Research Article Beam Structure Damage Identification...

Research ArticleBeam Structure Damage Identification Based onBP Neural Network and Support Vector Machine

Bo Yan1 Yao Cui1 Lin Zhang1 Chao Zhang1 Yongzhi Yang1

Zhenming Bao2 and Guobao Ning3

1 Transportation Management College Dalian Maritime University Dalian 116026 China2 School of Naval Architecture Engineering Dalian University of Technology Dalian 116024 China3 School of Automotive Studies Tongji University Shanghai 201804 China

Correspondence should be addressed to Guobao Ning guobao tj163com

Received 10 November 2013 Revised 29 November 2013 Accepted 30 November 2013 Published 6 January 2014

Academic Editor Rui Mu

Copyright copy 2014 Bo Yan et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

It is not easy to findmarine cracks of structures by directly manual testingWhen the cracks of important components are extendedunder extreme offshore environment the whole structure would lose efficacy endanger the staff rsquos safety and course a significanteconomic loss and marine environment pollutionThus early discovery of structure cracks is very important In this paper a beamstructure damage identification model based on intelligent algorithm is firstly proposed to identify partial cracks in supportedbeams on ocean platform In order to obtain the replacementmode and strainmode of the beams the paper takes simple supportedbeamwith single crack anddouble cracks as an exampleThe results show that the difference curves of strainmode change drasticallyonly on the injured part and different degrees of injury would result in different mutation degrees of difference curve more orless While the model based on support vector machine (SVM) and BP neural network can identify cracks of supported beamintelligently the methods can discern injured degrees of sound condition single crack and double cracks Furthermore the twomethods are comparedThe results show that the twomethods presented in the paper have a preferable identification precision andadaptation And damage identification based on support vector machine (SVM) has smaller error results

1 Introduction

The designed life of an offshore platform is usually in 15sim20 years The maintenance cost of it is extremely expensivebut compared with its purchasing expense it seems to beacceptable As a result from economic angle it is importantto evaluate the new platform estimate residual life of existingplatform and prolong the life time of jacket platform forinsuring production safety and improving production effi-ciency extending lifespan and savingmaintenance costThusit is necessary to provide an effective beam structure damageidentification model to timely detect damage evaluate dam-age degree then verify and improve the design method ofcurrent platform and provide references for future structureresidual life assessment

There are many literatures about the damage identi-fication problem Kim and Melhem [1] summarized theapplications of the wavelet analysismethod in system damagechecking and health monitoring in mechanical and otherstructures Sun and Chang [2] utilized wavelet packet trans-form to analyze the signal of structure measurement besidesdamage index based onwavelet packet is given and combinedwith neural network to identify the damage In the 1970sCawley andAdams [3] proposed that using vibration test datainto analog neural network is a method that could be appliedto detect and research material damage Elkordy et al [4] didstructural damage detection by BP network The research isbased on the experimental data of a shaker and a simulateddata of a finite element to carry out the network trainingAnd then the paper used network after training to identify

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 850141 8 pageshttpdxdoiorg1011552014850141

2 Mathematical Problems in Engineering

structural damage Pandey and Barai [5] took the replace-ment under static load asmultilayer perceptronmodelrsquos inputto test and recognize the damages of steel bridge Kirkegaardand Rytter [6] took advantage of the frequency change beforeand after the injury and used the BP neural network to locatethe damage and identify the damage degree of steel beamVakil-Baghmisheh et al [7] proposed an alternative methodof material structural damage identification based on geneticalgorithm An analysis model of a cantilever beamwith crackwas applied to obtain the frequency of structure by numericalsimulation Chou and Ghaboussi [8] thought of the damageproblem as optimization problem and solved the problemwith genetic algorithms Several freedom of static was usedtomeasure the displacement to determine the cross-sectionalarea and the changes of structural elastic modulus Othersuccessful applications can be found in literatures [9 10]

This paper attempts to propose a beam structure damageidentification model based on intelligent algorithm to iden-tify the crack of noncracked beam since BP neural networkand SVM have been successfully applied in solving thesekinds of complex problems [11ndash19] Thus BP neural networkand SVM are also applied to identify the damage degree ofthe beam with crack intelligently in the conditions of goodsingle and double cracks

This paper introduces beam structure damage identi-fication models based on BP neural network and SVMrespectively Therefore the remainder of this paper is orga-nized as follows Section 2 describes beam structure damageidentification models based on BP neural network and SVMrespectively Section 3 attempted to determinate the inputparameters In Section 4 an empirical example was used toexamine the effectiveness of the beam structure damage iden-tification models Conclusions are displayed in Section 5

