Research Article Displacement Prediction of Tunnel ...downloads.hindawi.com/journals/mpe/2014/351496.pdf · Displacement prediction of tunnel surrounding rock plays an important role

Research ArticleDisplacement Prediction of Tunnel SurroundingRock A Comparison of Support Vector Machine andArtificial Neural Network

Qingdong Wu1 Bo Yan2 Chao Zhang2 Lu Wang3 Guobao Ning4 and B Yu5

1 Shandong Luqiao Group CO Ltd Jinan 250021 China2 Transportation Management College Dalian Maritime University Dalian 116026 China3 China Academy of Civil Aviation Science and Technology Beijing 100028 China4 School of Automotive Studies Tongji University Shanghai 201804 China5 School of Traffic and Transportation Beijing Jiaotong University Beijing 100044 China

Correspondence should be addressed to Guobao Ning guobao tj163com and B Yu yubjjt126com

Received 5 May 2014 Revised 13 July 2014 Accepted 14 July 2014 Published 23 July 2014

Academic Editor Rui Mu

Copyright copy 2014 Qingdong Wu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Displacement prediction of tunnel surrounding rock plays an important role in safety monitoring and quality control tunnelconstruction In this paper two methodologies support vector machines (SVM) and artificial neural network (ANN) areintroduced to predict tunnel surrounding rock displacementThen the twomodes are texted with the data of Fangtianchong tunnelrespectively The comparative results show that solutions gained by SVM seem to be more robust with a smaller standard errorcompared to ANN Generally the comparison between artificial neural network (ANN) and SVM shows that SVM has a higheraccuracy prediction than ANN Results also show that SVM seems to be a powerful tool for tunnel surrounding rock displacementprediction

1 Introduction

Limited by geographic condition digging method and manyother factors the loading features of tunnel constructionare extremely complicated As a result the displacement oftunnel surrounding rock has random variations Althoughthe conditions of tunnel surrounding field monitoring couldbe gained by field monitoring the field monitor requiredmany resources that could not be afforded by constructors[1 2] Meanwhile tunnel surrounding rock distortion andtunnel lining crack could also lead to the instability of thetunnel during tunnel construction [3] So it is necessary toestimate the potential tunneling problems as early as possible

Along with the development of information technolo-gies a number of intelligent algorithms such as regressionanalysis gray theory data smoothing processing time seriesanalysis and genetic algorithm [4ndash13] have been applied topredict the displacement of tunnel surrounding rocks [1415] Till now there are many literatures that have studied

the displacement prediction of tunnel surrounding rock [16]Parlos et al [17] presented a multistep-ahead prediction forthe systems of high complexity and a new method that isproved that it could be used to increase the accuracy ofprediction relying on a dynamic recurrent neural networkBesides the dynamic model Cheng et al [18] also presented amultistep-ahead prediction model which is not relying on adynamic recurrent neural network but uses a method basedon support vector machine (SVM) to predict and diagnosethe type of long-term changes of hydropower structures Inthemodel to diagnose the long-term changes of hydropowera dynamic spline interpolation is established based on amultilayer adaptive time delayed network to ensure theprediction accuracy In order to solve the nonlinear timeseries problems Lee et al [19] also proposedmultistep-aheadmodel based on article neutral network to improve the robustand accuracy of predicting in solving this type of problemsAnd recently Chevillon et al [20] proposed that not onlythemultistep-aheadmodel but also the nonparametric direct

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 351496 6 pageshttpdxdoiorg1011552014351496

2 Mathematical Problems in Engineering

multistep-aheadmodel could be used to predict the reliabilityof surrounding rock and other geographic structures Thereare also some other studies that rely on multistep-aheadmodel to do the predicting [21 22] In general in recent yearsthere are more and more researchers and institutions whichtend to use themultistep-aheadmodel to predict the complexinternal structures

