Prediction of Typhoon Impact on Transportation Networks with Support Vector Regression

Transcription

1 Predcton of Typhoon Impact on Transportaton Networks wth Support Vector Regresson 0 Ta-Yn Hu Department of Transportaton and Communcaton Management Scence, Natonal Cheng Kung Unversty, No., Ta-Hsueh Road, Tanan 0, Tawan, R.O.C. TEL: --- FAX: -- tyhu@mal.ncku.edu.tw We-Mng Ho Department of Transportaton and Communcaton Management Scence, Natonal Cheng Kung Unversty, Tanan, Tawan, R.O.C. Submtted on July, 0 Revsed on Nov., 0 Word count:,0+ Tables+ Fgures=,0 Submtted for presentaton at the Annual Meetng of the Transportaton Research Board, Washngton, D. C., Jan 0, and publcaton n the Transportaton Research Record TRB 0 Annual Meetng

2 0 0 Predcton of Typhoon Impact on Transportaton Networks wth Support Vector Regresson Ta-Yn Hu *, We-Mng Ho Department of Transportaton and Communcaton Management Scence, Natonal Cheng Kung Unversty, R.O.C. TEL: --- FAX: -- tyhu@mal.ncku.edu.tw ABSTRACT Typhoon (or Pacfc tropcal cyclones) s one of the major natural dsasters n the world. Typhoons affect transportaton network, cause serous delay, damage roads, decrease the relablty of nfrastructure and threaten our lves. In order to avod serous delay due to the unexpected damaged roads under typhoons, the predcton of typhoon mpact on transportaton networks s mportant to reduce the rsk of lves. Ths research focuses on the predcton of typhoon mpact on transportaton networks wth Support vector regresson (SVR). Support vector regresson has been used for regresson problems and s capable of dealng wth complex systems wth small data. The nput data n SVR model are the hstorcal cumulatve damaged roads and maxmum cumulatve precptatons under typhoons n the past years. The output data are the cumulatve damaged roads n the target year. The calbrated model s then appled to predct possble damages and used to evaluate dfferent traffc management strateges n a realstc smulaton envronment. The calbraton results show that mean absolute percentage error (MAPE) of SVR predcton model s.%. Traffc strateges can be developed based on the predcton nformaton and can sgnfcantly mprove the network relablty. Keywords: Relablty; Support vector regresson; Typhoon; DynaTAIWAN TRB 0 Annual Meetng

3 0 0 INTRODCUTION Typhoon (or Pacfc tropcal cyclones) s one of the major natural dsasters n the world. In 00, Tawan was ht by Typhoon Morakot, and t caused a serous floodng. The economc loss was estmated to be around US$ one bllon and caused hundreds of death. Typhoons affect transportaton network, cause serous delay, damage roads, decrease the relablty of nfrastructure and threaten our lves. In order to avod serous delays due to the unexpected damaged roads under typhoons, the predcton of typhoon mpact s mportant to evaluate traffc networks qualtatvely and reduce the rsk of lves. Due to the characterstcs of typhoon and data lmtaton, the predcton problem could be treated as a non-lnear predcton problem for small sze data. The support vector regresson (SVR) s a kernel-based learnng algorthm for regresson analyss. Snce SVR s capable of dealng wth complex systems wth small data, ths research adopts SVR to study predcton of typhoon mpact on transportaton systems. However, the predcton of typhoon mpact on transportaton networks stll needs to be extended to model the network performance by usng an aggregate ndex. The concept of network relablty s used to evaluate dfferent network states nstead of tradtonal performance ndces. The network relablty s defned as the probablty or ablty of a traffc system to keep workable. For roads, network relablty s the probablty of the nfrastructure to keep operatonal for drvers (,,, and ). Network relablty measures can be used to evaluate the connectvty of networks, travel tme, and delay. Ths research focuses on the predcton of typhoon mpact on transportaton networks wth SVR. In the predcton problem, the nput data n SVR model are the hstorcal cumulatve damaged roads and maxmum cumulatve precptatons under typhoons n the past years. The output data are the cumulatve damaged roads n the target year. The cumulatve precptaton and cumulatve damaged nfrastructure data under typhoons are collected from Central Weather Bureau (CWB) () and Hghway Dsaster Informaton System (HDIS) (). The typhoon data from 00~0 are used for the tranng process and calbraton n the SVR model, and the data n 0 are used for verfcaton and comparsons. The developed model s then appled to predct possble damages n a real network through smulaton. Numercal experments are conducted on the bass of a real Jasan network to examne network relablty under dfferent traffc management strateges. Next secton presents a bref revew of related researches. The conceptual framework s presented n Secton. Numercal experments and results analyss for a real network are descrbed and dscussed n Secton and, follow by the bref summary. TRB 0 Annual Meetng