2 Beam Structure DamageIdentification Model

21 Artificial Neural Network Artificial network a com-puter artificial intelligence based on neural structure andphysiology simulates human thinking Modern computersspecialize in calculation and quick information processingBut for the capacity of dealing with complexity (schemaawareness pattern recognition and making final decisionin complex environment) modern computers are nowherenear as human Modern computers can only implementsome form of the stored-program architecture according toprogram edited in advance and do not have the capacity toadapt to complex environment and study in the environmentThe differences between the way human brain works andthe functions of computer system are great Brain is a highlycomplex nonlinear and parallel processing system which isformed from a jumble of interconnected basic units Thoughthe reaction speed of brain single neuron is lower than thespeed of general computerrsquos basic unit (logic gate) about 5orders ofmagnitude the number of neuron is huge and everysingle neuron can connect with thousands or more otherneurons The brainrsquos speed of processing complex problemsis far more quick than computer

Input signals

Summationy

Activation function

Output

x1

x2

xn

w1

w2

wn

Φ(middot)sum

Figure 1 Model of the neuron

Therefore human takes advantage of the characteristicsof brainrsquos operating mechanism and organizational structurefrom the perspective of emulating the brain intelligencelooking for a better way to storage and handle informationUltimately a new integrated information system based onnew intelligent computer is constructed which is closer tohuman intelligence and can be used for processing complexinformation In this paper artificial neural network is used toidentify the degree of damage of beam structural

211 Neural Model Themodel of neuron is shown in Figure1The basic unit of ANNand the basic elements are as follows

(1) A group of related connection The connectionstrength is represented by the weight given on theconnection line It is in the active state if the weightvalue is positive and in the suppressive state if theweight value is negative

(2) Summation unit It is used to require the weightedsum of a number of input signals

(3) Nonlinear activation function It plays the role of thenonlinear mapping and limits the output amplitudevariation range of neuron The common activationfunction includes segmented linear function thethreshold value function sigmoid function and soon

212 BP Neural Network BP neural network is mostly usedin the beam structure damage identification BP networkalgorithm consists of reverse and forward propagation Itcontains hidden layer output layer and input layer in whichthe states of neurons in each layer can only influence theneurons under them Initially through the process of forwardpropagation the signal is transmitted from the input layerto hidden layer and calculated in the hidden layer Theresults calculated in hidden layer are transmitted to outputlayer and outputted The results are compared with theexpected value and the error will be corrected through thereverse propagation that is backtrack The function in thehidden layer used in the process is called activation functionThis process will be repeated The weight will be changedaccording to the results in last layer during every reversecalculation to reduce the error When the error meets therequirement stop the calculation

The change of BP network connection weights has a highlevel of confidence However this algorithm is a method of

Mathematical Problems in Engineering 3

gradient descent search so it has some inherent characteris-tics which are shown as follows

(1) Slower Convergence In dealing with complex issuesBP algorithm may need training in repetition to achieveconvergence And when the whole network reaches a certainlevel after training the convergence speed of BP network willslow down to a very low level and occupy the machine for along time

(2) Easy to Fall into the Local Minima of Error FunctionAs the BP algorithm uses a gradient descent method tosolve problems the training results gradually approach theminimum of error along the curve surface of the errorfunction However when training for a complex problem itserror function is always high-dimensional space surface Thetraining results are easy to fall into the local minimum ratherthan the global minimum Therefore although the networkweights under the BP algorithm converge to a unique value itis difficult to ensure that the error surface obtained is a globalminimum solution

(3) The Instability of System Training The change of weightis determined by each learning rate If the learning rateis large it can cause the system to become unstable Inthe initial training of the network larger learning rate canobtain faster convergence rate and better error decreases Butit is limited to the early stage of training When trainingreaches later period the high-speed learning efficiency maymake the correction rate of network weight too large Soin the processing of error correction the error beyond theminimum and the system fall into the situation of neverconverge making the whole system unstable

In the classic BP algorithm the learning rate is often setto be a constant which largely determines the performanceof the algorithm High learning rate can improve the effi-ciency of the algorithm effectively but often causes excessivefluctuations in weight and makes the system not stable Lowlearning ratewill elongate learning time andoccupy toomuchmachine To solve this problem related researchers proposeda variety of adaptive learning rate methods In this papercompetitive learning method is used to fix the entire BPneural network

22 Basic Theory of Support Vector Machine Many tradi-tional statistical methods based on law of large numbersrequire large amounts of sample data to be the theoreticalbasis which often do not fit with the reality Because in prac-tice the situationwhere the sample number is shortage is verycommonTheuse of thesemethodsmakes it difficult to obtainsatisfactory results Thus in the last century Vapnik andso forth studied the statistical learning theory (SLT) deeplywhich is a specialized method to study how to use limitednumber of samples formachineThe statistical inference rulesof the theory only consider the asymptotic properties andcan find the optimal solution under the conditions of limitedinformation In mid-1990s the machine learning theoryunder the conditions of the limited sample was developed

and applied gradually And ultimately a relatively completetheoretical system is formed [20]

Support vector machine (SVM) was proposed by Vapnik[21ndash23] which is a statistical-based learning method SVM isbased on a limited sample data and balances the reasoningability and complexity of the model to achieve optimalresults This approach has its unique advantages in solvinghigh-dimensional pattern recognition nonlinear and smallsample event and can also be used in the regression analysisand so on [24]

