A Hybrid Model for Prediction in Asphalt Pavement...

Research ArticleAHybrid Model for Prediction in Asphalt Pavement PerformanceBased on Support Vector Machine and Grey Relation Analysis

Xuancang Wang 1 Jing Zhao 1 Qiqi Li 1 Naren Fang 1 Peicheng Wang 2

Longting Ding 1 and Shanqiang Li 1

1School of Highway Changrsquoan University Xirsquoan 710064 China2School of Information Engineering Changrsquoan University Xirsquoan 710064 China

Correspondence should be addressed to Jing Zhao zhaojingzi0203163com

Received 12 August 2019 Revised 25 October 2019 Accepted 26 November 2019 Published 12 February 2020

Academic Editor Maria Vittoria Corazza

Copyright copy 2020 Xuancang Wang et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Pavement performance prediction is a crucial issue in big data maintenance is paper develops a hybrid grey relation analysis(GRA) and support vector machine regression (SVR) technique to predict pavement performancee predictionmodel can solvethe shortcomings of the traditional model including a single consideration factor a short prediction period and easy overfittingGAR is employed in selecting themain factors affecting the performance of asphalt pavemente SVR is performed to predict theperformance Finally the data collected from the weather station installed on Guangyun Expressway were adopted to verify thevalidity of the GRA-SVR model Meanwhile the contrast with the grey model (GM (1 1)) genetic algorithm optimization BP[[parms resize(1)pos(5050)size(200200)bgcol(156)]]081 minus 0823 1270 and minus 4569 respectively e study concludedthat the nonlinear and multivariate prediction model established by GRA-SVR has higher precision and operability which can beused in long-period pavement performance prediction

1 Introduction

Big data maintenance is a central issue in highway man-agement Highway maintenance mileage accounted for977 of the mileage of traffic in China by the end of 2018Notably the expressway has been transferred from theconstruction to the maintenance periodWith the popularityof big data technology roads have entered the era of big datamaintenance However the reason why the performance ofasphalt pavement is a vital component of maintenancemanagement and operation is that the rational allocation ofmaintenance decision-making and maintenance funds aredetermined by an accurate prediction model in the laterperiod erefore the scientific establishment of the pave-ment performance predictionmodel is significant for asphaltpavement maintenance and can provide a model for big datamaintenance

e pavement management system (PMS) is applied forroad life cycle management However it generally usesanalytical tools and statistical methods to predict pavement

performance [1] Predicting of pavement performance iscritical but it is very complex because the performance ofasphalt pavement is affected by the combination of structuraldesign material properties construction quality traffic loadnatural factors and maintenance [2] e pavement per-formance prediction model is a relationship that charac-terizes the variation of pavement performance with timematerial and traffic load [3]

ere are different methods available for the determina-tion of pavement performance many scholars have attemptedto develop a scientifically derived accurate model ere arefour types of prediction models uncertainty model certaintymodel dynamic model and bionic model [4]

(i) Uncertainty model the commonly used model isthe grey theoretical model that has the character-istics of a small amount of data high predictionaccuracy and a simple calculation method ere-fore it is widely used in pavement performanceprediction For example Zhang et al [5] Shen and

HindawiJournal of Advanced TransportationVolume 2020 Article ID 7534970 14 pageshttpsdoiorg10115520207534970

Du [6] Wang and Li [7] and Zhang and Ji [8] usedthis model to predict pavement smoothness andrutting Peng et al [9] applied Weibull distributionto pavement performance prediction and obtainedideal results

(ii) Certainty model it is an empirical method it takesadvantage of using traditional regression as a tool tofit the data that come from experiments and finiteelement mechanics to get the form and parametersof the model For example Sun and Liu [10] pro-posed the decay equation of asphalt pavementperformance which was obtained through engi-neering experiment Abed et al [11] investigated thevariability effect of thickness and stiffness ofpavement layers they used theMonte Carlo methodto obtain the probability distribution function ofpavement performance by using the parametersGong et al [12] proposed a regularized regressionmethod to estimate the asphalt concrete moduliwith data available from the long-term pavementperformance (LTPP) database

(iii) Bionic model this model has high prediction ac-curacy Yang et al [13] used the genetic neuralnetwork model to estimate rutting and drivingquality Bianchini and Bandini [1] proposed theneuro-fuzzy hybrid model to predict the presentserviceability index (PSI) Ferreira and Lima Cav-alcante [14] and Beltran and Romo [15] presentedthe application of artificial neural networks (ANN)in pavement performance

(iv) Dynamicmodel it is based on the traditional modelFor instance Shen et al [16] improved the tradi-tional grey model and proposed a dynamic greymodel Chen et al [17] combined the US PMEmodel with grey prediction theory and mechanicalexperience method proposed a dynamic grey pre-diction model and established a DGM-PMEcombination model to forecast the rutting Chu andDurango-Cohen [18] used the autoregressivemoving average time series state space method topredict the structural strength of the pavement El-Badawy et al [19] developed a comprehensivebottom-up fatigue cracking distress dynamic pre-diction model integrating the Mechanistic-Empir-ical Pavement Design Guide (MEPDG) andperformance test methodology

To date various pavement performance predictionmodels have been proposed by scholars but the models stillhave defects For example the grey model just adopts thetime factor and does not take into account other factors suchas natural environment and traffic load which may havemaximum impact And as the forecast period increases thestability and accuracy of the prediction are decreasedWeibull distribution model is only suitable for small sampledata prediction e certainty model is mainly determinedby factors like the initial performance index of asphaltpavement and the road age It is simple and convenient to

use for it does not consider the reasonable dynamic data Itonly can predict short period performance e geneticneural network and ANN model are prone to overfittingwhen data are insufficient e dynamic prediction modelcan make full use of the later data to predict longer periodsSimultaneously the reason why the model can only considerthe impact of time on pavement performance is that themodel is based on time series Hence a new model is neededto be devised to be applied to pavement performanceprediction

Recently support vector machines have been applied invarious fields Zhao et al [20] proposed a k-means and SVMhybrid model for the development of an electric vehicleurban driving cycle Hoang et al [21] used it to recognize thepavement crack Wang et al [22] proposed a support vectormachine online model for predicting metro ridershipKarballaeezadeh et al [23] applied this model to the pre-diction of road residual life and compared the model with anartificial neural network (ANN) and multilayer perceptron(MLP) models e results show that the support vectormachine model has the highest accuracy

e factors affecting the performance of asphalt pave-ment were processed firstly by GRA e SVR with ad-vantages of minimizing structural risk and stronggeneralization performance was then used to establish ahyperplane as a decision surface Finally the asphaltpavement performance prediction model was established toprovide a model that can be applied to maintenance deci-sion-making maintenance fund investment and big data ofpavement maintenance

e structure of this paper is as follows Section 2 mainlyintroduces the main principles of GRA-SVR Section 3contains the modeling process of the whole model Section 4mainly uses the model to verify the example Finally theresults are analyzed

2 Methodology

21 Basic Principles of GRA-SVR

211 Basic Principle of Grey Relation Analysis e greysystem theory holds that the complex objective systemswhich are all ordered and discrete data must contain in-herent laws [24] ere are many factors affecting theperformance of asphalt pavement but the effects of variousfactors are not very clear so that we can call the factors greyerefore GRA is used to quantitatively reflect the corre-lation between asphalt pavement performance and variousfactors is method can find the main factors from manyfactors that affect pavement performance e corre-sponding statistical data of the influencing factors in thesystem are converted into geometric curves by the methodand the closer the curve geometry is to the dependentvariable the greater the degree of association is [25]

212 Basic Principle of Support Vector Machine RegressionSVR is a model derived from the support vector machine(SVM) proposed by VAPNIK [26] e SVM model is amachine learning method that mainly solves the

2 Journal of Advanced Transportation

classification problems of small samples nonlinearities andhigh-dimensional data [27 28] Its principle is based on theVC theory of statistical principle and structural risk mini-mization and the optimal solution in data mining is soughtby establishing an optimal hyperplane [29] Usually wereduce the dimension of the sample to simplify the problemwhile the SVM method is the opposite It uses the kernelfunction to map the sample points to high-dimensional andeven infinite-dimensional space to deal with linear problemsas shown in Figure 1

Regression is essentially similar to classification eSVM classification model is to manage a plane so that thesupport vectors of the two classification sets or all the dataare farthest from the classification plane and the SVRmodel is to find a regression plane so that all data of acollection could be closest to the plane as shown inFigure 2 e SVR can predict the prediction vector of thetest data by establishing a nonlinear relationship betweenthe data tested in the training data and the support vectorMost of the various influencing factors of asphalt pave-ment performance are nonlinear e specific method is asfollows

Assume the sample set (x1 y1) (x2 y2) (xl yl)x isin Rn y isin R x isin Rn y isin R en y and x in the sample setcan be expressed as follows [2]

f(x) w middot x + b (1)

where w and b are the coefficients of the hyperplaneIf the original data fit well with the support vector

machine regression then min 12w2 is as follows [2]

st

w middot xi + b minus yi le ε

yi minus w middot xi minus ble ε

i 1 2 l

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(2)

where ε is a positive numberEquation (1) is transformed into (3) by introducing the

Lagrangian logarithm [2]

f(x) w middot x + b 11139441

i1ai minus a

lowasti( 1113857 xi middot x( 1113857 + b (3)

where aI and alowasti are the sample support vectors which take avalue of zero in most cases

e above process is the linear regression principle ofSVR but the effects of the factors including rainfall trafficvolume maximum temperature and minimum temperaturefor the pavement performance are nonlinear When dealingwith the nonlinear problem of the SVR the sample xi ismapped to a high-dimensional space by ψ x⟶ H Anoptimal hyperplane should be constructed to solve theldquodimensionality disasterrdquo the inner space operation isimplemented using the original spatial parameters when ψ isunknown e internal kernel function K(xi xj) ψ(xi) times