Nevertheless as many researchers stated the accuracy ofthe predicting models based on the multistep-ahead modelextremely relied on the similarity between the present andprevious data And considering the complexity of internalstructure it is almost impossible to gain a large amountof accurate historical data Therefore with the unreliablehistorical data the predicting results could also becomeseriously incorrect Alongwith the development of intelligentrockmechanics artificial neural network (ANN) technique isgradually matured and widely used In recent years ANN hasbeen successfully applied in the field of tunnel surroundingrock displacement prediction Meanwhile thanks to thedevelopment of statistical learning theory support vectormachine (SVM) as a new machine learning technology hasdrawnmuch attention in the research area of time series fore-casting Therefore in the paper two models displacementprediction of tunnel surrounding rock based on ANN anddisplacement prediction of tunnel surrounding rock basedon SVM are presented And then in order to compare thetwo models in the last section the two models are evaluatedwith data of Fangtianchong tunnel respectively If the simplemodels presented in the paper could be applied to practicein the future the building security and effectiveness could bedefinitely improved

The objectives of this study are to examine and comparethe feasibility of applying ANN and SVM to predict tunnelsurrounding rock displacementThus this paper is structuredas follows Section 2 provides a brief introduction on ANNand then practices ANN to predict the displacement of tunnelsurrounding rock Section 3 provides a simple introductionof SVM and then applies SVM to predict the displacementof tunnel surrounding rock at the end of the paper theconclusions are presented

2 Artificial Neural Network (ANN) for TunnelSurrounding Rock Displacement

Artificial neural network (ANN) is considered as one ofthe most effective tools that could be used to predict non-linear problems especially the problem with a real worldbackground [23] The framework of artificial neural network(ANN) requires it to gain new data constantly the charac-teristic of ANN could be used to track even a little variationrepeatedly Besides the advantage ANN also has the abilityto learn from random and noisy data which the traditionalstatistical techniques cannot handle very well the abilitycould make them solve problems that are often resolved byextremely complex mythologies previously

While the BP neural network [24] is an ongoing andpopular academic area of ANN which has attracted muchattention of the researchers all over the world [1 25] ANN

Inputlayer

Hiddenlayer

Outputlayer

Figure 1 The structure of 3-layer BP neural network

is a hierarchical feed-forward network which also consistedof several different layers During the training BPN would beoffered by a series of input or output pattern sets over andover again Then the network would gradually ldquolearnrdquo theinput and output relationship by correcting the weights tomineralize the error between the actual and predicted outputpatterns of the training set And the trained networkwould beinspected through a separate set of data which is the test setthat is used tomonitor performance and validity of themodelIf there is a minimum in the mean squared error (MSE)network training is completed As shown in Figure 1 most ofthe BP neural networks consisted of three layers input layerhidden layer and output layer

The learning process of BP neural network for predictingtunnel surrounding rock displacement could be described asfollows

(a) Initialize the BP neural network by generating arandom number within [minus1 1]

(b) Input a set of learning samples into the input layerto gain the output set of each unit of hidden layer by thefollowing functions

119860119895 =

119898

sum119894=1

119908119894119895119883119894 minus 120579119895

119861119895 = 119891 (119860119895) 119895 = 1 2 119899

(1)

where 119898 is the number of the units belonging to the inputlayer 119899 is the number of the units belonging to the hiddenlayer 119894 could be any unit of the input layer 119895 could be anyunit of the hidden layer 119908119894119895 is the network link weight fromany unit of the input layer to that of the hidden one 120579119895 is thethreshold of the 119895 unit of the hidden layer and119861119895 is the outputvalue of the 119895 unit of the hidden layer

(c) Calculate the output values of the units of the outputlayer

Mathematical Problems in Engineering 3

The output values could be calculated by the followingfunctions

119862119896 =

119899

sum119895=1

119881119895119896119861119895 minus 119886119896

119863119896 = 119891 (119862119896)

(2)

where 119897 is the number of the units belonging to the outputlayer 119896 could be any unit of the output layer 119881119895119896 is thenetwork link weight from any unit of the hidden layer to thatof the output one 119886119896 is the threshold of the 119896 unit of thehidden layer and 119863119896 is the output value of the 119896 unit of theoutput layer

(d) Calculate the mean squared error (MSE) of each unitof the output layer

MSE (119864119896) could be calculated by the following functions

119864119896 = 119863119896 minus 119884119896 (3)

where 119884119896 is the output of the training samples(e) Calculate theMSE of each unit of the hidden layer (119865119895)

as the following functions

119865119895 =119889119891 (119860119895)

119889119909

119897

sum119896=1

119881119895119896119864119896 (4)