221 The Feature of SVM The basic features of SVM forclassifying and regressing problems are as follows [25]

(1) SVM is specific for the case of limited samples Thecalculated objective is to obtain the optimal solutionunder the existing data rather than when the samplesare infinity

(2) When the data is linear inseparability the linearlynonseparable data in low-dimensional vector space istransited to high-dimensional vector space by non-linear transformation to make it linearly separableThe data is analyzed and calculated according to thecharacteristics of nonlinear part in high-dimensionalvector space

(3) To minimize the risk experience confidence intervaland optimization of the overall results of learn-ing machine according to the theory of structuralrisk minimization an optimal separating hyperplanemust be obtained in space

222 Principle of SVM Generalized optimal separatinghyperplane Assume that the training data

(119909

1 119910

1) (119909

119897 119910

119897) 119909 isin 119877

119899 119910 isin (+1 minus1) (1)

can be separated by a hyperplane

(120596 sdot 119909) minus 119887 = 0 (2)

without error When the distance between the hyperplaneand its nearest training point is maximum the hyperplane isoptimal hyperplane

To describe the hyperplane the following forms are used

(120596 sdot 119909

119894) minus 119887 ge 1 if119910

119894= 1

(120596 sdot 119909

119894) minus 119887 le minus1 if119910

119894= minus1

(3)

Use the compact form of these inequalities

119910

119894[(120596 sdot 119909

119894) minus 119887] ge 1 119894 = 1 119897 (4)

It is easy to verify that the optimal hyperplane satisfies con-dition formula (3) and attains the following

120601 (120596) = 120596

2 (5)

minimum


120593

Figure 2 The mapping from the original space to feature space

For a hyperplane

(120596

lowastsdot 119909) minus 119887 = 0

1003817

1003817

1003817

1003817

120596

lowast10038171003817

1003817

1003817

= 1 (6)

if vector 119909 is classified according to the following form

119910 =

1 if (120596lowast sdot 119909) minus 119887 ge Δminus1 if (120596lowast sdot 119909) minus 119887 ge Δ

(7)

It is called Δ interval separating hyperplane and has thefollowing information about Δ collection interval separatinghyperplane of VC dimension theorem

Nonlinear problems change from low-dimensional fea-ture space to high-dimensional feature space and the optimallinear hyperplane can be obtained in this space Similarlywith regard to the linearly inseparable problem by thetransformation of nonlinearmapping function the input datain the low-dimensional space is converted into the high-dimensional space so as to achieve the purpose of solving theproblem To solve the above problem in the high-dimensionalfeature space it only needs to make inner product operationto kernel function 119870(119909

119894 119909

119895) = (119909

119894)(119909

119895) in original space

This is determined by the fact that there are no other opera-tions expecting the inner product operation among the train-ing samples of classification function and optimization func-tions

Therefore most of the nonlinear problems in originalspace can be transformed into a linear separable problemafterspace conversion as shown in Figure 2

However the difficulty of transforming the nonlinearproblem into a high-dimensional space is that the nonlinearmapping in this process may be very complex According tofunctional theory as long as the kernel function 119870(119909

119894 119909

119895)

satisfies Mercer conditions it must correspond to the innerproduct of one space For such conversion it is not necessaryto have a specific transformation process In order to avoidcomplex calculations in such high-dimensional space thekernel function 119870(119909 1199091015840) is used to replace the dot productof optimal separating hyperplane and the problem can besolved However this method is based on the fact that thelinear classification function does not include any other oper-ations expecting support vector inner product of the trainingsample and the sample to be classified At the same timein the solution process this function only takes the inner

Table 1 Common kernel function

Kernel function Expression ParameterLiner kernelfunction 119870(119909

119894 119909

119895) = 119909

119894sdot 119909

119895

Polynomial kernelfunction 119870(119909

119894 119909

119895) = (119909

119894sdot 119909

119895+ 1)

119889

119889

Radial basisfunction (RBF)kernel function

119870(119909

119894 119909

119895) = exp (minus120574100381710038171003817

1003817

1003817

119909

119894minus 119909

119895

1003817

1003817

1003817

1003817

1003817

2

) 120574 gt 0

Sigmoid kernelfunction 119870(119909

119894 119909

119895) = tanh (119887 (119909

119894 119909

119895) + 119888) 119887 119888

product operation to training samples The classificationfunction of this method in the sample space can be written as

119891 (119909) = sgn(119899

sum

119894=1

120572

lowast

119894119910

119894119870(119909

119894 119910

119894)) + 119887 (8)

The choice of kernel function needs to meet Mercer condi-tions and different forms of kernel functions can produce dif-ferent support vector machines (see Table 1)

3 Input Parameter Determination

In the process of damage identification when training thesample data is based on the parameters of displacement vibra-tion models or their derivatives whether it is artificial neuralnetwork or support vector machine the final recognitionresults may produce great error and sometimes even producedisorder phenomenon so the parameter settings must bepaid attention to Strain mode is a very sensitive parameter toinjury It has advantages of high accuracy being easy to testmature analytical methods and many others In fact whenthe artificial neural network is used to train if the accuracyof the input parameters is ensured to be high enough theresults of the degree of damage recognition must be accurateand efficient On the contrary if the precision is lacking therecognition results can not be guaranteedTherefore it is rea-sonable to select the strain mode difference parameter as theinput data of support vector machine model and the neuralnetwork in this chapterThe flowchart of the two smartmeth-ods of beam structure damage identification is in Figure 3