ψ(xj) can be obtained when the kernel function satisfies thecondition of Mercer [30] At the same time Lagrangechanges are introduced to get equation (4) [31]

L(w ξ b a β) 11139441

i1ai minus

12

1113944

1

i1yiyjaiajK xixj1113872 1113873 (4)

Finally the transformed regression function [31] is asfollows

f(x) w middot x + b 1113944

1

i1ai minus a

lowasti( 1113857K xi middot x( 1113857 + b (5)

is method can avoid overfitting caused by traditionalmethods SVR nonlinear regression fitting could control thefitting process by increasing the dimension e high gen-eralization performance that is closely related to the choiceof kernel function is a big advantage of SVR

Commonly used kernel functions are listed as follows[32]

(1) Linear kernel function K(x xi) xTxi(2) Polynomial kernel function K(x xi) (μxTxi +

r )p μgt 0(3) RBF kernel function K(x xi) exp(minus gx

minus xi2) ggt 0

(4) Sigmoid kernel function K(x xi) tanh(μxTxi

+ r) μgt 0

μ r and p are parameters of the kernel functionHowever each type of kernel function has different

advantages and disadvantages

① Linear kernel functions are used to generalize linearsamples② Polynomial kernel functions are mostly used toprocess text data③ Although Sigmoid kernel function has higher ac-curacy it is complicated which increases the com-plexity of the whole model

erefore in this paper the RBF kernel function is usedfor support vector machine regression prediction

22 Construction of GRA-SVR Asphalt PavementPerformance Model

221 Selection of the Best Parameters It is important toselect the appropriate penalty parameter c and kernel

K(X X1)

K(X X2)

K(X Xn)

Bias b

Output Y

X(1)

X(2)Input X

X(n)

Figure 1 Architecture diagram of support vector machine

Journal of Advanced Transportation 3

function parameter g to ensure the accuracy of the entiremodel when using SVR for prediction erefore the CVmethod is generally adopted to solve this problem which is astatistical analysis method for verifying the performance ofthe model e principle is to group the original data anddivide them into verification and training sets In this way itis possible to effectively avoid the states of underlearning andoverlearning and ultimately obtain the accuracy CommonCV methods are as follows

(1) Hold-Out Method the method randomly divides thedata into two categories one is the training set usedto train the model and the other is the verificationset used to verify the model [20]e final accuracy isthe performance metric of the model

(2) LOO-CV assuming there are N samples in theoriginal data that is why the model is called N-CVso each sample is an independent verification setand the remaining N-1 samples are training setsthus N models were obtained e average accuracyof the final validation set is used as a performanceindicator for the model However due to the highcomputational cost the model has difficulties inpractical operation

(3) K-CV the original data are equally divided into Kgroups e data of each group are used as verifi-cation set once and the remaining data of other K-1groups are used as a training set therefore Kmodelsare obtained en the average of the classificationaccuracy calculated from the final verification set ofthose K models is used as the performance index ofthis model [33] is method is more accurate due tothe fact that it can effectively avoid the states ofunderlearning and overlearning

According to the comparable selection of the threemethods theK-CVmodel is finally adopted to cross-validateand select the best penalty parameter c and function pa-rameter g e specific method is as follows Firstly theparameters c and g are limited to a specific range and thenthe K-CV model is used for the training set in the range toobtain the accuracy Finally the parameters c and g whichmake the training set with the highest accuracy are selectedas the optimal parameterse concrete implementation canbe implemented using the libsvm320 tool

222 Construction of Asphalt Pavement Performance Modele pavement performance is affected by many factorse factors acting on performance are uncertain and non-linear Hence the performance and factors integrate a greysystem erefore the grey correlation analysis can be used asan attribute processor to select several important influencingfactors and then the SVR is used to perform the regressionprediction rough the establishment of the comprehensivemodel GRA-SVR to predict the trend of pavement perfor-mance under the influence of various factors the specificmodeling process is shown in Figure 3

Specific steps are as follows

(1) Select dependent and independent variables(2) Establish a raw data matrix Xi xi(k) k 11113864

2 n i 1 2 3 4 xi(k) represents a certain levelof the first influencing factor

(3) Data normalization(4) Calculating the difference sequence [34]is as follows

Δi(k) x0prime(k) minus xiprime(k)

11138681113868111386811138681113868111386811138681113868

Δi Δi(1)Δi(2) Δi(n)( 1113857

i 1 2 m

(6)

(5) Achieving the largest and smallest difference of thesequence [34] is as equation (7) Write the maximumvalue as M and the minimum value as N

M maxi

maxkΔi(k)

N mini

minkΔi(k)

(7)

(6) Calculating the correlation coefficient of each sample[35] is as follows

c0i(k) m + ξM

Δi(k) + ξM ξ isin (0 1) k 1 2 n

i 1 2 m

(8)

ξ is called the resolution coefficient Whenξ le 05463 the resolution is the best Usually thevalue of ξ is 05 which is also taken in this paper

wx + b = 0 2||w||

2||w||

wx + b = 1

wx + b = 0

wx + b = ndashε

wx + b = ε

wx + b = ndash1

Figure 2 Difference of SVM and SVR diagram


(7) Calculating the correlation between each influencingfactor and the system [35] is as follows

c0i 1n

1113944

n

i1c0i(k) i 1 2 m (9)

(8) Choose the factors that have a greater influence onpavement performance

(9) To improve the accuracy and training speed of themodel and prevent big numbers of consuming dec-imals during the calculation process the data shouldbe normalized and processed to the interval [0 1]

(10) RBF which is researched has a high precision[36 37] and this paper selects the RBF kernelfunction to predict the performance

(11) K-CV model is used to cross-validate and select thebest penalty parameter c and function parameter g

(12) Using the optimal parameters for SVR fitting theprediction data are obtained

3 Case Verification

31 Data Acquisition is paper is based on the highwayfrom Guangzhou to Yunfu (Guangyun highway) and theinstalled weather station in 2010 and it can collect theclimate data including road temperature humidity windspeed and solar radiation e installation details andpavement structure are shown in Figures 4 and 5 Amongthem the pavement temperature detection uses the ZDR-41temperature sensor subgrade temperature and humiditytesting to use a 5TE sensor (see Figure 6) e climate ofGuangdong province is humid and the temperature is ex-tremely high rising to 41degC Under the influence of largetraffic volume the rutting is serious as shown in Figure 7e RDI predictionmodels GRA-SVR PPI GA-BP and GM

(1 1) were established to analyze the accuracy of each modelwhich were based on the RDI maintenance funds trafficvolume and data collected by the weather station from 2011to 2018 (see Table 1 for the survey results)

e factors pavement structure and materials should beconsidered in performance prediction Usually the pave-ment structure needs to be calculated as a numerical valueTo address this issue the structures number [12 38ndash40] isusually adopted However it needs to be calculated in twocases as follows

(i) Different structures in this case the thickness andmaterial of each layer of the road are different estructural number [41] (SN) is adopted according to theAASHTO guide for design of pavement structures eroad network level performance prediction can applythis case e specific calculation method is as follows

SN a1D1 + a2D2m2 + a3D3m3 (10)

where ai is ith layer coefficient this parameter needsto be obtained through experiments Di is ith layerthickness and mi is the ith layer drainage coefficient

(ii) Same structure the performance of the pavementmaterial can be affected by the environment and thestructural bearing capacity is changede pavementstructural bearing capacity can be expressed by thepavement structure strength ratio (SSR) [42] especific calculation method is

SSR l0

l (11)

where l0 is pavement deflection standard value(001mm) where l is pavement measurement

Multifunctionvehicle

Start

End

Datacollection

Buildingdata matrix

Normalizethe data

Finddifferencesequence

Maximumand

minimumdifference in

differencesequence

Seekingthe

correlationdegree of

each factor

Selectdependent

andindependent

variables

Fittingprediction

Train SVRwith

optimalparameters

Cross-validationselection returns

the best parametersc and g

Selectkernel

function

Selecttraining set

andtest set

Choice ofmain factors

SVR

Weatherstation

5TEhumidity sensor

ZDR-41temperature sensor

Grey

Figure 3 Flowchart of the GRA-SVR modeling process


4cm upper surface of antiskid-modified asphalt concrete

6cm middle surface of coarse-graded asphalt concrete

8cm lower surface of coarse-graded asphalt concrete20cm upper base of cement-stabilized crushed stones (4-5)

20cm lower base of cement-stabilized crushed stones (4-5)

20cm subbase of cement-stabilized crushed stones (4-5)

Soil subgradeA B

Bracket

B temperature of pavement structureC humidity of subbase

2

Medianstrip

Marginalstrip

Passing lane Hard shoulder Soil shoulderLane

075 375 2 times 375 3 05

C

B

A temperature of surfaceTemperature and humidity sensor

Figure 4 Sensor layout

(a) (b)

(c) (d)

Figure 5 Weather station layout (a) Drilling cores of asphalt pavement (b) installation of temperature sensor in a pavement structure (c)installation of temperature sensor on road surface and (d) bracket mounting


representing deflection (001mm) this parameterneeds to be obtained through multifunction vehicle

is paper relies on engineering only one pavementstructure so the calculation of SSR represents the influenceof pavement structure on pavement performance

32 Grey Relation Analysis e correlation of the data canbe analyzed in Table 2 the correlation degree of eachinfluencing factor can be obtained as shown in Table 2

e effects of various factors on rutting are sorted asfollows

c2 lt c9 lt c18 lt c7 lt c12 lt c10 lt c8 lt c17 lt c14 lt c13 lt c16

lt c5 lt c19 lt c11 lt c15 lt c6 lt c1 lt c4 lt c3

(12)