4 0 0 LITERATURE REVIEW Ths secton revews the related topcs, ncludng evaluaton ndces for the relablty of nfrastructure, mpact of natural dsasters on transportaton and SVR. Evaluaton Index Ida () ponted out that the network relablty would be nfluenced by the congeston and capacty and suggested two ndces to estmate the relablty of lnks. Two ndces, ncludng connectvty relablty and travel tme relablty, were recommended. Basc analyss of relablty was llustrated n normal and abnormal condtons. Chen et al. () appled three measures to quantfy the travel tme relablty durng dfferent tme perods. They were the coeffcent of varatons (CV), the plannng rate ndex (PRI), and the probablty ndcator (PI). The temporal dstrbuton characterstcs of the travel tme relablty were analyzed and the data were from taxs n Bejng. The results showed the relablty was hgh durng the off-peak hours and was low durng the peak hours. Knoop et al. () used a traffc smulator to study the consequences of the blockng on a lnk. The proposed smulator consdered the effects of spllback. Spllback and non-spllback cases were also evaluated for vulnerable lnks. The results showed that spllback should be ncluded n dentfyng vulnerable lnks. If a freeway lnk was damaged, the network performance dropped. Chen et al. () ndcated the performance measures need to be developed for assessment of network relablty under floodng, earthquake and hurrcane. The major performance measures ncluded travel tme and capacty relablty. Some research used the SVR n network performance evaluaton (, ). The back propagaton (BP) neural network was adopted for comparson. The comparson results showed that predcton ablty of support vector machne s better than that of BP neural network. Impact of Nature Dsasters on Transportaton Nature dsasters affected transportaton nfrastructure and deterorated the network performance, ncludng heavy precptaton, hurrcanes, typhoons and floodng. Suarez et al. () showed the operaton of the surface transportaton system was nfluenced by the clmate change n the Boston Metro Area. The urban transportaton modelng system (UTMS), a transportaton plannng procedure, was used to smulate the traffc flows n an urban network under floodng. The results showed that when there was floodng n a network, the trps may reduce because of some possble reasons, ncludng: the orgn or destnaton locaton s flooded and floodng of lnks. Watkns and Hallenbeck () TRB 0 Annual Meetng

5 focused on the mpact of adverse weather on freeway travel tmes n greater Seattle. The results showed adverse condtons would not cause sgnfcant changes n travel tme when the traffc volume was low. The ran would ncrease the travel tme slghtly when the freeway was already congested. In Tawan, the typhoon and heavy precptatons damaged the nfrastructure sgnfcantly. Data collected from Central Weather Bureau (CWB) and Hghway Dsaster Informaton System (HDIS) showed the number of cumulatve damaged roads under typhoons n Tawan from 00~0are more than 00. In 00, Tawan was ht by Typhoon Morakot, and t caused a serous floodng and led to about 0 cumulatve damaged roads and 00 deaths. The nature dsasters deterorated the nfrastructure and caused large number of damaged roads and deaths. Fgure shows the number of casualty due to typhoons n Tawan (). 0 Fgure Number of casualtes due to typhoons () SVR Model The SVR theory was frst developed by Vapnk n (). SVR was adaptve to complex systems and capable of dealng wth small sze data. SVR had also shown many applcatons, breakthroughs and robust performances, such as:. forecastng of fnancal market,. predcton of electrcty prce,. decson support system,. falure and relablty predcton of car engnes,. bankruptcy predcton,. estmaton of power consumpton,. reconstructon of chaotc systems, and. ntellgent transportaton systems (ITSs), ncluded: vehcle detecton and traffc-pattern recognton (,, and ). TRB 0 Annual Meetng

