in concreteslab structures making this method applicable and effective in wireless sensor network basedstructural health monitoring Further study is needed to test the applicability of this algorithmin various structures and to develop the embedded algorithm for wireless sensor units

References[1] Clayton E H Koh B H Xing G Fok C L Dyke S J and Lu C (2005) Damage detection and

correlation-based localization using wireless mote sensors Proceedings of the 2005 IEEE InternationalSymposium on Mediterrean Conference on Control and Automation Intelligent Control pp 304-309

[2] Fugate M L Sohn H and Farrar C R (2001) Vibration-based damage detection using statistical processcontrol Mechanical Systems and Signal Processing 15(4) 707-721

[3] Lei Y Kiremidjian A S Nair K K Lynch J P Law K H Kenny T W Carryer E and Kottapalli A(2003) Statistical damage detection using time series analysis on a structural health monitoring benchmarkproblem Proceedings of the 9th International Conference on Applications of Statistics and Probability inCivil Engineering San Francisco CA USA July 6-9 2003


10

[4] Liu X Cao J Xu Y Wu H and Liu Y (2009) A multi-scale strategy in wireless sensor networks forstructural health monitoring Proceedings of 5th International Conference on Intelligent Sensors SensorNetworks and Information Processing (ISSNIP) pp 361-366

[5] Lynch J P Sundararajan A Law K H Kiremidjian A S Kenny T and Carryer E (2003) Embedmentof structural monitoring algorithms in a wireless sensing unit Structural Engineering and Mechanics 15(3)285-297

[6] Lynch J P Sundararajan A Law K H Kiremidjian A S and Carryer E (2004) Embedding damagedetection algorithms in a wireless sensing unit for operational power efficiency Smart Materials andStructures 13(4) 800-810

[7] Messina A Williams E J and Contursi T (1998) Structural damage detection by a sensitivity andstatistical-based method Journal of Sound and Vibration 216(5) 791-808

[8] Montgomery D C (1996) Introduction to statistical quality control 3rd Ed Wiley New York[9] Nair K K Kiremidjian A S and Law K H (2005) Time series-based damage detection and localization

algorithm with application to the ASCE benchmark structure Journal of Sound and Vibration 291(1-2)349-368

[10] Sohn H Czarnecki J A and Farrar C R (2000) Structural health monitoring using statistical processcontrol Journal of Structural Engineering 26(11) 1356-1363

[11] Sohn H and Farrar C R (2001) Damage diagnosis using time series analysis of vibration signals SmartMaterials and Structures 10(3) 1-6


11

An experimental study on distributed damage

detection algorithms for structural health monitoring

Madhuka Jayawardhana Xinqun Zhu and Ranjith LiyanapathiranaSchool of Engineering University of Western Sydney Penrith South DC NSW 1797 Australia

E-mail mjayawardhanauwseduau xinqunzhuuwseduau ranjithieeeorg

Abstract Distributed structural damage detection has become the subject of many recentstudies in Structural Health Monitoring (SHM) Development of smart sensor nodes hasfacilitated the growth of this concept enabling decentralized data processing capabilities ofnodes whose sole responsibility once was acquisition of data An experimental study has beencarried out on a two span reinforced concrete slab in this paper Different crack damages arecreated by the static loads and the impact tests that are carried out on the slab Two damagedetection and localization methods one based on Auto Correlation Function-Cross CorrelationFunction (ACF-CCF) and the other on Auto Regressive (AR) time series model are used todetect damage from measured responses The results from the two methods are compared inorder to determine which method has been more effective and reliable in determining the damageto the concrete structure

1 IntroductionWith the advancements of wireless communication technologies and smart devices structuralhealth monitoring is no longer a concept limited only to theory and research WirelessSensor Networks (WSNs) have made the deployment of SHM systems practically realisable andmanageable These actual applications have brought the attention of engineers and researchersto many new areas and issues related to SHM Distributed structural damage detection is onesuch new area with high potential for development In the light of development of sensor nodes asintelligent devices distributed computing strategy for structural damage detection has proved tosignificantly reduce the power consumption of the system while giving more robust and accurateresults with increased efficiency

Several Time-Series based methods are available in the literature for SHM Many of these areprimarily based on the Auto Regressive (AR) model AR (Sohn et al 2000 Fugate et al 2001)AR-ARX (Auto Regressive with exogenous input) (Sohn and Farrar 2001 Lynch et al 2003Lynch et al 2004 Lei et al 2003) and ARMA (Auto Regressive Moving Average) (Nair et al2005) are some The main concept behind these methods is that if the structure is damagedthe prediction model developed from the undamaged response data time series will not be ableto reproduce the new data series obtained from the unknown state of the structure Time-seriescomputations can be time consuming and complex in implementation

The Damage Location Assurance Criterion (DLAC) (Messina et al 1998 Clayton et al2005) is a correlation based method which uses modal frequencies It correlates modal frequencychange caused by possible structural damages between the actual structural response data andthose synthesized from an analytical model of the structure to identify and localize damage


Published under licence by IOP Publishing Ltd 1















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xk =psumi=1




xk =asumi=1

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An experimental study on distributed damage detection algorithms

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