Generally the greater the degree of relevance the betterthe correlation of factors to the main direction of systemdevelopment that is the greater the influence of this factor onthe evaluation index When cgt 08 is well correlated whenc 06sim08 the correlation is good We can see that c of these18 factors is greater than 06 indicating that these factors havean impact on the rutting Among the 19 factors c of 12 factorsis greater than 08 indicating that these 12 factors have astrong influence on the formation of rutting

So the better relevant factors that have the greatestimpact were selected to establish the model and the otherfactors were removed e selected results are as follows

Equivalent single axle loadsgtmaintenance fundsgtpave-ment structure strength ratiogtmean value of soil mois-turegthighest temperature in the middle surfacegthighesttemperature in the road surfacegt annual cumulative totalradiationgt annual average rainfallgt lowest temperature inmiddle surfacegthighest temperature in the upper sur-facegt lowest temperature of upper surfacegthighesttemperature in lower surface

e following can be observed from the above analysis

(1) e primary factor the formation of rutting is theequivalent single axle loads e greater equivalentsingle axle loads are themore serious the rutting isereason is that under the action of traffic load largeshear stress will be generated in the asphalt pavementwhichwill cause irreversible cumulative deformation inthe surface layer

(2) e maintenance funds have a significant repairingeffect on the rutting For example in this section of thehighway the maintenance funds were RMB 81500 in2013e traffic volume and rainfall increased but therutting disease was significantly improved in 2014

Temperatureindicator

Temperaturesensor

(a)

Temperaturesensor

Humiditysensor

(b)

Figure 6 (a) Pavement sensor and (b) subgrade sensor

(a) (b)

Figure 7 Rutting of Guangyun Expressway


(3) e degree of relevance SSN is 09301 It shows thatSSN has a greater impact on the rutting e specificreason is that water solar radiation and temperaturehave an impact on the pavement material and thestructural bearing capacity is insufficient resulting inthe occurrence of rutting

(4) e annual cumulative radiation ages the asphalt andaccelerates the formation of the rutting After theaging of the asphalt the overall shear resistance ofthe asphalt surface layer is reduced resulting in adecrease in the rutting resistance For example theannual cumulative radiation was the largest in 2015and the rutting in 2016 was more serious

(5) e maximum shear stress generally occurs in themidsurface and the rainfall and wind speed accel-erate the heat dissipation of the highest temperatureof the environment and road surface Based on theabove factors the influence of the highest temper-ature of the middle layer on the formation of therutting is greater than the highest temperature of theroad surface and the upper layer

(6) Under the action of traffic load the water infiltratedinto the asphalt surface layer by soil and rainfall willbecome high-pressure water which will reduce thebond behavior between asphalt and aggregateresulting in lower pavement strength and lowerresistance to rutting

(7) e lowest temperature of the road surface wouldcause other diseases on the asphalt pavement whichindirectly lead to the occurrence of rutting

e dimensionally reduced data are normalized bysoftware and the processing results are shown in Table 3

33 Penalty Parameter Selection In this paper the optimalpenalty parameter c and function parameter g are solved byK-CV cross-validation model to select the best penaltyparameter c and function parameter g (see Figure 8) eaxis of abscissa indicates the value of c after taking the base 2logarithm e ordinate axis represents the value of g aftertaking the base 2 logarithm Contour lines indicate errors inthe range of c and g When the error is the smallest thecorresponding c and g are the best First c and g are initiallyselectede range of c is within 2and(minus 6)sim2and(6) and that of g

is within 2and(minus 8)sim2and(8) When the error is 00572 theoptimal penalty parameter is c 640 and g 00039

By primary election the range of values for c can bereduced to 2and(minus 3)sim2and(2) and g can be reduced to2and(minus 4)sim2and(4)(see Figure 9) At the same time reduce theinterval between the contour and the three-dimensionalview When the error is 00605 the optimal penalty pa-rameter is c 40 and g 00884

4 Results and Discussion

e GRA-SVR GM (1 1) [43] GA-BP [44] and PPI modelwere applied and compared to predict the RDI of 2018which was based on the training set consisting of variousfactors and RDI from 2011 to 2017 e PPI [10]model is asfollows

PPI PPI0 1 minus exp minusa

y1113888 1113889

β⎡⎣ ⎤⎦

⎧⎨

⎩

⎫⎬

⎭ (13)

where PPI is the performance index PPI0 is the initialperformance index y is the road age α and β are modeparameters In this paper PPI0 94 y 8 α 132β 1409

Table 1 Datasheet of RDI and various influencing factors of Guangyun Expressway (2011ndash2018)

Year 2011 2012 2013 2014 2015 2016 2017 2018RDI 94 902 901 914 898 864 846 855PCI 997 979 971 951 925 914 887 875SRI 98 955 895 808 869 842 844 856SSR 261 163 158 192 136 127 135 115Service life 2 3 4 5 6 7 8 9Equivalent single axle loads (103) 1214 1504 1600 186015 198446 217391 238693 202345Maintenance funds (million yuan) 323 0875 815 634 764 854 80 657Annual average rainfall (mm) 16677 14905 16476 22245 17525 16456 2321 20131Mean value of soil moisture 174 178 195 221 186 175 224 191Mean value of environment humidity (RH) 753 745 838 773 76 737 721 888Annual maximum wind speed (ms) 74 62 61 58 53 63 56 79Highest temperature of environment (degC) 376 378 389 392 396 39 404 382Lowest temperature of environment (degC) 34 25 25 27 01 38 37 42Highest temperature of road surface (degC) 651 618 603 624 685 625 651 652Lowest temperature of road surface (degC) 42 63 59 43 59 6 64 58Highest temperature of upper surface (degC) 551 562 571 602 586 588 579 631Lowest temperature of upper surface (degC) 75 79 69 78 65 75 8 81Highest temperature in middle surface (degC) 567 603 594 585 605 594 612 428Lowest temperature in middle surface (degC) 63 54 58 65 68 69 6 61Highest temperature in lower surface (degC) 467 476 469 455 442 467 432 449Lowest temperature in lower surface (degC) 91 85 89 93 95 102 98 104Annual cumulative total radiation 1014 1085 1045 1054 1240 1093 1105 1166


Tabl

e2

Relevanceof

each

influ

encing

factor

Influ

encing

factor

c1

c2

c3

c4

c5

c6

c7

c8

c9

c10

c11

c12

c13

c14

c15

c16

c17

c18

c19

c09301

06794

10397

09698

08539

09241

07685

07999

07052

07998

08806

07866

08409

08326

09049

08472

08077

07593

08622

c1ispavementstructure

streng

thratio

c2istheservicelife

c3istheequivalent

singleaxleloads

c4isthemaintenance

fund

sc5istheaverageannu

alrainfall

c6isthemeanvalueof

soilmoisture

c7isthemean

valueof

environm

enth

umidity

c8istheannu

almaxim

umwindspeed

c9isthehigh

esttem

perature

ofenvironm

ent

c10

isthelowesttem

perature

oftheenvironm

ent

c11

isthehigh

esttem

perature

ofroad

surface

c12isthelow

esttem

peratureof

road

surface

c13istheh

ighesttemperatureof

uppersurfacec

14isthelow

esttem

peratureof

uppersurfacec

15istheh

ighesttemperaturein

middlesurfacec

16isthelow

est

temperature

inmiddlesurface

c17

isthehigh

esttem

perature

inlower

surface

c18

isthelowesttemperature

inlower

surface

c19

istheannu

alcumulativetotalradiatio

n


Table 3 Standardized data after normalization

Time 2011 2012 2013 2014 2015 2016 2017RDI 1 0596 0585 0723 0553 0191 0Equivalent single axle loads 0 0247 0329 0551 0657 0818 1Maintenance funds 0307 0 0949 0713 0883 1 0930Pavement structure strength ratio 1 0269 0231 0485 0067 0 0060Mean value of soil moisture 0 0080 0420 0940 0240 0020 1Highest temperature in middle surface 0 0800 0600 0400 0844 0600 1Highest temperature of road surface 0585 0183 0 0256 1 0268 0585Annual cumulative total radiation 0 0314 0137 0177 1 0350 0403Average annual rainfall 0213 0 0189 0884 0315 0187 1Lowest temperature in middle surface 0600 0 0267 0733 0933 1 0400Highest temperature of upper surface 0 0216 0392 1 0686 0725 0549Lowest temperature of upper surface 0667 0933 0267 0867 0 0667 1000Highest temperature in lower surface 0795 1 0841 0523 0227 0795 0

04203603024018012006

048

042

036 03

024

018

012

0060

48

006012018024

03036042048

00601201802403036042048

ndash6 ndash4 ndash2 0 2 4 6Log2c

ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Log2

g

(a)

5 6

MSE

4Log2g

0 2

Log2c0

0

02

04

06

08

1

ndash2ndash5 ndash4ndash6

(b)

Figure 8 Best primary selection of penalty parameters (a) Parameters c and g versus the accuracy rate in two dimensions (b) parameters cand g versus the accuracy rate in three dimensions

0035

0035

00350035

007

007

007007

0105

0105

01050105

014

014

014014

0175

0175

01750175

021

021

021021

0245

0245

02450245

028

028

028028

0315

0315

03150315

035

035

035

035

0385

0385

0385

038

5

042

042

042

042

0455

0455

0455

045

5

049

049

049

049

ndash3 ndash25 ndash2 ndash15 ndash1 ndash05 0 05 1 15 2Log2c

ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Log2

g

(a)

04

0102

3

0304

22

05

15

MSE

06

1 1

07

Log2g050

08

0

09

Log2cndash1 ndash05

1

ndash1ndash2 ndash15ndash2ndash3 ndash25ndash4 ndash3

(b)