Determine thenumerical model

Model analysisObtain the

parameters ofstrain model

Constructdamage index

Preprocess theindex

Determine the inputparameters ofSVM (ANN)

Realize the algorithm ofSVM (ANN) byprogramming

Confirm related parametersof SVM (ANN)

Train and evaluate the training effectTest and evaluate the testing effect

Finally confirm the resultsof damage identification

Dissatisfaction Dissatisfaction

Satisfaction

Figure 3 Flowchart of damage identification for beam structure

Figure 4 FEMmodel of a supported beam with local damage

4 Empirical Example

A simple supported beam with localized damage is shownin Figure 4 The geometric dimensions are that the length is400mm the width is 10mm and the height is 2mm Thebeam is used to simulate the conditions the fourth quartersingle crack across the fourth quarter double cracks acrossand so on The crack length is 15 of the beam width andthe crack depth is 3125 6250 12500 and 15625 ofthe effective section height The crack width is 2mm Themodulus is 211 GPa and density is 7850Kgm3 The Poissonrsquosratio is set to be 033 Eight-node SOLID45 solid element ofANSYS finite element analysis software is applied to modelGrid is divided into 25 equal parts in horizon 16 equal partsvertically and 40 equal parts in length

41 Intelligent Recognition with BP Neural Network Thetraining samples of BP neural network should choose contin-uous third strainmode difference of beamThus input vectorof network training is three-dimensional and the outputvector is one-dimensionalThey represent the damage degree

Table 2 The damage identification results of single quarter crackwith 1 noise level

Workingconditionnumber

Damageelement number

Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3150No 2 10 6250 6300No 3 10 12500 12520No 4 10 15625 15650

of one unit So in order to build a three-tier network threeinput layer neurons and output layer neurons are neededThrough repeated trials when the neurons in hidden layerare 6 in the final the training effect is optimal (speed andaccuracy of training) Assuming the damage degree of beamwas 3125 6250 12500 and 15625 the sampleswhose damage degree is 20 are used as test samples to verifythe damage identification capability of the neural networkAt the same time the effects of noise are taken into accountThus random noise is added into the strain model when thedamage cases were calculated The added noise levels are 1and 3 The test results of the network are shown in Tables 2and 3

It can be seen from Table 2 when the level of noise is 1the effect of identification is good while the identificationerrors of each unit are all small The largest error is only 08which occurred in the case 3 The recognition effect is stillgood when the level of noise is 3 but the biggest error isslightly larger reaching 112 which appeared in the case 3Therefore when the noise level is 1 the recognition resultsof damage are more excellent which can be seen in Tables 4and 5





Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3160No 2 10 6250 6310No 3 10 12500 12540No 4 10 15625 15680

Table 4The damage identification results of double cracks with 1noise level



Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 318020 3125 3150

No 2 10 6250 632020 6250 6300

No 3 10 12500 1249020 12500 12460

No 4 10 15625 1566020 15625 15640




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 319020 3125 3170

No 2 10 6250 635020 6250 6330

No 3 10 12500 1246020 12500 12470

No 4 10 15625 1569020 15625 15670

42 Intelligent Recognition with Support Vector MachineAssuming that the damage extent of beam is 3125 625012500 and 15625 these samples are taken as the trainingsamples The samples whose damage extent is 20 are usedas test samples to verify the damage identification capabilityof this neural network The input parameters are the strainmodes difference of the first 3 structural orders The damagerecognition results are shown in Tables 6 and 7

43 The Comparison of Recognition Performance between BPNeural Networks and Support Vector Machine

(1) The Comparison of Run Time It needs at least 37 times ofiterations on average that the BP neural network can achieve

Table 6 Damage degree recognition results of single crack insupport vector machine



Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3200No 2 10 6250 6290No 3 10 12500 12510No 4 10 15625 15640

Table 7 Damage degree recognition results of double cracks insupport vector machine



Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 314020 3125 3130

No 2 10 6250 629020 6250 6280

No 3 10 12500 1247020 12500 12450

No 4 10 15625 1565020 15625 15630

the specified error while the average running time is 3minutes and 12 seconds The SVM requires only one minutetime to achieve the results This showed that the learningconvergence speed of SVM is quick and can approximate anynonlinear function

(2) The Contrast of Recognition Results The difference ofprediction error between SVMmodel and BP neural networkmodel is less The error has been very small in some unitsand did not affect the discrimination of damage elementsThrough the errors of the two methods support vectormachine is slightly better than BP neural networkmodelThisis because the support vector machine is built on the VCdimension theory and structural riskminimization principleIts generalization ability is stronger and can effectively avoidthe overlearning problems So SVM can ensure finding theglobal optimal solution Therefore support vector machinealgorithm is more accurate for solving the damage positionproblem of beam structural The accuracy of recognitionresults for single crack and double cracks with the SVMis better than the results of BP neural network So it is abetter approach to identify the degree of injury The averagerecognition accuracy of structural damage degree of the twomethods is shown in Table 8