6 0 Some research used SVR for tme seres data predctons. Moura et al. () ponted out the applcaton of SVR was not wdely explored. Ths research used SVR for the applcaton of forecastng tme-to-falure and relablty of car engnes. Several models were used for comparsons, ncludng: tradtonal mult-layer perceptron model, autoregressve (AR) model, and neural network method. The results showed SVR outperformed other technques. Wu et al. () appled SVR for travel-tme predcton and compared the results of SVR to other travel-tme predcton methods on freeways. The results showed SVR predctor can lead to lower relatve mean errors and root-mean-squared errors. The results showed that SVR was applcable and performed well for travel-tme predctons on freeways. In summary, nature dsasters and adverse weathers deterorate travel tme relablty, delay, speed, safety of drvers and nfrastructure. Several models are proposed and used for predctons under normal condtons. Several researches used travel tme relablty to evaluate the network performances. However, the applcaton n predctons of mpact under nature dsasters s stll lmted. Thus, the ssue of mpact predctons s mportant to address mpact predcton by usng SVR model under nature dsasters for mprovng safety and effcency. RESEACH METHODOLOGY Conceptual Framework A conceptual framework s shown n Fgure. The hstorcal data are collected from dfferent sources as well as government authortes. The SVR models are then calbrated for the predcton purpose on the bass of the hstorcal parameters. Before typhoon, partal nformaton can be obtaned and used to forecast the mpact of typhoons on transportaton systems. Based on the predcton, transportaton networks and traffc management strateges are evaluated through relablty ndex. Thus, the results of relablty can be feedback to the predcton model. TRB 0 Annual Meetng

7 Hstorcal Data Model Partal Informaton Forecast Relablty Evaluaton Feedback 0 Strateges Fgure Conceptual framework An overall framework wth stages s shown n Fgure. Each stage s descrbed n detal hereafter. Stage : Data collecton. Emprcal data are collected through dfferent sources. The maxmum cumulatve precptaton data are collected from Central Weather Bureau (CWB), the cumulatve damaged road data are collected from Hghway Dsaster Informaton System (HDIS) and the length and area of nfrastructure data are collected from Mnstry of Transportaton and Communcatons (MOTC) (). Stage : Model constructon and comparsons. In ths stage, three models, ncludng SVR model, autoregressve ntegrated movng average (ARIMA) model and cubc regresson model are appled to predct the cumulatve damaged roads based on the hstorcal data. Several measurement crtera are consdered to compare the accuracy of the predcton, and they are R-squared test, root mean squared error (RMSE) and MAPE. Stage : Smulaton. A real Jasan netwrok, heavly affected by Typhoon Morakot n 00, s coded for smulaton experments. The road length and related nfrastructure data from MOTC are used to calculate the damaged roads n the Jasan network. Dfferent scenaros are developed based on the predcton results of SVR. Stage : Strateges development. TRB 0 Annual Meetng

8 Stage : Strateges Development Several strateges, ncludng real-tme nformaton and varable message sgn (VMS), are developed to observe the performance, to reduce the possble mpact and to mprove safety under nature dsaster. Stage : Performance assessment. Travel tme relablty ndex s used to examne the network performance under dfferent scenaros. Stage : Data Collecton Mnstry of Transportaton and Communcatons (MOTC) Length and area of Infrastructure Central Weather Bureau (CWB) Maxmum Cumulatve Precptaton Hghway Dsaster Informaton System (HDIS) Cumulatve Damaged Roads Stage : Model Constructon and Comparsons Stage : Smulaton Support Vector Regresson Calbraton and Predcton R-squared Test RMSE and MAPE ARIMA Predcton p, d, q RMSE and MAPE Model Comparsons Accuracy of Predcted Cumulatve Damaged Roads Smulaton Scenaros. Under Normal Condton. Under Typhoon MEARI. Under Typhoon NANMADOL Smulaton Calculate Cumulatve Damaged Lnks under Smulaton Scenaros, and Cubc Regresson Predcton R-squared Test RMSE and MAPE Network Codng Jasan Network Stage : Performances Assessment Strateges Development. Real Tme Informaton. VMS- Strongly Suggest to Change Route to New Alternatve Route. Buldng Alternatve Routes+VMS Performances Assessment Travel Tme Relablty Fgure Overall framework TRB 0 Annual Meetng

