Procedia - Social and Behavioral Sciences 138 ( 2014 ) Bus Arrival Time Prediction Using RBF Neural Networks Adjusted by Online Data

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1 Available online at ScienceDirect Procedia - Social and Behavioral Sciences 138 ( 014 ) The 9 th International Conference on Traffic & Transportation Stdies (ICTTS 014) Bs Arrival Time Prediction Using RBF Neral Networks Adjsted by Online Data Lei Wang a, Zhongyi Zo a,*, Jnhao F b a School of Traffic and Transportation Engineering, Dalian Jiaotong University, No. 794 Hanghe Road, Shaheko District, Dalian 11608, P.R. China b Navigation College, Dalian Maritime University, 1 Linghai Road, Dalian 11606, P.R. China Abstract This paper proposes an approach combining historical data and real-time sitation information to forecast the bs arrival time. The approach incldes two phases. Firstly, Radial Basis Fnction Neral Networks (RBFNN) model is sed to learn and approximate the nonlinear relationship in historical data in the first phase. Then, in the second phase, an online oriented method is introdced to adjst to the actal sitation, which means to se the practical information to modify the predicted reslt of RBFNN in the first phase. Afterwards, the system designing otline is given to smmarize the strctre and components of the system. We did an experimental stdy on bs rote No.1 in Dalian by deploying this system to demonstrate the validity and effectiveness of this approach. In addition, Mltiple Linear Regression model, BP Neral Networks and RBFNN withot online adjstment are sed in contrast. Reslts show that the approach with RBFNN and online adjstment has a better predicting performance Pblished The Athors. by Elsevier Pblished Ltd. by This Elsevier is an Ltd. open access article nder the CC BY-NC-ND license ( Peer-review nder responsibility of Beijing Jiaotong University (BJU), Systems Engineering Society of China (SESC). Peer-review nder responsibility of Beijing Jiaotong University(BJU), Systems Engineering Society of China (SESC). Keywords: Intelligent Transportation; Arrival Time Prediction; RBFNN; Pblic Transport; System Design 1. Introdction With the continos development of the Intelligent Transportation System (ITS), the Advanced Pblic Transportation System (APTS) and Advanced Traffic Information System (ATIS) become more and more important. * Corresponding athor. Tel.: ; +86-(0) address: zozy@djt.ed.cn Pblished by Elsevier Ltd. This is an open access article nder the CC BY-NC-ND license ( Peer-review nder responsibility of Beijing Jiaotong University(BJU), Systems Engineering Society of China (SESC). doi: /j.sbspro

2 68 Lei Wang et al. / Procedia - Social and Behavioral Sciences 138 ( 014 ) Bs arrival time forecasting system belongs to these systems (as shown in Fig.1.). Releasing bs arrival time information to passengers mobile devices, helps them to plan their travel time, and to save their waiting time at bs stops. It makes more sense to attract additional passenger flow by providing bs arrival time information to improve the service qality of transit systems. Besides, operators will be able to monitor the exection of schedle, to react instantly and to evalate the operational efficiency. Cross Region APTS ATIS Advanced Transportation Information System ITS Advanced Pblic Transportation System Intelligent Transportation System Fig. 1. Relationship among ITS, APTS and ATIS Bs arrival time predicting method or algorithm designing was considered to be the most complicated part in the former stdies. Researches on bs arrival time forecasting started by the end of 1990s which aims to extract bs operating information from vehicle monitoring systems (Lin and Zeng, 1999). With the idea of providing bs arrival information to passengers comes into or sights lately, stdies focs on this domain afresh. A case stdy in Jinan, China was processed by Lin, et al, who proposed two artificial neral network (ANN) models to predict the realtime bs arrivals, based on historical Global Positioning System (GPS) data and atomatic fare collection (AFC) system data, which illstrated ANN models are valid to bs arrival time predicting (Lin et al., 013). Zho, et al developed an entire system solely relies on the collaborative effort of the participating sers and is independent from the bs operating companies instead of referring to GPS enabled location information from specific transit agencies (Zho et al., 01). Zh et al explicitly incorporated the bs stop delays and signalized intersection delays associated with the total travel times of the bses (Zh et al, 011). Biagioni, et al developed an online dynamic algorithm of atomatic transit tracking, mapping, and arrival time prediction by sing smartphones (Biagioni et al, 011). While Y, et al sed several methods sch as spport vector machine (SVM), artificial neral network (ANN), k nearest neighbors algorithm (k-nn) and linear regression (LR) as comparisons (Y et al., 011). A heristic method was proposed by Y, et al which contains two main steps, in which firstly SVM was trained to perceive the historical data and Kalman Filter was applied to import the real-time data (Y et al., 008). Nowadays, the stage comes to the implementation and application of sch systems from the bleprints with the gigantic development of the electronic, commnication, compter software and network engineering since 1th centry. Especially profiting from the poplarization of smartphones, makes it possible to establish a bs arrival time forecasting system to deliver real-time bs information to both operators and passengers. On the other hand, Atomobile Data Recorder and Atomatic Vehicle Location (AVL) devices are eqipped on bs vehicles as reglar eqipment, which signify that real-time location of vehicle can be available. Several cities in China have adopted bs arrival predicting systems for bs information offering online (website) or offline (electronic station board), althogh they can only provide an accracy by the nmber of stops instead of terms of time, for example in Dalian, Xiamen and Szho, etc. While, can we develop a kind of system with accracy, stability and simplification that can predict the exact time when will the next bs arrive? In this paper, we propose an approach combining historical data and real-time sitation information to forecast the bs arrival time. Firstly, Radial Basis Fnction Neral Networks (RBFNN) are sed to learn and approximate the nonlinear relationship in historical data, so that the reslts can be given by the trained networks as the basic information references in the first phase. Then, in the second phase, in order to mitigate the inflence from discrepancy between historical and real-time data, an online oriented method is introdced to adjst to the actal sitation, which means to se the practical information to modify the predicted reslt of RBFNN in the first phase. Conseqently, the reslt considered to be more dependable can be offered to transit operators, electronic station boards or passengers smartphones. Afterwards, the system designing otline is given to smmarize the strctre