Figure 9 Best final selection of penalty parameters (a) Parameters c and g versus the accuracy rate in two dimensions and (b) parameters cand g versus the accuracy rate in three dimensions


e comparative analysis of the predicted and actualvalues of different models is shown in Table 4 the accuracycomparison was shown in Table 5 sand the correspondingvariation trend and actual value of different models wereshown in Figures 10 and 11

e evaluation parameters of the four models obtainedfrom Table 5 in predicting RDI are as follows

Correlation coefficient GM (1 1) (0856) ltPPI (0879)ltGA-BP (0984) ltGRA-SVR (0992)

RMSE GA-BP (0298) ltGRA-SVR (0499) ltGM (1 1)(1304) ltPPI (3270)

Relative error GRA-SVR (0081) ltGM (1 1) (0823)ltGA-BP (1270) ltPPI (4569)

e GRA-SVR and GA-BP models all showed goodperformance in terms of the overall correlation and devi-ation of the predicted value from the true value Howeverwith respect to relative error in 2018 GRA-SVR is the bestfollowed by GM (1 1) Figure 11 shows the relative errors ofthe predicted and true values for the four models from 2011to 2018 It can be observed that the relative error of the GA-BPmodel is the smallest higher than GRA-SVR in 2016 andhigher than GM (1 1) in 2018 from 2011 to 2015 is is

Table 4 Comparison of predicted and actual values of RDI

Time Originalvalue

GRA-SVR GM (1 1) GA-BP PPIPredictivevalue

Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror

2011 940 9400 mdash 9400 mdash 9400 mdash 9400 minus 02012 902 9027 minus 0070 9165 1447 9019 0 9397 38012013 901 9003 0068 9047 0368 9010 minus 0002 9357 3872014 914 9063 0724 8930 minus 2096 9141 0003 9215 21662015 898 8973 0070 8816 minus 1645 8980 0 8949 23482016 864 8647 minus 0070 8702 0621 8605 minus 0352 8584 30912017 846 8467 minus 0066 8590 1301 8426 minus 0341 8159 12422018 855 8556 minus 0069 8480 minus 0704 8658 1082 7910 3907

Table 5 Precision comparison of forecast results for the three models

Model Correlation coefficient RMSE Relative error ()GRA-SVR 0992 0298 minus 0081GM (1 1) 0856 1304 minus 0823GA-BP 0984 0448 1270PPI 0879 3270 minus 4569

2010 2012 2014 2016 2018 202075

80

85

90

95

RDI

Time (year)

Original valueGRA-SVR predictive valueGM (1 1) predictive value

GA-BP predictive valuePPI predictive value

(a) (b) (c)

Figure 10 Trend charts of RDI predicted value of different models


because the model is prone to overfitting for samples withsmall data resulting in reduced prediction accuracy

e trends of the predicted and actual values fromdifferent model RDIs were depicted in Figure 10(a) It can beseen that the GRA-SVR and GA-BP models display non-linear trends which are close to the actual value e othertwo models show a linear relationship which is differentfrom the actual value

All four models have good accuracy in short periodprediction (see Figure 10(b)) but the accuracy would changewith the prediction period increasing (see Figure 10(c)) theGRA-SVR model has the highest prediction accuracy be-cause the old data were replaced by the new prediction dataas the new training set e GA-BP takes second placeirdly the GM (1 1) model just used the data of 7 yearsand the accuracy reduced as the new data are not replenishedin time with the time increases e PPI model has the worstprediction accuracy which was due to the fact that themodelonly uses the first-year data for prediction As the predictionperiod increases the controllability of the model decreasesIn order to verify the accuracy of the model the pavementsurface condition index (PCI) and pavement skidding re-sistance index (SRI) prediction applied this model erelative error was minus 0115 and 0111 respectively

For the GRA-SVR and GA-BP model modeling processmore important factors that affect the production of ruttingshould be considered so the modeling process is more

complex than the other two models but the predictionresults are stable e PPI model just considers the age andregional conditions and the main factors affecting thepavement performance were unutilized therefore theprediction accuracy is lower In the GM (1 1) model thetime factor was only considered whose prediction accuracydepends greatly on the accuracy of the annual data If thedata of a certain year are deviated the whole system trendwill have a large error and the ease of operation of the modelis between the other modelserefore the GRA-SVRmodelis suitable for multivariate long-period and nonlinearprediction of pavement performance

e accuracy prediction period and operability of thethree models are compared and analyzed e results areshown in Table 6

Overall our study establishes the model that has offeredbetter performance than other models However there arealso limitations In the future study we want to choose thebest parameters with better methods including genetic al-gorithm and particle swarm optimization ese algorithmsare also widely used in other fields If we find a better op-timization method we can make the prediction accuracyhigher We will build the database with more road infor-mation en the GRA-SVR model at the computing ter-minal is used to predict the performance Some decisionmodel is applied to maintenance decision Finally the results

2010 2012 2014 2016 2018

0

1

2

3

4

5

Abso

lute

erro

r

Time (year)

GRA-SVR absolute errorGM (1 1) absolute error

PPI absolute errorGA-BP absolute error

Figure 11 Trend charts of the actual value of different models

Table 6 Performance comparison of four models

Model Operability Prediction period Accuracy Consideration of factorsGRA-SVR PPI GM (1 1) GA-BP means performance in general means better performance and means the best performance


are uploading the pavement management system (seeFigure 12) We firmly believe that this will have far-reachingimplications for road maintenance projects

5 Conclusion

In this study a GRA-SVR predictive hybrid model com-bining the grey correlation analysis with support vectormachine regression was proposed for the first time to beapplied to predict the performance of asphalt pavement emain conclusions are drawn as follows

(1) e main factors including equivalent single axle loadsmaintenance funds highest temperature in the middlesurface pavement structure strength ratio averagevalue of soil moisture highest temperature in the roadsurface lowest temperature in the road surface highesttemperature in the upper surface annual averagerainfall annual cumulative total radiation highesttemperature in the upper surface annual averagerainfall lowest temperature of upper surface highesttemperature in lower surface lowest temperature inlower surface and annual maximum wind speed arewell correlated in pavement performance

(2) Compared with other models the GRA-SVR modelis highly accurate and time-independent whichmakes it suitable for short and long periodpredictions

In conclusion the GRA-SVR model is applicable for amultivariate long period and nonlinear performance ofpavement prediction and is restricted by the amount of dataIt is reliable for asphalt pavement maintenance decision-making At the same time this model can also be applied tobig data road maintenance prediction

Data Availability

is paper is from the Guangdong Provincial Department ofTransportation (2015-02-011) and the data come from theproject team experiment

Conflicts of Interest

e authors declare no conflicts of interest

Acknowledgments

is research was funded by Guangdong Provincial Com-munication Department Science and Technology Project(Grant no 2015-02-011)e authorsrsquo special thanks go to allthe subjects that participated in the data acquisition

References

[1] A Bianchini and P Bandini ldquoPrediction of pavement per-formance through neuro-fuzzy reasoningrdquo Computer-AidedCivil And Infrastructure Engineering vol 25 no 1 pp 39ndash542010

[2] Q R Li Z Y Guo and Y J Wang ldquoEvaluation of theperformance of expressway asphalt pavement based on PCA-SVMrdquo Journal of Beijing University of Technology vol 44no 2 pp 283ndash288 2018

[3] Z Lan ldquoPerformance evaluation and prediction of expresswayasphalt pavementrdquo Southeast University Nanjing ChinaDoctor degree 2015

[4] C Jin and J X Zhang ldquoSummary of research on performanceprediction of asphaltrdquo Journal of China amp Foreign Highwayvol 37 no 5 pp 31ndash35 2017

[5] D Zhang X Li Y Zhang and H Zhang ldquoPrediction methodof asphalt pavement performance and corrosion based on greysystem theoryrdquo International Journal of Corrosion vol 2019Article ID 2534794 9 pages 2019

[6] D Shen and J Du ldquoGrey model for asphalt pavement per-formance predictionrdquo in Proceedings of the IntelligentTransportation Systems Conference pp 668ndash672WashingtonWA USA October 2004

[7] K Wang and Q Li ldquoGray clustering-based pavement per-formance evaluationrdquo Journal of Transportation Engineering-ASCE - J TRANSP ENG-ASCE vol 136 no 1 pp 38ndash44 2010

[8] X Zhang and C Ji ldquoAsphalt pavement roughness predictionbased on gray GM (1 1 | sin) modelrdquo International Journal ofComputational Intelligence Systems vol 12 no 2 pp 897ndash902 2019

[9] T Peng X L Wang and S F Chen ldquoPavement performanceprediction model based on Weibull distributionrdquo AppliedMechanics and Materials vol 378 pp 61ndash64 2013

[10] L J Sun and X P Liu ldquoStandard decay equation for pavementperformancerdquo Journal of Tongji University (Natural Science)vol 23 no 5 pp 512ndash518 1995

[11] A Abed N om and L Neves ldquoProbabilistic prediction ofasphalt pavement performancerdquo Road Materials and Pave-ment Design vol 20 pp 247ndash264 2019

[12] H Gong Y R Sun and B S Huang ldquoEstimating asphaltconcrete modulus of existing flexible pavements for mecha-nistic-empirical rehabilitation analysesrdquo Journal of Materialsin Civil Engineering vol 31 no 11 Article ID 04019252 2019

[13] J Yang J J Lu and M Gunaratne ldquoApplication of neuralmodels for forecasting or pavement crack index and pavementcondition ratingrdquo in Gain access to New Resources through theTRB Global Affiliate Program Vol 152 Department of Civiland Environmental Engineering University of South FloridaTampa FL USA 2003

[14] A Ferreira and R Lima Cavalcante ldquoApplication of an ar-tificial neural network based tool for prediction of pavement