44 Performance Analysis of the Identification Models Basedon BP Neural Networks and SVM The results of SVM andBP neural network are significantly better than the resultsof ordinary SVM or BP neural network model Due tocontinuous interactive analysis and improvement the resultsof the improved model are obtained from smart model This


Table 8 Damage degree determination accuracy of the two meth-ods

TypeWorkingconditionnumber

Recognitionefficiency of BPneural network

Recognitionefficiency of

SVMSingle crack 1 999 100Double cracks 2 996 999

suggests that support vectormachinemodel or BP neural net-work model can effectively remove outliers to ensure higherprediction accuracy The computing inspiration of BP neuralnetwork is from the structure and function of biologicalneural network The neurons of BP neural network are inter-connected to form a group which handles the calculationmethod of link information Inmost cases BPneural networkis an adaptive system Compared with BP neural networkmodel BP neural network algorithm is difficult to achievesatisfactory results SVM model can identify beam struc-ture damage better The computational complexity of SVMdepends on the number of support vectors Support vectormachines can reach the global optimum while the BP neuralnetwork tends to fall into a local optimal solution So supportvector machine is a powerful tool to identify the degree ofstructural damage

5 Conclusions

The paper expounds the basic theories of neural network andsupport vector machine Using the two methods damagesin local damaged beams structure is located And the strainmodel differences are selected to be input parameters Inthe example of a simple supported beam the strain modeldifferentials of sound condition a quarter of single crackedcondition a quarter of double cracked condition and doublecracked midspan condition are imported The crack depthsof these conditions are 3125 6250 12500 and 15625respectively The samples are taken as training samples and20 damage degree samples served as testing samples thatverified the capacities of damage identification of supportvector machine and BP neural network Considering noiseeffect the noise levels of BP neural network are added into1 and 3 In this paper both of the two methods could gaina preferable identification precision and adaptation under theconditions of single crack and double cracks And the beamstructure damage identification model base on SVM is ofsmaller error less operation time and better veracity

Thus themain contributions of this paper to the literaturecan be summarized as follows Firstly it attempts to developthe models to identify the beam structure damage It isexpected to help to efficiently make reasonable and effectivemeasures to reduce the harm of damage Secondly in order toimprove the identification accuracy the beam structure dam-age identification model based on support vector machineand BP neural network is used to identify the damage levelThe performance of the proposed model can provide somevaluable insight for researchers as well as practitioners

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of the paper

Acknowledgment

This work was supported by Grants from the FundamentalResearch Funds for the Central Universities nos 3132013337-4-5 and 3132013079

References

[1] H Kim and H Melhem ldquoDamage detection of structures bywavelet analysisrdquo Engineering Structures vol 26 no 3 pp 347ndash362 2004

[2] Z Sun and C C Chang ldquoStructural damage assessment basedon wavelet packet transformrdquo Journal of Structural Engineeringvol 128 no 10 pp 1354ndash1361 2002

[3] P Cawley and R D Adams ldquoImproved frequency resolutionfrom transient tests with short record lengthsrdquo Journal of Soundand Vibration vol 64 no 1 pp 123ndash132 1979

[4] M F Elkordy K C Chang and G C Lee ldquoNeural networkstrained by analytically simulated damage statesrdquo Journal ofComputing in Civil Engineering vol 7 no 2 pp 130ndash145 1993

[5] P C Pandey and S V Barai ldquoMultilayer perceptron in damagedetection of bridge structuresrdquo Computers and Structures vol54 no 4 pp 597ndash608 1995

[6] P H Kirkegaard and A Rytter ldquoThe use of neural networksfor damage detection and location in a steel memberrdquo inNeural Networks and Combinatorial Optimization in Civil andStructural Engineering pp 1ndash9 Civil-Comp Press EdinburghUK 1993

[7] M-TVakil-BaghmishehM PeimaniMH Sadeghi andMMEttefagh ldquoCrack detection in beam-like structures using geneticalgorithmsrdquo Applied Soft Computing Journal vol 8 no 2 pp1150ndash1160 2008

[8] J-H Chou and J Ghaboussi ldquoGenetic algorithm in structuraldamage detectionrdquoComputers and Structures vol 79 no 14 pp1335ndash1353 2001

[9] W J Yi and X Liu ldquoDamage diagnosis of structures by geneticalgorithmsrdquo Engineering Mechanics vol 18 no 2 pp 64ndash712001

[10] Y Y Lee and K W Liew ldquoDetection of damage location in abeam using the wavelet analysisrdquo International Journal of Struc-tural Stability and Dynamics vol 1 no 3 pp 455ndash465 2001

[11] B-Z Yao C-Y Yang J-B Yao and J Sun ldquoTunnel surroundingrock displacement prediction using support vector machinerdquoInternational Journal of Computational Intelligence Systems vol3 no 6 pp 843ndash852 2010