9 SVR Model Consder a set of data{ x, y ) = ( x, y ),...,( x, y )}. Where, ( n n k x R s the k-dmensonal nput space, y = f ( x ) represents a hyperplane n h R (h > k), and n s the total number of observatons. The man objectve of the support vector regresson s to accurately predct values on the bass of a determned functon. Support vector regresson has the followng mathematcal form: y = f ( x ) = wf( x ) + b () Where, φ ( ) s the non-lnear transformaton from k R to the hgher dmensonal space w and b are coeffcents. Coeffcents w and b are obtaned by mnmzng the followng structural rsk functon n Eq. (). R reg Where ( f ) = C n = c( f ( x ), y ) + w () h R. c( fˆ ( x ), y ) = 0 f ( x ) y ε f f ( othεrwsε x ) y ε () In Eq. (), the frst term C n = c( f ( x ), y ) means the emprcal rsk, and the rsk s 0 measured by the ε-nsenstve lost functon c( ) n Eq. (). The second term regularzaton term whch represents the flatness of the SVR functon. w s the Penalty C s the regularzaton parameter, and C determnes the trade-off between the emprcal rsk and model flatness. Radus ε s the tube sze whch determnes the data nsde the tube to be gnored n regresson. Fnal SVR functon n Eq. () can be obtaned by mnmzaton Eq. (). f ( X, α, β ) = n = ( α β )K( x,x ) + β K( ) s the kernel functon. Kernel functon calculates the dstance between x and x (the th observed nput). α, structural rsk functon n Eq. (). β and b are the coeffcents obtaned from mnmzng the The kernel functon enables operatons to be performed n the nput space and do not need to be performed n the hgh dmensonal feature space. In the nput space, the nner () TRB 0 Annual Meetng

10 product does not need to be evaluated. Thus, kernel functon provdes an effcent way to determne the dmenson. The kernel functon needs to be calbrated to determne a best ft functon n SVR model. Some common kernel functons n SVR are lsted below. The kernel functon ncludes lnear, polynomal and radal bass functon (RBF). Lnear: x y. Polynomal: [( x* x +. d ) ] 0 Radal Bass Functon (RBF): exp{ γ x x }. Three parameters, ncludng penalty value C, coeffcent γ and radus value ε, n the SVR model need to be calbrated. Penalty value C determnes penaltes to estmaton errors. larger C means a hgher penalty to errors n the model so that the regresson s traned to mnmze error wth lower generalzaton. A smaller C means a lower penalty to errors n the model so that the regresson allows the mnmzaton of errors wth hgher generalzaton (). Coeffcent γ and radus value ε needs to be calbrated n kernel functon. Evaluaton Index: Travel tme relablty Travel tme relablty s used to represent the network relablty. Travel tme relablty r s defned as the probablty that trps arrve at the destnaton n a tme perod, and s shown n Eq. (). t s the predcted travel tme, t s real travel tme and π s the coeffcent. (). π s set to be. under dsaster. r = P[ t πt ] () Where, µ s the expected travel tme of lnk, and A σ s the varance of lnk The standard form of travel tme relablty s shown n Eq. (). The upper value s, the lower value s 0. P( t πt ) = P( t Measurement Crtera t µ t π P ) = f( ) () π σ P Several crtera are chosen to evaluate the errors between true and predcted values. The measurement crtera nclude root mean squared error (RMSE) and mean absolute percentage error (MAPE). The nterpretaton of MAPE values are shown n Table (). The crtera are shown as follows: TRB 0 Annual Meetng

11 RMSE n = = ( y ŷ ) n () n MAPE = n = y ŷ % y 0 () 0 Where, y :the observaton value, ŷ :the predcted value. Table Interpretaton of MAPE values () MAPE (% ) Interpretaton < Hghly accurate forecastng -0 Good forecastng 0-0 Reasonable forecastng >0 Inaccurate forecastng CALIBRATION OF SVR AND NUMERICAL COMPARISONS The nput data and calbraton results of SVR model are descrbed n ths secton. The major ssue s how to calbrate the SVR model and how to valdate the predcton model. Input Data: Typhoon and Infrastructure The typhoon data, whch nclude year, month, name, maxmum cumulatve precptaton and cumulatve damaged roads under each typhoons, are collected from 00~0. The maxmum cumulatve precptaton data are collected from Central Weather Bureau (CWB), and the cumulatve damaged road data are collected from Hghway Dsaster Informaton System (HDIS). The scatter plots of typhoon data are llustrated n Fgure. The vertcal axs represents the cumulatve damaged roads, and the horzontal axs represents the maxmum cumulatve precptaton. Two sets of data are shown n Fgure. Hstorcal typhoon data from 00~0 are used for calbratng the SVR model. The typhoon data n 0 are used to valdate wth the predcton results from the calbrated SVR model. TRB 0 Annual Meetng