Uploading

Data acquisition deviceComputing

terminal

Database

Feedback

Data cleaningGRA-SVR predict the pavement

and maintenance decision

Pavement management system

Figure 12 Conception of use of the model


performancerdquo in Proceedings of the ISAP Conference on As-phalt Pavements Fortaleza Brazil 2018

[15] G I Beltran andM P Romo ldquoAssessing artificial neural networkperformance in estimating the layer properties of pavementsrdquoIngenierıa e Investigacion vol 34 no 2 pp 11ndash16 2014

[16] J M Shen Y G Dong W J Zhou and X Wang ldquoA greydynamic multi-attribute association decision model based onexponential functionrdquo Control and Decision vol 31 no 8pp 1441ndash1445 2016

[17] X W Chen H N Wang Z Chen and Y Zhan-pingldquoCorrection of MEPDG rutting prediction model based onmathematical statistics methodrdquo Journal of Changrsquoan Uni-versity (Natural Science Edition) vol 33 no 6 2013

[18] C-Y Chu and P L Durango-Cohen ldquoEstimation of infra-structure performance models using state-space specificationsof time series modelsrdquo Transportation Research Part CEmerging Technologies vol 15 no 1 pp 17ndash32 2007

[19] S M El-Badawy M G Jeong and M El-Basyouny ldquoMeth-odology to Predict Alligator Fatigue Cracking Distress Based onAsphalt Concrete Dynamic Modulusrdquo Transportation ResearchRecord vol 2095 pp 115ndash124 2009

[20] X Zhao Q Yu J Ma YWuM Yu and Y Ye ldquoDevelopmentof a representative EV urban driving cycle based on a k-meansand SVM hybrid clustering algorithmrdquo Journal of AdvancedTransportation vol 2018 Article ID 1890753 18 pages 2018

[21] N-D Hoang Q Nguyen and D T Bui ldquoImage processing-based classification of asphalt pavement cracks using supportvector machine optimized by artificial bee colonyrdquo Journal ofComputing in Civil Engineering vol 32 no 5 pp 1ndash14 2018

[22] X Wang N Zhang Y Zhang and Z Shi ldquoForecasting ofshort-term metro ridership with support vector machineonline modelrdquo Journal of Advanced Transportation vol 2018Article ID 3189238 13 pages 2018

[23] N Karballaeezadeh S Danial MohammadzadehS Shamshirband P Hajikhodaverdikhan A Mosavi andK-w Chau ldquoPrediction of remaining service life of pavementusing an optimized support vector machine (case study ofSemnan-Firuzkuh road)rdquo Engineering Applications of Com-putational Fluid Mechanics vol 13 no 1 pp 188ndash198 2019

[24] M Dong ldquoA grey relational analysis between some selectedaffective factors and English test performancerdquo CanadianSocial Science vol 10 no 6 pp 195ndash200 2014

[25] K J Chen X N Li and Y Y Qiu ldquoGray correlation analysison influencing factors of engineering material price in Fujianprovincerdquo Journal of Highway and Transportation Researchand Development vol 35 no 4 pp 137ndash145 2018

[26] V N Vapnik Fe Nature of Statistical Learning FeorySpringer New York NY USA 1995

[27] M J Abdi and D Giveki ldquoAutomatic detection of eryth-emato-squamous diseases using PSO-SVM based on associ-ation rulesrdquo Engineering Applications of Artificial Intelligencevol 26 no 1 pp 603ndash608 2013

[28] Z Liu H Cao X Chen Z He and Z Shen ldquoMulti-faultclassification based on wavelet SVM with PSO algorithm toanalyze vibration signals from rolling element bearingsrdquoNeurocomputing vol 99 pp 399ndash410 2013

[29] Q H Liu Z X Zhang H F Lin and Y Zhu ldquoStudy onprediction of asphalt pavement performance based on supportvector machinerdquo Highway Engineering vol 43 no 2pp 201ndash205 2018

[30] J P Yin ldquoResearch on model selection and parameter se-lection of SVMrdquo Harbin Institute of Technology HarbinChina Doctor degree 2016

[31] X Xue and M Xiao ldquoApplication of genetic algorithm-basedsupport vector machines for prediction of soil liquefactionrdquoEnvironmental Earth Sciences vol 75 no 10 2016

[32] S Abdollahi H R Pourghasemi G A Ghanbarian andR Safaeian ldquoPrioritization of effective factors in the occur-rence of land subsidence and its susceptibility mapping usingan SVM model and their different kernel functionsrdquo Bulletinof Engineering Geology and the Environment vol 78 no 6pp 4017ndash4034 2019

[33] X W Dong Y W Wang G S Zhang and C X Zhou ldquoeprediction of cross-company software defects based on mi-gration learningrdquo Computer Engineering and Design vol 37no 3 pp 684ndash689 2016

[34] X Wang C An Q Fu et al ldquoGrey relational analysis andoptimization of guide vane for reactor coolant pump in thecoasting transient processrdquoAnnals of Nuclear Energy vol 133pp 431ndash440 2019

[35] M Zhang J Yi and D Feng ldquoReasonable thickness design ofexpressway pavement structures based on gray relationanalysis of subgrade soil improvementrdquo Science Progress

[36] I Aydin M Karakose and E Akin ldquoA multi-objective ar-tificial immune algorithm for parameter optimization insupport vector machinerdquo Applied Soft Computing vol 11no 12 pp 204ndash211 2011

[37] X Wang Z Q Wang G Jin and J Yang ldquoLand reserveprediction using different kernel-based support vector re-gressionrdquo Transactions of the Chinese Society of AgriculturalEngineering vol 30 no 4 pp 204ndash211 2014

[38] U Rusmanto I Syafi and D Handayani ldquoStructural andfunctional prediction of pavement condition (A case study onsouth arterial road Yogyakarta)rdquo in Proceeings of the AIPConference Proceedings H Prasetyo N Hidayati E Setiawanet al Eds American Institute of Physics Paris France June2018

[39] C Jia-Ruey and C Sao-Jeng ldquoDevelopment of a ruttingprediction model through accelerated pavement testing usinggroup method of data handling (GMDH)rdquo in Proceedings ofthe 2009 Fifth International Conference on Natural Compu-tation (ICNC 2009) pp 367ndash371 Tianjin China August 2009

[40] J R Chang S H Chen D H Chen and Y B Liu ldquoRuttingprediction model developed by genetic programming methodthrough full scale accelerated pavement testingrdquo in Pro-ceedings of the 2008 Fourth International Conference onNatural Computation M Z Guo L Zhao and L P WangEds IEEE Computer Society p 326 Jinan China October2008

[41] AASHTO guide for design of pavement structures AASHTOGuide for Design of Pavement Structures e American As-sociation of State Highway and Transportation OfficialsWashington DC USA 1993

[42] Highway Performance Assessment Standards Highway Per-formance Assessment Standards Ministry of Transport of thePeoplersquos Republic Beijing China 2018

[43] J L Deng ldquoIntroduction to the grey theoryrdquo Grey Systemsvol 1 no 1 pp 1ndash24 1989

[44] D Zheng Z-D Qian Y Liu and C-B Liu ldquoPrediction andsensitivity analysis of long-term skid resistance of epoxy as-phalt mixture based on GA-BP neural networkrdquo ConstructionAnd Building Materials vol 158 no 15 pp 614ndash623 2018


Du [6] Wang and Li [7] and Zhang and Ji [8] usedthis model to predict pavement smoothness andrutting Peng et al [9] applied Weibull distributionto pavement performance prediction and obtainedideal results

(ii) Certainty model it is an empirical method it takesadvantage of using traditional regression as a tool tofit the data that come from experiments and finiteelement mechanics to get the form and parametersof the model For example Sun and Liu [10] pro-posed the decay equation of asphalt pavementperformance which was obtained through engi-neering experiment Abed et al [11] investigated thevariability effect of thickness and stiffness ofpavement layers they used theMonte Carlo methodto obtain the probability distribution function ofpavement performance by using the parametersGong et al [12] proposed a regularized regressionmethod to estimate the asphalt concrete moduliwith data available from the long-term pavementperformance (LTPP) database

(iii) Bionic model this model has high prediction ac-curacy Yang et al [13] used the genetic neuralnetwork model to estimate rutting and drivingquality Bianchini and Bandini [1] proposed theneuro-fuzzy hybrid model to predict the presentserviceability index (PSI) Ferreira and Lima Cav-alcante [14] and Beltran and Romo [15] presentedthe application of artificial neural networks (ANN)in pavement performance

(iv) Dynamicmodel it is based on the traditional modelFor instance Shen et al [16] improved the tradi-tional grey model and proposed a dynamic greymodel Chen et al [17] combined the US PMEmodel with grey prediction theory and mechanicalexperience method proposed a dynamic grey pre-diction model and established a DGM-PMEcombination model to forecast the rutting Chu andDurango-Cohen [18] used the autoregressivemoving average time series state space method topredict the structural strength of the pavement El-Badawy et al [19] developed a comprehensivebottom-up fatigue cracking distress dynamic pre-diction model integrating the Mechanistic-Empir-ical Pavement Design Guide (MEPDG) andperformance test methodology

To date various pavement performance predictionmodels have been proposed by scholars but the models stillhave defects For example the grey model just adopts thetime factor and does not take into account other factors suchas natural environment and traffic load which may havemaximum impact And as the forecast period increases thestability and accuracy of the prediction are decreasedWeibull distribution model is only suitable for small sampledata prediction e certainty model is mainly determinedby factors like the initial performance index of asphaltpavement and the road age It is simple and convenient to

use for it does not consider the reasonable dynamic data Itonly can predict short period performance e geneticneural network and ANN model are prone to overfittingwhen data are insufficient e dynamic prediction modelcan make full use of the later data to predict longer periodsSimultaneously the reason why the model can only considerthe impact of time on pavement performance is that themodel is based on time series Hence a new model is neededto be devised to be applied to pavement performanceprediction