[12] B Yao C Yang J Hu J Yao and J Sun ldquoAn improved antcolony optimization for flexible job shop scheduling problemsrdquoAdvanced Science Letters vol 4 no 6-7 pp 2127ndash2131 2011

[13] B Z Yao PHuMH Zhang and SWang ldquoArtificial bee colonyalgorithm with scanning strategy for periodic vehicle routingproblemrdquo SIMULATION vol 89 no 6 pp 762ndash770 2013

[14] B YuWHK Lam andM L Tam ldquoBus arrival time predictionat bus stopwithmultiple routesrdquoTransportation Research C vol19 no 6 pp 1157ndash1170 2011

[15] B Yu and Z Z Yang ldquoAn ant colony optimization model theperiod vehicle routing problem with time windowsrdquo Trans-portation Research E vol 47 no 2 pp 166ndash181 2011


[16] B Yu Z Z Yang and S Li ldquoReal-time partway deadheadingstrategy based on transit service reliability assessmentrdquo Trans-portation Research A vol 46 no 8 pp 1265ndash1279 2012

[17] Y Bin Y Zhongzhen and Y Baozhen ldquoBus arrival time pre-diction using support vector machinesrdquo Journal of IntelligentTransportation Systems vol 10 no 4 pp 151ndash158 2006

[18] B Yu Z-Z Yang and B Yao ldquoAn improved ant colony opti-mization for vehicle routing problemrdquo European Journal of Ope-rational Research vol 196 no 1 pp 171ndash176 2009

[19] H Zhou W Li C Zhang and J Liu ldquoIce breakup forecastin the reach of the Yellow River the support vector machinesapproachrdquo Hydrology and Earth System Sciences Discussionsvol 6 no 2 pp 3175ndash3198 2009

[20] M K Mayer ldquoA network parallel genetic algorithm for the onemachine sequencing problemrdquo Computers amp Mathematics withApplications vol 37 no 3 pp 71ndash78 1999

[21] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[22] V N Vapnik ldquoAn overview of statistical learning theoryrdquo IEEETransactions on Neural Networks vol 10 no 5 pp 988ndash9991999


[24] B Dengiz F Altiparmak and A E Smith ldquoLocal search gen-etic algorithm for optimal design of reliable networksrdquo IEEETransactions on Evolutionary Computation vol 1 no 3 pp 179ndash188 1997

[25] M L M Beckers E P P A Derks W J Melssen and L M CBuydens ldquoParallel processing of chemical information in a localarea networkmdashIII Using genetic algorithms for conformationalanalysis of biomacromoleculesrdquo Computers and Chemistry vol20 no 4 pp 449ndash457 1996

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structural damage Pandey and Barai [5] took the replace-ment under static load asmultilayer perceptronmodelrsquos inputto test and recognize the damages of steel bridge Kirkegaardand Rytter [6] took advantage of the frequency change beforeand after the injury and used the BP neural network to locatethe damage and identify the damage degree of steel beamVakil-Baghmisheh et al [7] proposed an alternative methodof material structural damage identification based on geneticalgorithm An analysis model of a cantilever beamwith crackwas applied to obtain the frequency of structure by numericalsimulation Chou and Ghaboussi [8] thought of the damageproblem as optimization problem and solved the problemwith genetic algorithms Several freedom of static was usedtomeasure the displacement to determine the cross-sectionalarea and the changes of structural elastic modulus Othersuccessful applications can be found in literatures [9 10]

This paper attempts to propose a beam structure damageidentification model based on intelligent algorithm to iden-tify the crack of noncracked beam since BP neural networkand SVM have been successfully applied in solving thesekinds of complex problems [11ndash19] Thus BP neural networkand SVM are also applied to identify the damage degree ofthe beam with crack intelligently in the conditions of goodsingle and double cracks

This paper introduces beam structure damage identi-fication models based on BP neural network and SVMrespectively Therefore the remainder of this paper is orga-nized as follows Section 2 describes beam structure damageidentification models based on BP neural network and SVMrespectively Section 3 attempted to determinate the inputparameters In Section 4 an empirical example was used toexamine the effectiveness of the beam structure damage iden-tification models Conclusions are displayed in Section 5

2 Beam Structure DamageIdentification Model

21 Artificial Neural Network Artificial network a com-puter artificial intelligence based on neural structure andphysiology simulates human thinking Modern computersspecialize in calculation and quick information processingBut for the capacity of dealing with complexity (schemaawareness pattern recognition and making final decisionin complex environment) modern computers are nowherenear as human Modern computers can only implementsome form of the stored-program architecture according toprogram edited in advance and do not have the capacity toadapt to complex environment and study in the environmentThe differences between the way human brain works andthe functions of computer system are great Brain is a highlycomplex nonlinear and parallel processing system which isformed from a jumble of interconnected basic units Thoughthe reaction speed of brain single neuron is lower than thespeed of general computerrsquos basic unit (logic gate) about 5orders ofmagnitude the number of neuron is huge and everysingle neuron can connect with thousands or more otherneurons The brainrsquos speed of processing complex problemsis far more quick than computer