12 0 Fgure Scatter plots of typhoon data Calbraton Results In the calbraton process, the frst step s to determne an approprate functon wth ntal parameters and the second step s to fnd the optmal parameters based on the functon. Three types of kernel functons, ncludng lnear, polynomal and radal bass functon are tested. The ntal parameters are assumed: C=, γ= -, ε=. The calbraton of C, γ and ε are desgned on the bass of calbraton range { -,, -, -, 0,,,, }. When the values are more than or less than -, the parameters dverge (). After the determnaton of kernel functon, the best combnaton of C, γ and ε need to be calbrated n radal bass functon. The crteron s to choose the combnaton wth lowest errors n the calbraton range. The results are summarzed n Table. The results show that the radal bass functon has hgher R-squared value and lower RMSE and MAPE. The best calbraton results n radal bass functon are [C, γ, ε] = [, -, ]. The MAPE s about. %, whch means hghly accurate predctons. The predcton result s shown n Fgure. The SVR model can have accurate predctons n 0. TRB 0 Annual Meetng

13 Table Calbraton results Kernel Functon R-squared Predcted dependent RMSE MAPE varable: cumulatve damaged roads Lnear 0. [.,.0]..% Polynomal 0. [., 0.0]..% Radal bass functon 0. [., 0.0].0.% 0 Cumulatve damaged roads hstorcal 00~0 SVR estmaton real 0 SVR predcton Maxmum cumulatve precptaton(mm) Result Comparsons Fgure Predcton result based on best combnaton In order to llustrate the predcton performance of the SVR model, both cubc regresson functons and ARIMA models are used n comparsons. The results are summarzed n Table and llustrated n Fgure. The results show that the SVR model can have better results than other models. Based on the calbrated SVR model, numercal experments for the Jasan network are dscussed hereafter. TRB 0 Annual Meetng

14 Measurement Crtera Models Table Predcton error of dfferent models R-squared or orders Predcted dependent varable: cumulatve damaged roads RMSE MAPE Cubc functon 0. [.,0.].0.0% ARIMA p=, d=, q= [.,.]..% SVR 0. [., 0.0].0.% Fgure Comparson results of dfferent models APPLICATIONS OF SVR MODEL IN NUMERICAL EXPERIMENTS Network Characterstcs and Smulaton Scenaros Snce the Jasan network was heavly affected by Typhoon Morakot n 00, numercal analyss and possble traffc management strateges are dscussed to llustrate the proposed SVR model. As shown n Fgure, the Jasan network ncludes 0 nodes, lnks and traffc zones.. TRB 0 Annual Meetng

15 Fgure Jasan network The populaton data are from the Mnstry of Interor (MOI) (). km The total vehcles are about, passenger car unts (PCUs) n hours. As shown n Table, three scenaros are developed based on hstorcal maxmum precptaton data under typhoons n 0. Scenaro s the base case wth normal condton. Scenaro s under Typhoon MEARI (maxmum cumulatve precptaton 0. mm). Scenaro s under Typhoon NANMADOL (maxmum cumulatve precptaton. mm). The cumulatve damaged roads n Jasan network s calculated based on predcton of the SVR model. Scenaro Table Smulaton scenaros Maxmum cumulatve Predcted cumulatve precptaton (mm) damaged roads In Tawan Predcted cumulatve damaged roads n Jasan network Three traffc strateges are also desgned. Strateges and are llustrated n Fgure. Strategy s to provde real tme nformaton to all trpmakers. Strategy utlzes varable TRB 0 Annual Meetng

16 message sgns (VMSs) for route gudance and the message shows the locaton of damaged roads and the alternatve routes. Strategy s to buld new alternatve roads + VMSs. 0 VMS X VMS 0 VMS X 0 VMS Damaged Road: X Alternatve Road: km VMS Road: VMS Fgure Illustraton of traffc strateges Results of Traffc Strategy Performance ndces, ncludng average travel tme (ATT), average stopped tme (AST), and average travel dstance (ATD), and travel tme relablty, are used to evaluate traffc network performance. The results are summarzed n Table. The results show that ATT, AST and ATD ncrease wth respect to the maxmum cumulatve precptaton. Also, the values of travel tme relablty drop sgnfcantly. The results ndcate that travel tme relablty s very senstve. The results show that the travel tme relabltes are nfluenced and decreased due to the heavy precptaton n Scenaros and. In Scenaro, the travel tme relablty drops to 0.0 due to the heavy precptaton under typhoon NANMADOL (wth maxmum cumulatve precptaton. mm). TRB 0 Annual Meetng