Recently support vector machines have been applied invarious fields Zhao et al [20] proposed a k-means and SVMhybrid model for the development of an electric vehicleurban driving cycle Hoang et al [21] used it to recognize thepavement crack Wang et al [22] proposed a support vectormachine online model for predicting metro ridershipKarballaeezadeh et al [23] applied this model to the pre-diction of road residual life and compared the model with anartificial neural network (ANN) and multilayer perceptron(MLP) models e results show that the support vectormachine model has the highest accuracy

e factors affecting the performance of asphalt pave-ment were processed firstly by GRA e SVR with ad-vantages of minimizing structural risk and stronggeneralization performance was then used to establish ahyperplane as a decision surface Finally the asphaltpavement performance prediction model was established toprovide a model that can be applied to maintenance deci-sion-making maintenance fund investment and big data ofpavement maintenance

e structure of this paper is as follows Section 2 mainlyintroduces the main principles of GRA-SVR Section 3contains the modeling process of the whole model Section 4mainly uses the model to verify the example Finally theresults are analyzed

2 Methodology

21 Basic Principles of GRA-SVR

211 Basic Principle of Grey Relation Analysis e greysystem theory holds that the complex objective systemswhich are all ordered and discrete data must contain in-herent laws [24] ere are many factors affecting theperformance of asphalt pavement but the effects of variousfactors are not very clear so that we can call the factors greyerefore GRA is used to quantitatively reflect the corre-lation between asphalt pavement performance and variousfactors is method can find the main factors from manyfactors that affect pavement performance e corre-sponding statistical data of the influencing factors in thesystem are converted into geometric curves by the methodand the closer the curve geometry is to the dependentvariable the greater the degree of association is [25]

212 Basic Principle of Support Vector Machine RegressionSVR is a model derived from the support vector machine(SVM) proposed by VAPNIK [26] e SVM model is amachine learning method that mainly solves the








st



i 1 2 l

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(2)



f(x) w middot x + b 11139441

i1ai minus a





L(w ξ b a β) 11139441

i1ai minus

12

1113944

1




1

i1ai minus a






minus xi2) ggt 0


+ r) μgt 0







K(X X1)

K(X X2)

K(X Xn)

Bias b

Output Y

X(1)

X(2)Input X

X(n)














11138681113868111386811138681113868111386811138681113868

Δi Δi(1)Δi(2) Δi(n)( 1113857

i 1 2 m

(6)


M maxi

maxkΔi(k)

N mini

minkΔi(k)

(7)


c0i(k) m + ξM

Δi(k) + ξM ξ isin (0 1) k 1 2 n

i 1 2 m

(8)


wx + b = 0 2||w||

2||w||

wx + b = 1

wx + b = 0

wx + b = ndashε

wx + b = ε

wx + b = ndash1




c0i 1n

1113944

n

i1c0i(k) i 1 2 m (9)






3 Case Verification





SN a1D1 + a2D2m2 + a3D3m3 (10)



SSR l0

l (11)



Start

End

Datacollection

Buildingdata matrix

Normalizethe data


Maximumand


differencesequence

Seekingthe


each factor

Selectdependent

andindependent

variables

Fittingprediction

Train SVRwith

optimalparameters



Selectkernel

function

Selecttraining set

andtest set


SVR

Weatherstation

5TEhumidity sensor


Grey








Soil subgradeA B

Bracket


2

Medianstrip

Marginalstrip


075 375 2 times 375 3 05

C

B



(a) (b)

(c) (d)









(12)








Temperaturesensor

(a)

Temperaturesensor

Humiditysensor

(b)


(a) (b)















y1113888 1113889

β⎡⎣ ⎤⎦

⎧⎨

⎩

⎫⎬

⎭ (13)





Tabl

e2

Relevanceof

each

influ

encing

factor

Influ

encing

factor

c1

c2

c3

c4

c5

c6

c7

c8

c9

c10

c11

c12

c13

c14

c15

c16

c17

c18

c19

c09301

06794

10397

09698

08539

09241

07685

07999

07052

07998

08806

07866

08409

08326

09049

08472

08077

07593

08622


streng

thratio

c2istheservicelife

c3istheequivalent

singleaxleloads

c4isthemaintenance

fund

sc5istheaverageannu

alrainfall

c6isthemeanvalueof

soilmoisture

c7isthemean

valueof

environm

enth

umidity

c8istheannu

almaxim

umwindspeed

c9isthehigh

esttem

perature

ofenvironm

ent

c10

isthelowesttem

perature

oftheenvironm

ent

c11

isthehigh

esttem

perature

ofroad

surface

c12isthelow

esttem

peratureof

road

surface

c13istheh

ighesttemperatureof

uppersurfacec

14isthelow

esttem

peratureof

uppersurfacec

15istheh

ighesttemperaturein

middlesurfacec

16isthelow

est

temperature

inmiddlesurface

c17

isthehigh

esttem

perature

inlower

surface

c18


inlower

surface

c19

istheannu


n




04203603024018012006

048

042

036 03

024

018

012

0060

48

006012018024

03036042048

00601201802403036042048


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Log2

g

(a)

5 6

MSE

4Log2g

0 2

Log2c0

0

02

04

06

08

1


(b)


0035

0035

00350035

007

007

007007

0105

0105

01050105

014

014

014014

0175

0175

01750175

021

021

021021

0245

0245

02450245

028

028

028028

0315

0315

03150315

035

035

035

035

0385

0385

0385

038

5

042

042

042

042

0455

0455

0455

045

5

049

049

049

049


ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Log2

g

(a)

04

0102

3

0304

22

05

15

MSE

06

1 1

07

Log2g050

08

0

09

Log2cndash1 ndash05

1


(b)










Time Originalvalue


Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror




2010 2012 2014 2016 2018 202075

80

85

90

95

RDI

Time (year)



(a) (b) (c)










2010 2012 2014 2016 2018

0

1

2

3

4

5

Abso

lute

erro

r

Time (year)








5 Conclusion





Data Availability




Acknowledgments


References















Uploading


terminal

Database

Feedback












































st



i 1 2 l

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(2)



f(x) w middot x + b 11139441

i1ai minus a





L(w ξ b a β) 11139441

i1ai minus

12

1113944

1




1

i1ai minus a






minus xi2) ggt 0


+ r) μgt 0







K(X X1)

K(X X2)

K(X Xn)

Bias b

Output Y

X(1)

X(2)Input X

X(n)














11138681113868111386811138681113868111386811138681113868

Δi Δi(1)Δi(2) Δi(n)( 1113857

i 1 2 m

(6)


M maxi

maxkΔi(k)

N mini

minkΔi(k)

(7)


c0i(k) m + ξM

Δi(k) + ξM ξ isin (0 1) k 1 2 n

i 1 2 m

(8)


wx + b = 0 2||w||

2||w||

wx + b = 1

wx + b = 0

wx + b = ndashε

wx + b = ε

wx + b = ndash1




c0i 1n

1113944

n

i1c0i(k) i 1 2 m (9)






3 Case Verification





SN a1D1 + a2D2m2 + a3D3m3 (10)



SSR l0

l (11)



Start

End

Datacollection

Buildingdata matrix

Normalizethe data


Maximumand


differencesequence

Seekingthe


each factor

Selectdependent

andindependent

variables

Fittingprediction

Train SVRwith

optimalparameters



Selectkernel

function

Selecttraining set

andtest set


SVR

Weatherstation

5TEhumidity sensor


Grey








Soil subgradeA B

Bracket


2

Medianstrip

Marginalstrip


075 375 2 times 375 3 05

C

B



(a) (b)

(c) (d)









(12)








Temperaturesensor

(a)

Temperaturesensor

Humiditysensor

(b)


(a) (b)















y1113888 1113889

β⎡⎣ ⎤⎦

⎧⎨

⎩

⎫⎬

⎭ (13)





Tabl

e2

Relevanceof

each

influ

encing

factor

Influ

encing

factor

c1

c2

c3

c4

c5

c6

c7

c8

c9

c10

c11

c12

c13

c14

c15

c16

c17

c18

c19

c09301

06794

10397

09698

08539

09241

07685

07999

07052

07998

08806

07866

08409

08326

09049

08472

08077

07593

08622


streng

thratio

c2istheservicelife

c3istheequivalent

singleaxleloads

c4isthemaintenance

fund

sc5istheaverageannu

alrainfall

c6isthemeanvalueof

soilmoisture

c7isthemean

valueof

environm

enth

umidity

c8istheannu

almaxim

umwindspeed

c9isthehigh

esttem

perature

ofenvironm

ent

c10

isthelowesttem

perature

oftheenvironm

ent

c11

isthehigh

esttem

perature

ofroad

surface

c12isthelow

esttem

peratureof

road

surface

c13istheh

ighesttemperatureof

uppersurfacec

14isthelow

esttem

peratureof

uppersurfacec

15istheh

ighesttemperaturein

middlesurfacec

16isthelow

est

temperature

inmiddlesurface

c17

isthehigh

esttem

perature

inlower

surface

c18


inlower

surface

c19

istheannu


n




04203603024018012006

048

042

036 03

024

018

012

0060

48

006012018024

03036042048

00601201802403036042048


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Log2

g

(a)

5 6

MSE

4Log2g

0 2

Log2c0

0

02

04

06

08

1


(b)


0035

0035

00350035

007

007

007007

0105

0105

01050105

014

014

014014

0175

0175

01750175

021

021

021021

0245

0245

02450245

028

028

028028

0315

0315

03150315

035

035

035

035

0385

0385

0385

038

5

042

042

042

042

0455

0455

0455

045

5

049

049

049

049


ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Log2

g

(a)

04

0102

3

0304

22

05

15

MSE

06

1 1

07

Log2g050

08

0

09

Log2cndash1 ndash05

1


(b)