(f) Based on the MSE of each unit of the output layer 119864119896to adjust 119881119895119896 that is the network link weight from any unitof the hidden layer to that of the output one and 119886119896 that isthe threshold of the 119896 unit of the hidden layer the adjustingfunctions are shown as follows

1198811015840119895119896 = 119881119895119896 + 120573119864119896119863119896

1198861015840119896 = 119886119896 + 120573119864119896

(5)

where 120573 is the learning speed(g) Adjust 119908119894119895 that is the network link weight from any

unit of the input layer to that of the hidden one and adjust 120579119895that is the threshold of the 119895 unit of the hidden layer

1199081015840119894119895 = 119908119894119895 + 120573119865119895119861119895

1205791015840119895 = 120579119895 + 120573119865119895

(6)

when 119864119896 is less than the maximum permissible errors thelearning process is complete if not go back to Step (a)

3 Support Vector Machines (SVM) for TunnelSurrounding Rock Displacement

SVM is a type of learning technique that is based on thestructural risk minimization principle and whose objective istominimize an upper bound of generalization error Based onthe text result from several high dimensional linear functionsSVM is shown to have very high generalization abilityRelying on the ability SVM could easily attain relatively morereliable data patterns than the traditional predictingmethods

SVM

Input

Output

middot middot middot

x

i

x

i+1

x

i+pminus1

x

i+p

Figure 2 The framework of SVM

Thebasic of support vectormachine is shown in Figure 2 [26ndash28]

The time sequence of tunnel surrounding rock displace-ment is gained by monitoring Given time sequence data set119909119894 = 1199091 1199092 119909119873 119894 = 1 2 119873 in order to predict thetime sequence the relationship between 119909119894 119909119894+1 119909119894+119901minus1and the displacement value 119909119894+119901 of themoment 119894+119901 should beanalyzedThe relationship is shownby the following function

119909119894+119901 = 119891 (119909119894 119909119894+1 119909119894+119901minus1) (7)

According to the theory of SVM the nonlinear relationshipcould be gained by learning the displacement sequence119909119894 119909119894+1 119909119894+119901minus1 119894 = 1 2 119899 minus 119901 SVM estimates thefunction by the following function

119891 (119909119899+119898) =

119899minus119901

sum119894=1

(120572119894 minus 120572lowast119894 )119870 (119883119899+119898 119883119894) + 119887 (8)

where 119891(119909119899+119898) is the displacement value of the time119899 + 119898 119883119899+119898 = (119909119899+119898minus119901 119909119899+119898minus119901+1 119909119899+119898minus1) 119883119894 =

(119909119894 119909119894+1 119909119894+119901minus1) and the value of 120572 120572lowast and 119887 could begained by the following function

Max 119908 (120572119894 120572lowast119894 ) = minus

1

2

119899minus119901

sum119894119895=1

(120572119897 minus 120572lowast119897 ) (120572119895 minus 120572

lowast119895 )119870 (119883119894119883119895)

+

119896

sum119894=1

119909119894+119901 (120572119897 minus 120572lowast119897 ) minus 120576

119899minus119901

sum119894=1

(120572119894 + 120572lowast119894 )

st

119899minus119901

sum119894=1

(120572119894 minus 120572lowast119894 ) = 0

0 le 120572119894 120572lowast119894 le 119862 (119894 = 1 2 119899 minus 119901)

(9)

An overall description of the steps of the algorithm based onSVM is shown as follows


(b) Resort the data in an ascending sort And inspect ifthere are any infeasible individuals in the set if so delete theinfeasible ones and then move to next step


(c) In this set 119899minus119901 sets should be gained from119899 sets Select119899 sets from the general pool and choose 119899 of them randomly

(d) Use competitive complex evolution algorithm whichcould be called CCE algorithm to expand the sets

(e) A single population which consisted of the setsprovided by the former step (c) should be generated in thisstep

(f) If all the conjunction standards are satisfied thencalculating process could be stopped if not please move toStep (g)

(g) If the number of the sets is less than 119899 minus 119901 theminimum set should be removed and thenmove back to Step(b)