Input signals

Summationy

Activation function

Output

x1

x2

xn

w1

w2

wn

Φ(middot)sum

Figure 1 Model of the neuron

Therefore human takes advantage of the characteristicsof brainrsquos operating mechanism and organizational structurefrom the perspective of emulating the brain intelligencelooking for a better way to storage and handle informationUltimately a new integrated information system based onnew intelligent computer is constructed which is closer tohuman intelligence and can be used for processing complexinformation In this paper artificial neural network is used toidentify the degree of damage of beam structural

211 Neural Model Themodel of neuron is shown in Figure1The basic unit of ANNand the basic elements are as follows

(1) A group of related connection The connectionstrength is represented by the weight given on theconnection line It is in the active state if the weightvalue is positive and in the suppressive state if theweight value is negative

(2) Summation unit It is used to require the weightedsum of a number of input signals

(3) Nonlinear activation function It plays the role of thenonlinear mapping and limits the output amplitudevariation range of neuron The common activationfunction includes segmented linear function thethreshold value function sigmoid function and soon

212 BP Neural Network BP neural network is mostly usedin the beam structure damage identification BP networkalgorithm consists of reverse and forward propagation Itcontains hidden layer output layer and input layer in whichthe states of neurons in each layer can only influence theneurons under them Initially through the process of forwardpropagation the signal is transmitted from the input layerto hidden layer and calculated in the hidden layer Theresults calculated in hidden layer are transmitted to outputlayer and outputted The results are compared with theexpected value and the error will be corrected through thereverse propagation that is backtrack The function in thehidden layer used in the process is called activation functionThis process will be repeated The weight will be changedaccording to the results in last layer during every reversecalculation to reduce the error When the error meets therequirement stop the calculation

The change of BP network connection weights has a highlevel of confidence However this algorithm is a method of















(119909

1 119910

1) (119909

119897 119910

119897) 119909 isin 119877

119899 119910 isin (+1 minus1) (1)


(120596 sdot 119909) minus 119887 = 0 (2)



(120596 sdot 119909

119894) minus 119887 ge 1 if119910

119894= 1

(120596 sdot 119909

119894) minus 119887 le minus1 if119910

119894= minus1

(3)


119910

119894[(120596 sdot 119909

119894) minus 119887] ge 1 119894 = 1 119897 (4)


120601 (120596) = 120596

2 (5)

minimum


120593


For a hyperplane

(120596


1003817

1003817

1003817

1003817

120596

lowast10038171003817

1003817

1003817

= 1 (6)


119910 =


(7)



119894 119909

119895) = (119909

119894)(119909





119894 119909

119895)




119894 119909

119895) = 119909

119894sdot 119909

119895


119894 119909

119895) = (119909

119894sdot 119909

119895+ 1)

119889

119889


119870(119909

119894 119909

119895) = exp (minus120574100381710038171003817

1003817

1003817

119909

119894minus 119909

119895

1003817

1003817

1003817

1003817

1003817

2

) 120574 gt 0


119894 119909

119895) = tanh (119887 (119909

119894 119909

119895) + 119888) 119887 119888


119891 (119909) = sgn(119899

sum

119894=1

120572

lowast

119894119910

119894119870(119909

119894 119910

119894)) + 119887 (8)









Preprocess theindex







Satisfaction



4 Empirical Example






Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3150No 2 10 6250 6300No 3 10 12500 12520No 4 10 15625 15650







Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3160No 2 10 6250 6310No 3 10 12500 12540No 4 10 15625 15680




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 318020 3125 3150

No 2 10 6250 632020 6250 6300

No 3 10 12500 1249020 12500 12460

No 4 10 15625 1566020 15625 15640




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 319020 3125 3170

No 2 10 6250 635020 6250 6330

No 3 10 12500 1246020 12500 12470

No 4 10 15625 1569020 15625 15670







Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3200No 2 10 6250 6290No 3 10 12500 12510No 4 10 15625 15640




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 314020 3125 3130

No 2 10 6250 629020 6250 6280

No 3 10 12500 1247020 12500 12450

No 4 10 15625 1565020 15625 15630











5 Conclusions





Acknowledgment


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra























(119909

1 119910

1) (119909

119897 119910

119897) 119909 isin 119877

119899 119910 isin (+1 minus1) (1)


(120596 sdot 119909) minus 119887 = 0 (2)



(120596 sdot 119909

119894) minus 119887 ge 1 if119910

119894= 1

(120596 sdot 119909

119894) minus 119887 le minus1 if119910

119894= minus1

(3)


119910

119894[(120596 sdot 119909

119894) minus 119887] ge 1 119894 = 1 119897 (4)


120601 (120596) = 120596

2 (5)

minimum


120593


For a hyperplane

(120596


1003817

1003817

1003817

1003817

120596

lowast10038171003817

1003817

1003817

= 1 (6)


119910 =


(7)



119894 119909

119895) = (119909

119894)(119909





119894 119909

119895)