Time Originalvalue


Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror




2010 2012 2014 2016 2018 202075

80

85

90

95

RDI

Time (year)



(a) (b) (c)










2010 2012 2014 2016 2018

0

1

2

3

4

5

Abso

lute

erro

r

Time (year)








5 Conclusion





Data Availability




Acknowledgments


References















Uploading


terminal

Database

Feedback

















































11138681113868111386811138681113868111386811138681113868

Δi Δi(1)Δi(2) Δi(n)( 1113857

i 1 2 m

(6)


M maxi

maxkΔi(k)

N mini

minkΔi(k)

(7)


c0i(k) m + ξM

Δi(k) + ξM ξ isin (0 1) k 1 2 n

i 1 2 m

(8)


wx + b = 0 2||w||

2||w||

wx + b = 1

wx + b = 0

wx + b = ndashε

wx + b = ε

wx + b = ndash1




c0i 1n

1113944

n

i1c0i(k) i 1 2 m (9)






3 Case Verification





SN a1D1 + a2D2m2 + a3D3m3 (10)



SSR l0

l (11)



Start

End

Datacollection

Buildingdata matrix

Normalizethe data


Maximumand


differencesequence

Seekingthe


each factor

Selectdependent

andindependent

variables

Fittingprediction

Train SVRwith

optimalparameters



Selectkernel

function

Selecttraining set

andtest set


SVR

Weatherstation

5TEhumidity sensor


Grey








Soil subgradeA B

Bracket


2

Medianstrip

Marginalstrip


075 375 2 times 375 3 05

C

B



(a) (b)

(c) (d)









(12)








Temperaturesensor

(a)

Temperaturesensor

Humiditysensor

(b)


(a) (b)















y1113888 1113889

β⎡⎣ ⎤⎦

⎧⎨

⎩

⎫⎬

⎭ (13)





Tabl

e2

Relevanceof

each

influ

encing

factor

Influ

encing

factor

c1

c2

c3

c4

c5

c6

c7

c8

c9

c10

c11

c12

c13

c14

c15

c16

c17

c18

c19

c09301

06794

10397

09698

08539

09241

07685

07999

07052

07998

08806

07866

08409

08326

09049

08472

08077

07593

08622


streng

thratio

c2istheservicelife

c3istheequivalent

singleaxleloads

c4isthemaintenance

fund

sc5istheaverageannu

alrainfall

c6isthemeanvalueof

soilmoisture

c7isthemean

valueof

environm

enth

umidity

c8istheannu

almaxim

umwindspeed

c9isthehigh

esttem

perature

ofenvironm

ent

c10

isthelowesttem

perature

oftheenvironm

ent

c11

isthehigh

esttem

perature

ofroad

surface

c12isthelow

esttem

peratureof

road

surface

c13istheh

ighesttemperatureof

uppersurfacec

14isthelow

esttem

peratureof

uppersurfacec

15istheh

ighesttemperaturein

middlesurfacec

16isthelow

est

temperature

inmiddlesurface

c17

isthehigh

esttem

perature

inlower

surface

c18


inlower

surface

c19

istheannu


n




04203603024018012006

048

042

036 03

024

018

012

0060

48

006012018024

03036042048

00601201802403036042048


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Log2

g

(a)

5 6

MSE

4Log2g

0 2

Log2c0

0

02

04

06

08

1


(b)


0035

0035

00350035

007

007

007007

0105

0105

01050105

014

014

014014

0175

0175

01750175

021

021

021021

0245

0245

02450245

028

028

028028

0315

0315

03150315

035

035

035

035

0385

0385

0385

038

5

042

042

042

042

0455

0455

0455

045

5

049

049

049

049


ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Log2

g

(a)

04

0102

3

0304

22

05

15

MSE

06

1 1

07

Log2g050

08

0

09

Log2cndash1 ndash05

1


(b)










Time Originalvalue


Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror




2010 2012 2014 2016 2018 202075

80

85

90

95

RDI

Time (year)



(a) (b) (c)










2010 2012 2014 2016 2018

0

1

2

3

4

5

Abso

lute

erro

r

Time (year)








5 Conclusion





Data Availability




Acknowledgments


References















Uploading


terminal

Database

Feedback







































c0i 1n

1113944

n

i1c0i(k) i 1 2 m (9)






3 Case Verification





SN a1D1 + a2D2m2 + a3D3m3 (10)



SSR l0

l (11)



Start

End

Datacollection

Buildingdata matrix

Normalizethe data


Maximumand


differencesequence

Seekingthe


each factor

Selectdependent

andindependent

variables

Fittingprediction

Train SVRwith

optimalparameters



Selectkernel

function

Selecttraining set

andtest set


SVR

Weatherstation

5TEhumidity sensor


Grey








Soil subgradeA B

Bracket


2

Medianstrip

Marginalstrip


075 375 2 times 375 3 05

C

B



(a) (b)

(c) (d)









(12)








Temperaturesensor

(a)

Temperaturesensor

Humiditysensor

(b)


(a) (b)















y1113888 1113889

β⎡⎣ ⎤⎦

⎧⎨

⎩

⎫⎬

⎭ (13)





Tabl

e2

Relevanceof

each

influ

encing

factor

Influ

encing

factor

c1

c2

c3

c4

c5

c6

c7

c8

c9

c10

c11

c12

c13

c14

c15

c16

c17

c18

c19

c09301

06794

10397

09698

08539

09241

07685

07999

07052

07998

08806

07866

08409

08326

09049

08472

08077

07593

08622


streng

thratio

c2istheservicelife

c3istheequivalent

singleaxleloads

c4isthemaintenance

fund

sc5istheaverageannu

alrainfall

c6isthemeanvalueof

soilmoisture

c7isthemean

valueof

environm

enth

umidity

c8istheannu

almaxim

umwindspeed

c9isthehigh

esttem

perature

ofenvironm

ent

c10

isthelowesttem

perature

oftheenvironm

ent

c11

isthehigh

esttem

perature

ofroad

surface

c12isthelow

esttem

peratureof

road

surface

c13istheh

ighesttemperatureof

uppersurfacec

14isthelow

esttem

peratureof

uppersurfacec

15istheh

ighesttemperaturein

middlesurfacec

16isthelow

est

temperature

inmiddlesurface

c17

isthehigh

esttem

perature

inlower

surface

c18


inlower

surface

c19

istheannu


n




04203603024018012006

048

042

036 03

024

018

012

0060

48

006012018024

03036042048

00601201802403036042048


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Log2

g

(a)

5 6

MSE

4Log2g

0 2

Log2c0

0

02

04

06

08

1


(b)


0035

0035

00350035

007

007

007007

0105

0105

01050105

014

014

014014

0175

0175

01750175

021

021

021021

0245

0245

02450245

028

028

028028

0315

0315

03150315

035

035

035

035

0385

0385

0385

038

5

042

042

042

042

0455

0455

0455

045

5

049

049

049

049


ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Log2

g

(a)

04

0102

3

0304

22

05

15

MSE

06

1 1

07

Log2g050

08

0

09

Log2cndash1 ndash05

1


(b)










Time Originalvalue


Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror




2010 2012 2014 2016 2018 202075

80

85

90

95

RDI

Time (year)



(a) (b) (c)










2010 2012 2014 2016 2018

0

1

2

3

4

5

Abso

lute

erro

r

Time (year)








5 Conclusion





Data Availability




Acknowledgments


References















Uploading


terminal

Database

Feedback











































Soil subgradeA B

Bracket


2

Medianstrip

Marginalstrip


075 375 2 times 375 3 05

C

B



(a) (b)

(c) (d)









(12)








Temperaturesensor

(a)

Temperaturesensor

Humiditysensor

(b)


(a) (b)















y1113888 1113889

β⎡⎣ ⎤⎦

⎧⎨

⎩

⎫⎬

⎭ (13)





Tabl

e2

Relevanceof

each

influ

encing

factor

Influ

encing

factor

c1

c2

c3

c4

c5

c6

c7

c8

c9

c10

c11

c12

c13

c14

c15

c16

c17

c18

c19

c09301

06794

10397

09698

08539

09241

07685

07999

07052

07998

08806

07866

08409

08326

09049

08472

08077

07593

08622


streng

thratio

c2istheservicelife

c3istheequivalent

singleaxleloads

c4isthemaintenance

fund

sc5istheaverageannu

alrainfall

c6isthemeanvalueof

soilmoisture

c7isthemean

valueof

environm

enth

umidity

c8istheannu

almaxim

umwindspeed

c9isthehigh

esttem

perature

ofenvironm

ent

c10

isthelowesttem

perature

oftheenvironm

ent

c11

isthehigh

esttem

perature

ofroad

surface

c12isthelow

esttem

peratureof

road

surface

c13istheh

ighesttemperatureof

uppersurfacec

14isthelow

esttem

peratureof

uppersurfacec

15istheh

ighesttemperaturein

middlesurfacec

16isthelow

est

temperature

inmiddlesurface

c17

isthehigh

esttem

perature

inlower

surface

c18


inlower

surface

c19

istheannu


n




04203603024018012006

048

042

036 03

024

018

012

0060

48

006012018024

03036042048

00601201802403036042048


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Log2

g

(a)

5 6

MSE

4Log2g

0 2

Log2c0

0

02

04

06

08

1


(b)


0035

0035

00350035

007

007

007007

0105

0105

01050105

014

014

014014

0175

0175

01750175

021

021

021021

0245

0245

02450245

028

028

028028

0315

0315

03150315

035

035

035

035

0385

0385

0385

038

5

042

042

042

042

0455

0455

0455

045

5

049

049

049

049


ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Log2

g

(a)

04

0102

3

0304

22

05

15

MSE

06

1 1

07

Log2g050

08

0

09

Log2cndash1 ndash05

1


(b)