4 Case Study

To further analyze and compare the predicting model fortunnel surrounding rock based on SVM and BP neuralnetwork this paper uses the Fangtianchong tunnel ofWuhan-Guangzhou railway as the test bed DK1658+905 is chosen asthe typical section to attain the data of tunnel surroundingrock displacement And in the case study the paper selects 3sections the first section the second section and the thirdsection as the test bed The measurement frequency shouldbe mentioned the frequency of this study is decided to beonce per dayThe data used in this case is collected during theperiod fromOctober 8 to 14 2013The reason why we choosethis period to detect the displacement of tunnel surroundingrock is that the rock of Fantianchong is a kind of soft rockwhichwould be affected by the environment temperature andhumidity And from October 8 to 14 the temperature andhumidity around the tunnel are stable and appropriate fordetecting based on researching and constructing experiences

In order to test the twomodels proposed in the paper thetotal data gained by observing is divided into 3 groups whichare the testing samples training samples and inspectionsamples In the models the 3 groups are used as three setsThe data of training and testing sets are provided by the firstand third sections and the data of the inspection set is fromthe second section of the test bed In this case we use root-mean-square error (RMSE) to evaluate the predictingmodelsmentioned in this paper And RMSE of each dayrsquos predictingresults could be gained by the following functions

RMSE = radicsum119899119894minus1 (119909119894 minus 119909119894)

2

119899 (10)

where the predicted value of tunnel surrounding rock dis-placement is 119909119894 119909119894 is the actual value of variable tunnelsurrounding rock displacement and 119899 is the number ofverifying points

This paper compares the performance of the two modelson the same test bed The results are shown in Figure 3

The predicting errors of SVM and ANN are shown inFigure 3 it is obvious that the errors of SVM models aremuch smaller than that of the model based on ANN Thecomparative results show that solutions attained by SVM aremore robust with a smaller standard error compared to ANN

24

29

34

39

44

49

8 9 10 11 12 13 14

RMSE

Day

ObservationSVMANN

Figure 3 Comparison between the prediction results amongobservations SVM and ANN

25

30

35

40

45

50

25 30 35 40 45 50

RMSE

Day

ANNSVM

Figure 4 Comparison between the predicting errors of SVM andANN

As shown in Figure 4 with time the variations between thepredicting results of ANN and the actual displacement valueare small However the variations between the predictingresults of SVM and the actual displacement value keep tobe random and not in order So it could be concluded thatthe structural risk minimization principle to minimize thegeneralization error is used by SVM and the empirical riskminimization principle to minimize the training error isused by BP neural network Besides the method based onSVM tends to search for a global solution while that ofBP neural network tends to fall in a certain local optimalsolution However the predicting speed of ANN is muchquicker than that of SVM Based on our tests the runningtime of the method based on SVM is about twice as much asthe running time of ANN The difference is mainly causedby the framework of SVM which is a little more complexthan the structure of ANN Thus in the real world it is moreacceptable to adapt to SVM techniques to predict the futuredisplacements if you prefer a more accurate prediction but


if it is emergency it could be better to rely on ANN whosespeed is quicker and errors are acceptable

5 Conclusions

Considering the potential danger that could be caused bytunnel surrounding rock displacement it is important andnecessary to have a relatively accurate and in time pre-diction of the displacement Therefore in this paper twomethodologies support vectormachines (SVM) and artificialneural network (ANN) are introduced to predict tunnelsurrounding rock displacement To compare the two modelsthe data of Fangtianchong tunnel are applied to test the tworespectively In general the comparison between artificialneural network (ANN) and SVM shows that SVM has higheraccuracy prediction than ANN But the predicting speed ofANN is much quicker than that of SVM Thus SVM canbe a potential and accurate tool for tunnel surrounding rockdisplacement prediction but if it is emergency it could bebetter to rely on ANN whose speed is quicker and errors areacceptable

Conflict of Interests

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

References

[1] C L Zhang X W Wang and H Chen ldquoStudy on forecastand prediction methods for tunnel wall rock deformationrdquoTechnology of Highway and Transport vol 4 pp 88ndash92 2008

[2] W Xiao and W Leng ldquoDynamic displacement prediction forthe retaining structure of the deep excavation pit in subwayrdquoChina Railway Science vol 25 no 5 pp 84ndash88 2004

[3] Q N Chen Y X Zhang and J G Chen ldquoThe displacementprediction of surrounding rock based on BP neural network forthe tunnelrdquo Journal ofHighway andTransportation Research andDevelopment vol 21 no 2 pp 65ndash69 2004