17 Table Results of travel tme relablty Scenaro ATT (mnutes)... AST (mnutes) 0... ATD (km).. 0. Travel tme relablty In order to mprove the effcency and safety of drvers under heavy precptaton, three traffc strateges are tested. The results are lsted n Table. The results show that the travel tme relabltes slghtly mprove under Strateges and n Scenaro. However, the travel tme relablty does not mprove n Scenaro. The results from Strategy are promsng due to new alternatve roads. In general, the results show that traffc management strateges can mprove the system only when fundamental nfrastructure s suffcent. Moreover, travel tme relabltes can provde more nformaton than other performance ndces, such as ATT and AST. Table Results of traffc strateges Scenaro Improvement Improvement Traffc strateges Percentage Percentage. Real tme nformaton 0. % 0.0 %. VMS 0. % 0.0 0%. Buldng new alternatve roads + VMS 0. 0% 0.,% CONCLUSIONS Ths research focuses on the predcton of typhoon mpact on transportaton networks wth SVR models. The predcton results are compared wth ARIMA and cubc regresson 0 model. The calbraton results show the SVR model provdes more accurate predctons wth lower errors and hgher sgnfcance than other models. Typhoon mpact on transportaton networks s smulated based on the calbrated SVR model. Three scenaros and three traffc management strateges are desgned to observe the system performance. The proposed traffc strateges can mprove travel tme relabltes under typhoons. However, the results show that traffc management strateges can mprove the system only when fundamental nfrastructure s suffcent. TRB 0 Annual Meetng

18 0 0 REFERENCES. Ang, A. H. S. and Tang, W. H. (0). Probablty Concepts n Engneerng Plannng and Desgn, Vol. Basc Prncple; Vol. Decson, Rsk and Relablty., Wley, New York.. Ida Y. (), Basc Concepts And Future Drectons Of Road Network Relablty Analyss, Journal of Advanced Transportaton, Vol., No., pp. -.. Chen, K., Yu, L., Guo, J., and Wen H. (00), Characterstcs analyss of road network relablty n Bejng based-on the data logs from taxs, Transportaton Research Board Annual Meetng, Natonal Academes Press, Washngton, D. C., USA.. Knoop V. L., Hoogendoorn S. P., and van Zuylen H. J. (00), Quantfcaton of the mpact of spllback modelng n assessng network relablty, Transportaton Research Board Annual Meetng, Natonal Academes Press, Washngton, D. C., USA.. Chen, A., Zhou, Z., Chootnan, P. and Wong, S. C. (00), A B-Objectve Relable Network Desgn Problem, Transportaton Research Board Annual Meetng, Natonal Academes Press, Washngton, D. C., USA.. Central Weather Bureau (CWB): Hghway Dsaster Informaton System (HDIS): Song H. S. (0). Applcaton of Support Vector Regresson n Network Performance Evaluaton, Energy Proceda,, Zhao L. (0). Network Relablty Predcton Based on Support Vector Machne, Energy Proceda,, -.. Suarez, P., Anderson, W., Mahal, V., and Lakshmanan, T.R., (00). Impacts of floodng and clmate change on urban transportaton: A system-wde performance assessment of the Boston Metro Area, Transportaton Research Part D, (), -.. Watkns, E.K. and Hallenbeck, M., (0). Impact of weather on freeway travel tmes n the ran cty, th Transportaton Research Board Annual Meetng, Washngton DC, USA.. Drectorate General of Budget, Accountng and Statstcs (DGBAS), Vapnk, V. N., (), The Nature of Statstcal Learnng Theory. New York: Sprnger.. L Y.F., Ng S.H., Xe M., Goh T.N., (0), A systematc comparson of metamodelng technques for smulaton optmzaton n Decson Support Systems, Appled Soft Computng,.. Shn K. S., Lee T. S., Km H. J., (00), An applcaton of support vector machnes n bankruptcy predcton model, Expert Systems wth Applcatons,,. TRB 0 Annual Meetng

19 . Moura M. D. C., Zo E., Lns I. D., Droguett E., (0), Falure and relablty predcton by support vector machnes regresson of tme seres data, Relablty, Engneerng and System Safety,.. Wu C. H.,, Ho J. M., and Lee D. T., (00), Travel-Tme Predcton Wth Support Vector Regresson, IEEE Transactons On Intellgent Transportaton Systems, Vol., No., -.. Mnstry of Transportaton and Communcatons (MOTC): Asakura, Y. and Kashwadan, M. (), Road network relablty caused by daly fluctuaton of traffc flow, proceedngs of the th PTRC Summer Annual Meetng, Brghton, pp.. 0. Mnstry of Interor (MOI): Lews, C.D. (). Industral and Busness Forecastng Methods: A Practcal Gude to Exponental Smoothng and Curve Fttng, Butterworth Scentfc, London. TRB 0 Annual Meetng