Time Originalvalue


Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror




2010 2012 2014 2016 2018 202075

80

85

90

95

RDI

Time (year)



(a) (b) (c)










2010 2012 2014 2016 2018

0

1

2

3

4

5

Abso

lute

erro

r

Time (year)








5 Conclusion





Data Availability




Acknowledgments


References















Uploading


terminal

Database

Feedback












































(12)








Temperaturesensor

(a)

Temperaturesensor

Humiditysensor

(b)


(a) (b)















y1113888 1113889

β⎡⎣ ⎤⎦

⎧⎨

⎩

⎫⎬

⎭ (13)





Tabl

e2

Relevanceof

each

influ

encing

factor

Influ

encing

factor

c1

c2

c3

c4

c5

c6

c7

c8

c9

c10

c11

c12

c13

c14

c15

c16

c17

c18

c19

c09301

06794

10397

09698

08539

09241

07685

07999

07052

07998

08806

07866

08409

08326

09049

08472

08077

07593

08622


streng

thratio

c2istheservicelife

c3istheequivalent

singleaxleloads

c4isthemaintenance

fund

sc5istheaverageannu

alrainfall

c6isthemeanvalueof

soilmoisture

c7isthemean

valueof

environm

enth

umidity

c8istheannu

almaxim

umwindspeed

c9isthehigh

esttem

perature

ofenvironm

ent

c10

isthelowesttem

perature

oftheenvironm

ent

c11

isthehigh

esttem

perature

ofroad

surface

c12isthelow

esttem

peratureof

road

surface

c13istheh

ighesttemperatureof

uppersurfacec

14isthelow

esttem

peratureof

uppersurfacec

15istheh

ighesttemperaturein

middlesurfacec

16isthelow

est

temperature

inmiddlesurface

c17

isthehigh

esttem

perature

inlower

surface

c18


inlower

surface

c19

istheannu


n




04203603024018012006

048

042

036 03

024

018

012

0060

48

006012018024

03036042048

00601201802403036042048


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Log2

g

(a)

5 6

MSE

4Log2g

0 2

Log2c0

0

02

04

06

08

1


(b)


0035

0035

00350035

007

007

007007

0105

0105

01050105

014

014

014014

0175

0175

01750175

021

021

021021

0245

0245

02450245

028

028

028028

0315

0315

03150315

035

035

035

035

0385

0385

0385

038

5

042

042

042

042

0455

0455

0455

045

5

049

049

049

049


ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Log2

g

(a)

04

0102

3

0304

22

05

15

MSE

06

1 1

07

Log2g050

08

0

09

Log2cndash1 ndash05

1


(b)










Time Originalvalue


Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror




2010 2012 2014 2016 2018 202075

80

85

90

95

RDI

Time (year)



(a) (b) (c)










2010 2012 2014 2016 2018

0

1

2

3

4

5

Abso

lute

erro

r

Time (year)








5 Conclusion





Data Availability




Acknowledgments


References















Uploading


terminal

Database

Feedback


















































y1113888 1113889

β⎡⎣ ⎤⎦

⎧⎨

⎩

⎫⎬

⎭ (13)





Tabl

e2

Relevanceof

each

influ

encing

factor

Influ

encing

factor

c1

c2

c3

c4

c5

c6

c7

c8

c9

c10

c11

c12

c13

c14

c15

c16

c17

c18

c19

c09301

06794

10397

09698

08539

09241

07685

07999

07052

07998

08806

07866

08409

08326

09049

08472

08077

07593

08622


streng

thratio

c2istheservicelife

c3istheequivalent

singleaxleloads

c4isthemaintenance

fund

sc5istheaverageannu

alrainfall

c6isthemeanvalueof

soilmoisture

c7isthemean

valueof

environm

enth

umidity

c8istheannu

almaxim

umwindspeed

c9isthehigh

esttem

perature

ofenvironm

ent

c10

isthelowesttem

perature

oftheenvironm

ent

c11

isthehigh

esttem

perature

ofroad

surface

c12isthelow

esttem

peratureof

road

surface

c13istheh

ighesttemperatureof

uppersurfacec

14isthelow

esttem

peratureof

uppersurfacec

15istheh

ighesttemperaturein

middlesurfacec

16isthelow

est

temperature

inmiddlesurface

c17

isthehigh

esttem

perature

inlower

surface

c18


inlower

surface

c19

istheannu


n




04203603024018012006

048

042

036 03

024

018

012

0060

48

006012018024

03036042048

00601201802403036042048


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Log2

g

(a)

5 6

MSE

4Log2g

0 2

Log2c0

0

02

04

06

08

1


(b)


0035

0035

00350035

007

007

007007

0105

0105

01050105

014

014

014014

0175

0175

01750175

021

021

021021

0245

0245

02450245

028

028

028028

0315

0315

03150315

035

035

035

035

0385

0385

0385

038

5

042

042

042

042

0455

0455

0455

045

5

049

049

049

049


ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Log2

g

(a)

04

0102

3

0304

22

05

15

MSE

06

1 1

07

Log2g050

08

0

09

Log2cndash1 ndash05

1


(b)










Time Originalvalue


Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror




2010 2012 2014 2016 2018 202075

80

85

90

95

RDI

Time (year)



(a) (b) (c)










2010 2012 2014 2016 2018

0

1

2

3

4

5

Abso

lute

erro

r

Time (year)








5 Conclusion





Data Availability




Acknowledgments


References















Uploading


terminal

Database

Feedback






































Tabl

e2

Relevanceof

each

influ

encing

factor

Influ

encing

factor

c1

c2

c3

c4

c5

c6

c7

c8

c9

c10

c11

c12

c13

c14

c15

c16

c17

c18

c19

c09301

06794

10397

09698

08539

09241

07685

07999

07052

07998

08806

07866

08409

08326

09049

08472

08077

07593

08622


streng

thratio

c2istheservicelife

c3istheequivalent

singleaxleloads

c4isthemaintenance

fund

sc5istheaverageannu

alrainfall

c6isthemeanvalueof

soilmoisture

c7isthemean

valueof

environm

enth

umidity

c8istheannu

almaxim

umwindspeed

c9isthehigh

esttem

perature

ofenvironm

ent

c10

isthelowesttem

perature

oftheenvironm

ent

c11

isthehigh

esttem

perature

ofroad

surface

c12isthelow

esttem

peratureof

road

surface

c13istheh

ighesttemperatureof

uppersurfacec

14isthelow

esttem

peratureof

uppersurfacec

15istheh

ighesttemperaturein

middlesurfacec

16isthelow

est

temperature

inmiddlesurface

c17

isthehigh

esttem

perature

inlower

surface

c18


inlower

surface

c19

istheannu


n




04203603024018012006

048

042

036 03

024

018

012

0060

48

006012018024

03036042048

00601201802403036042048


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Log2

g

(a)

5 6

MSE

4Log2g

0 2

Log2c0

0

02

04

06

08

1


(b)


0035

0035

00350035

007

007

007007

0105

0105

01050105

014

014

014014

0175

0175

01750175

021

021

021021

0245

0245

02450245

028

028

028028

0315

0315

03150315

035

035

035

035

0385

0385

0385

038

5

042

042

042

042

0455

0455

0455

045

5

049

049

049

049


ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Log2

g

(a)

04

0102

3

0304

22

05

15

MSE

06

1 1

07

Log2g050

08

0

09

Log2cndash1 ndash05

1


(b)










Time Originalvalue


Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror




2010 2012 2014 2016 2018 202075

80

85

90

95

RDI

Time (year)



(a) (b) (c)










2010 2012 2014 2016 2018

0

1

2

3

4

5

Abso

lute

erro

r

Time (year)








5 Conclusion





Data Availability




Acknowledgments


References















Uploading


terminal

Database

Feedback








































04203603024018012006

048

042

036 03

024

018

012

0060

48

006012018024

03036042048

00601201802403036042048


ndash8

ndash6

ndash4

ndash2

0

2

4

6

8

Log2

g

(a)

5 6

MSE

4Log2g

0 2

Log2c0

0

02

04

06

08

1


(b)


0035

0035

00350035

007

007

007007

0105

0105

01050105

014

014

014014

0175

0175

01750175

021

021

021021

0245

0245

02450245

028

028

028028

0315

0315

03150315

035

035

035

035

0385

0385

0385

038

5

042

042

042

042

0455

0455

0455

045

5

049

049

049

049


ndash4

ndash3

ndash2

ndash1

0

1

2

3

4

Log2

g

(a)

04

0102

3

0304

22

05

15

MSE

06

1 1

07

Log2g050

08

0

09

Log2cndash1 ndash05

1


(b)










Time Originalvalue


Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror




2010 2012 2014 2016 2018 202075

80

85

90

95

RDI

Time (year)



(a) (b) (c)










2010 2012 2014 2016 2018

0

1

2

3

4

5

Abso

lute

erro

r

Time (year)








5 Conclusion





Data Availability




Acknowledgments


References















Uploading


terminal

Database

Feedback













































Time Originalvalue


Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror

Predictivevalue

Absoluteerror




2010 2012 2014 2016 2018 202075

80

85

90

95

RDI

Time (year)



(a) (b) (c)










2010 2012 2014 2016 2018

0

1

2

3

4

5

Abso

lute

erro

r

Time (year)








5 Conclusion





Data Availability




Acknowledgments


References















Uploading


terminal

Database

Feedback













































2010 2012 2014 2016 2018

0

1

2

3

4

5

Abso

lute

erro

r

Time (year)








5 Conclusion





Data Availability




Acknowledgments


References















Uploading


terminal

Database

Feedback







































5 Conclusion





Data Availability




Acknowledgments


References















Uploading


terminal

Database

Feedback






































































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A Hybrid Model for Prediction in Asphalt Pavement...

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