[4] B Z Yao P Hu X H Lu J J Gao and M H Zhang ldquoTransitnetwork design based on travel time reliabilityrdquo TransportationResearch C Emerging Technologies vol 43 part 3 pp 233ndash2482014

[5] B Z Yao P Hu M H Zhang and X M Tian ldquoImprovedant colony optimization for seafood product delivery routingproblemrdquo PROMET-TRAFFIC amp Transportation vol 26 no 1pp 1ndash10 2014

[6] B Yao P Hu M Zhang and S Wang ldquoArtificial bee colonyalgorithm with scanning strategy for the periodic vehiclerouting problemrdquo Simulation vol 89 no 6 pp 762ndash770 2013

[7] B Z Yao J B Yao M H Zhang and L Yu ldquoImproved supportvector machine regression in multi-step-ahead prediction forrock displacement surrounding a tunnelrdquo Scientia Iranica InPress httpwwwscientiairanicacomenArticlesInPress

[8] 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

[9] B Z Yao C Y Yang J B Yao J J Hu and J Sun ldquoAn improvedant colony optimization for flexible job shop scheduling prob-lemsrdquo Advanced Science Letters vol 4 no 6-7 pp 2127ndash21312011

[10] B Yu Z Yang and K Chen ldquoHybrid model for predictionof bus arrival times at next stationrdquo Journal of AdvancedTransportation vol 44 no 3 pp 193ndash204 2010

[11] B Yu Z Z Yang and B Z Yao ldquoA hybrid algorithm forvehicle routing problem with time windowsrdquo Expert Systemswith Applications vol 38 no 1 pp 435ndash441 2011

[12] B Yu Z Yang and J Yao ldquoGenetic algorithm for bus frequencyoptimizationrdquo Journal of Transportation Engineering vol 136no 6 pp 576ndash583 2010

[13] B Yu H B Zhu W J Cai N Ma and B Z Yao ldquoTwo-phase optimization approach to transit hub locationmdashthe caseof Dalianrdquo Journal of Transport Geography vol 33 pp 62ndash712013

[14] X H Li Y Zhao X G Jin Y Y Lu and X FWang ldquoApplicationof grey majorized model in tunnel surrounding rock displace-ment forecastingrdquo inAdvances inNatural Computation vol 3611of Lecture Notes in Computer Science pp 584ndash591 2005

[15] Y S Li X P Li and C L Zhang ldquoThe displacement predictionof surrounding rock based on BP neural network for thetunnelrdquo Journal of Highway and Transportation Research andDevelopment vol 25 supplement 1 pp 2970ndash2973 2006

[16] P J Sellner and W Schubert ldquoPrediction of displacements intunnellingrdquo in Proceedings of the ISRM International Sympo-sium International Society for Rock Mechanics 2000

[17] A G Parlos O T Rais and A F Atiya ldquoMulti-step-aheadprediction using dynamic recurrent neural networksrdquo NeuralNetworks vol 13 no 7 pp 765ndash786 2000

[18] C H Cheng J Lehmann and M H Engelhard ldquoNaturaloxidation of black carbon in soils Changes in molecular formand surface charge along a climosequencerdquo Geochimica etCosmochimica Acta vol 72 no 6 pp 1598ndash1610 2008

[19] H S Lee H J Billings and M N Lehman ldquoThe Suprachias-matic Nucleus A Clock of Multiple Componentsrdquo Journal ofBiological Rhythms vol 18 no 6 pp 435ndash449 2003

[20] G Chevillon and D F Hendry ldquoNon-parametric direct multi-step estimation for forecasting economic processesrdquo Interna-tional Journal of Forecasting vol 21 no 2 pp 201ndash218 2005

[21] J LiuWWang and F Golnaraghi ldquoAmulti-step predictor witha variable input pattern for system state forecastingrdquoMechanicalSystems and Signal Processing vol 23 no 5 pp 1586ndash1599 2009

[22] B Yu Z Z Yang and B Yu ldquoHybridmodel for prediction of busarrival timesrdquo Neural Network World vol 19 no 3 pp 321ndash3322009