119894 119909

119895) = 119909

119894sdot 119909

119895


119894 119909

119895) = (119909

119894sdot 119909

119895+ 1)

119889

119889


119870(119909

119894 119909

119895) = exp (minus120574100381710038171003817

1003817

1003817

119909

119894minus 119909

119895

1003817

1003817

1003817

1003817

1003817

2

) 120574 gt 0


119894 119909

119895) = tanh (119887 (119909

119894 119909

119895) + 119888) 119887 119888


119891 (119909) = sgn(119899

sum

119894=1

120572

lowast

119894119910

119894119870(119909

119894 119910

119894)) + 119887 (8)









Preprocess theindex







Satisfaction



4 Empirical Example






Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3150No 2 10 6250 6300No 3 10 12500 12520No 4 10 15625 15650







Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3160No 2 10 6250 6310No 3 10 12500 12540No 4 10 15625 15680




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 318020 3125 3150

No 2 10 6250 632020 6250 6300

No 3 10 12500 1249020 12500 12460

No 4 10 15625 1566020 15625 15640




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 319020 3125 3170

No 2 10 6250 635020 6250 6330

No 3 10 12500 1246020 12500 12470

No 4 10 15625 1569020 15625 15670







Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3200No 2 10 6250 6290No 3 10 12500 12510No 4 10 15625 15640




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 314020 3125 3130

No 2 10 6250 629020 6250 6280

No 3 10 12500 1247020 12500 12450

No 4 10 15625 1565020 15625 15630











5 Conclusions





Acknowledgment


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










120593


For a hyperplane

(120596


1003817

1003817

1003817

1003817

120596

lowast10038171003817

1003817

1003817

= 1 (6)


119910 =


(7)



119894 119909

119895) = (119909

119894)(119909





119894 119909

119895)




119894 119909

119895) = 119909

119894sdot 119909

119895


119894 119909

119895) = (119909

119894sdot 119909

119895+ 1)

119889

119889


119870(119909

119894 119909

119895) = exp (minus120574100381710038171003817

1003817

1003817

119909

119894minus 119909

119895

1003817

1003817

1003817

1003817

1003817

2

) 120574 gt 0


119894 119909

119895) = tanh (119887 (119909

119894 119909

119895) + 119888) 119887 119888


119891 (119909) = sgn(119899

sum

119894=1

120572

lowast

119894119910

119894119870(119909

119894 119910

119894)) + 119887 (8)









Preprocess theindex







Satisfaction



4 Empirical Example






Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3150No 2 10 6250 6300No 3 10 12500 12520No 4 10 15625 15650







Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3160No 2 10 6250 6310No 3 10 12500 12540No 4 10 15625 15680




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 318020 3125 3150

No 2 10 6250 632020 6250 6300

No 3 10 12500 1249020 12500 12460

No 4 10 15625 1566020 15625 15640




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 319020 3125 3170

No 2 10 6250 635020 6250 6330

No 3 10 12500 1246020 12500 12470

No 4 10 15625 1569020 15625 15670







Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3200No 2 10 6250 6290No 3 10 12500 12510No 4 10 15625 15640




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 314020 3125 3130

No 2 10 6250 629020 6250 6280

No 3 10 12500 1247020 12500 12450

No 4 10 15625 1565020 15625 15630











5 Conclusions





Acknowledgment


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














Preprocess theindex







Satisfaction



4 Empirical Example






Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3150No 2 10 6250 6300No 3 10 12500 12520No 4 10 15625 15650







Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3160No 2 10 6250 6310No 3 10 12500 12540No 4 10 15625 15680




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 318020 3125 3150

No 2 10 6250 632020 6250 6300

No 3 10 12500 1249020 12500 12460

No 4 10 15625 1566020 15625 15640




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 319020 3125 3170

No 2 10 6250 635020 6250 6330

No 3 10 12500 1246020 12500 12470

No 4 10 15625 1569020 15625 15670







Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3200No 2 10 6250 6290No 3 10 12500 12510No 4 10 15625 15640




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 314020 3125 3130

No 2 10 6250 629020 6250 6280

No 3 10 12500 1247020 12500 12450

No 4 10 15625 1565020 15625 15630











5 Conclusions





Acknowledgment


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3160No 2 10 6250 6310No 3 10 12500 12540No 4 10 15625 15680




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 318020 3125 3150

No 2 10 6250 632020 6250 6300

No 3 10 12500 1249020 12500 12460

No 4 10 15625 1566020 15625 15640




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 319020 3125 3170

No 2 10 6250 635020 6250 6330

No 3 10 12500 1246020 12500 12470

No 4 10 15625 1569020 15625 15670







Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 3200No 2 10 6250 6290No 3 10 12500 12510No 4 10 15625 15640




Ideal result ofSVM

Actual result ofSVM

No 1 10 3125 314020 3125 3130

No 2 10 6250 629020 6250 6280

No 3 10 12500 1247020 12500 12450

No 4 10 15625 1565020 15625 15630











5 Conclusions





Acknowledgment


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















5 Conclusions





Acknowledgment


References


































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article Beam Structure Damage Identification...

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