[23] B Yegnanarayana Artificial Neural Networks PHI Learning2009

[24] W Jin Z J Li L S Wei and H Zhen ldquoThe improvements ofBP neural network learning algorithmrdquo in Proceedings of the5th International Conference on Signal Processing (WCCC-ICSPrsquo00) vol 3 pp 1647ndash1649 IEEE 2000

[25] Y Bin Y Zhongzhen and Y Baozhen ldquoBus arrival timeprediction using support vector machinesrdquo Journal of IntelligentTransportation Systems vol 10 no 4 pp 151ndash158 2006

[26] V Cherkassky and Y Ma ldquoPractical selection of SVM parame-ters and noise estimation for SVM regressionrdquoNeural Networksvol 17 no 1 pp 113ndash126 2004


[27] C W Hsu C C Chang and C J Lin ldquoA practical guide tosupport vector classificationrdquo Tech Rep Department of Com-puter Science and Information Engineering National TaiwanUniversity 2003

[28] C W Hsu C C Chang and C J Lin A Practical Guide toSupport Vector Classification 2003

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Differential EquationsInternational Journal of

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Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


multistep-aheadmodel could be used to predict the reliabilityof surrounding rock and other geographic structures Thereare also some other studies that rely on multistep-aheadmodel to do the predicting [21 22] In general in recent yearsthere are more and more researchers and institutions whichtend to use themultistep-aheadmodel to predict the complexinternal structures

Nevertheless as many researchers stated the accuracy ofthe predicting models based on the multistep-ahead modelextremely relied on the similarity between the present andprevious data And considering the complexity of internalstructure it is almost impossible to gain a large amountof accurate historical data Therefore with the unreliablehistorical data the predicting results could also becomeseriously incorrect Alongwith the development of intelligentrockmechanics artificial neural network (ANN) technique isgradually matured and widely used In recent years ANN hasbeen successfully applied in the field of tunnel surroundingrock displacement prediction Meanwhile thanks to thedevelopment of statistical learning theory support vectormachine (SVM) as a new machine learning technology hasdrawnmuch attention in the research area of time series fore-casting Therefore in the paper two models displacementprediction of tunnel surrounding rock based on ANN anddisplacement prediction of tunnel surrounding rock basedon SVM are presented And then in order to compare thetwo models in the last section the two models are evaluatedwith data of Fangtianchong tunnel respectively If the simplemodels presented in the paper could be applied to practicein the future the building security and effectiveness could bedefinitely improved

The objectives of this study are to examine and comparethe feasibility of applying ANN and SVM to predict tunnelsurrounding rock displacementThus this paper is structuredas follows Section 2 provides a brief introduction on ANNand then practices ANN to predict the displacement of tunnelsurrounding rock Section 3 provides a simple introductionof SVM and then applies SVM to predict the displacementof tunnel surrounding rock at the end of the paper theconclusions are presented

2 Artificial Neural Network (ANN) for TunnelSurrounding Rock Displacement

Artificial neural network (ANN) is considered as one ofthe most effective tools that could be used to predict non-linear problems especially the problem with a real worldbackground [23] The framework of artificial neural network(ANN) requires it to gain new data constantly the charac-teristic of ANN could be used to track even a little variationrepeatedly Besides the advantage ANN also has the abilityto learn from random and noisy data which the traditionalstatistical techniques cannot handle very well the abilitycould make them solve problems that are often resolved byextremely complex mythologies previously

While the BP neural network [24] is an ongoing andpopular academic area of ANN which has attracted muchattention of the researchers all over the world [1 25] ANN

Inputlayer

Hiddenlayer

Outputlayer

Figure 1 The structure of 3-layer BP neural network

is a hierarchical feed-forward network which also consistedof several different layers During the training BPN would beoffered by a series of input or output pattern sets over andover again Then the network would gradually ldquolearnrdquo theinput and output relationship by correcting the weights tomineralize the error between the actual and predicted outputpatterns of the training set And the trained networkwould beinspected through a separate set of data which is the test setthat is used tomonitor performance and validity of themodelIf there is a minimum in the mean squared error (MSE)network training is completed As shown in Figure 1 most ofthe BP neural networks consisted of three layers input layerhidden layer and output layer

The learning process of BP neural network for predictingtunnel surrounding rock displacement could be described asfollows


(b) Input a set of learning samples into the input layerto gain the output set of each unit of hidden layer by thefollowing functions

119860119895 =

119898

sum119894=1

119908119894119895119883119894 minus 120579119895

119861119895 = 119891 (119860119895) 119895 = 1 2 119899

(1)

where 119898 is the number of the units belonging to the inputlayer 119899 is the number of the units belonging to the hiddenlayer 119894 could be any unit of the input layer 119895 could be anyunit of the hidden layer 119908119894119895 is the network link weight fromany unit of the input layer to that of the hidden one 120579119895 is thethreshold of the 119895 unit of the hidden layer and119861119895 is the outputvalue of the 119895 unit of the hidden layer

(c) Calculate the output values of the units of the outputlayer



119862119896 =

119899

sum119895=1

119881119895119896119861119895 minus 119886119896

119863119896 = 119891 (119862119896)

(2)




119864119896 = 119863119896 minus 119884119896 (3)



119865119895 =119889119891 (119860119895)

119889119909

119897

sum119896=1

119881119895119896119864119896 (4)


1198811015840119895119896 = 119881119895119896 + 120573119864119896119863119896

1198861015840119896 = 119886119896 + 120573119864119896

(5)



1199081015840119894119895 = 119908119894119895 + 120573119865119895119861119895

1205791015840119895 = 120579119895 + 120573119865119895

(6)




SVM

Input

Output


x

i

x

i+1

x

i+pminus1

x

i+p




119909119894+119901 = 119891 (119909119894 119909119894+1 119909119894+119901minus1) (7)


119891 (119909119899+119898) =

119899minus119901

sum119894=1

(120572119894 minus 120572lowast119894 )119870 (119883119899+119898 119883119894) + 119887 (8)



Max 119908 (120572119894 120572lowast119894 ) = minus

1

2

119899minus119901

sum119894119895=1


lowast119895 )119870 (119883119894119883119895)

+

119896

sum119894=1


119899minus119901

sum119894=1

(120572119894 + 120572lowast119894 )

st

119899minus119901

sum119894=1

(120572119894 minus 120572lowast119894 ) = 0


(9)










4 Case Study




2

119899 (10)




24

29

34

39

44

49

8 9 10 11 12 13 14

RMSE

Day

ObservationSVMANN


25

30

35

40

45

50

25 30 35 40 45 50

RMSE

Day

ANNSVM





5 Conclusions




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119862119896 =

119899

sum119895=1

119881119895119896119861119895 minus 119886119896

119863119896 = 119891 (119862119896)

(2)




119864119896 = 119863119896 minus 119884119896 (3)



119865119895 =119889119891 (119860119895)

119889119909

119897

sum119896=1

119881119895119896119864119896 (4)


1198811015840119895119896 = 119881119895119896 + 120573119864119896119863119896

1198861015840119896 = 119886119896 + 120573119864119896

(5)



1199081015840119894119895 = 119908119894119895 + 120573119865119895119861119895

1205791015840119895 = 120579119895 + 120573119865119895

(6)




SVM

Input

Output


x

i

x

i+1

x

i+pminus1

x

i+p




119909119894+119901 = 119891 (119909119894 119909119894+1 119909119894+119901minus1) (7)


119891 (119909119899+119898) =

119899minus119901

sum119894=1

(120572119894 minus 120572lowast119894 )119870 (119883119899+119898 119883119894) + 119887 (8)



Max 119908 (120572119894 120572lowast119894 ) = minus

1

2

119899minus119901

sum119894119895=1


lowast119895 )119870 (119883119894119883119895)

+

119896

sum119894=1


119899minus119901

sum119894=1

(120572119894 + 120572lowast119894 )

st

119899minus119901

sum119894=1

(120572119894 minus 120572lowast119894 ) = 0


(9)










4 Case Study




2

119899 (10)




24

29

34

39

44

49

8 9 10 11 12 13 14

RMSE

Day

ObservationSVMANN


25

30

35

40

45

50

25 30 35 40 45 50

RMSE

Day

ANNSVM





5 Conclusions




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















4 Case Study




2

119899 (10)




24

29

34

39

44

49

8 9 10 11 12 13 14

RMSE

Day

ObservationSVMANN


25

30

35

40

45

50

25 30 35 40 45 50

RMSE

Day

ANNSVM





5 Conclusions




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











5 Conclusions




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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