3 Lei Wang et al. / Procedia - Social and Behavioral Sciences 138 ( 014 ) and components of the system. We did an experimental stdy on bs rote No.1 in Dalian by deploying this system to demonstrate the validity and effectiveness of this approach. In addition, Mltiple Linear Regression model, BP Neral Networks and RBFNN withot online adjstment are sed in contrast. Reslts show that the approach with RBFNN and online adjstment has a better predicting performance.. Radial Basis Fnction Neral Networks One ideal method to predict bs arrival time is to acqire the transformation law of vehicle operation by data mining, then to amend the mined data by bringing the real-time sitation in as well. The first phase of this approach considered to be the historical data acqirement or data mining, as we assme that historical data involves comprehensive information and they are significative to imply the bs travel time in ftre. However data analysis and mining is a complicated and laborios work with massive data. RBFNN offer s a new way to set p a mapping among all the detectable inflence factors and dependent variable..1. RBF Neral Networks c 1 x 1 1 y 1 Inpt vector x c y Otpt vector c h kj x m Inpt layer h Hidden Otpt layer layer Fig.. Strctre of RBFNN y n x 1 x x m Neron k c k 1 R exp( xi ck ) k Fig. 3. Neron Strctre of RBFNN y j h kjr i1 Radial Basis Fnction Neral Networks are feedforward networks with RBF as activation fnction which can process niversal approximation to any continos fnction by cstom accracy. RBFNN have the strctre of only three layers which are inpt layer, hidden layer, and the otpt layer (see fig..), while Back Propagation Neral Networks (BPNN) can possess more hidden layer. RBFNN are considered to be more effective, more accrate, faster to converge, and able to avoid problem of local extremm. The neron strctre is shown as Fig.3. As described in reference (Park and Sandberg, 1991), RBFNN model can be conclded. The mapping method between inpt vector and otpt vector is given as O F() I (1)

4 70 Lei Wang et al. / Procedia - Social and Behavioral Sciences 138 ( 014 ) ,,, m 1,,, n ; F is the nonlinear mapping between I and O. Sppose the nmber of nodes in hidden layer is h. For the inpt layer neron, the only effect is to pass the signal, which means the connection weights between inpt layer and hidden layer are constant 1. Using the Gassian fnction as RBF, the activation fnction will be For I is the inpt vector and I x x x ; O is the otpt vector and O y y y 1 Rx ( c) exp( x c ) () i k i k k Where xi I, i 1,,, m, k 1,,, h; xi ck means the Eclidean norm; x i is the inpt vale of inpt node i ; ck is the centric vale of basis node k in hidden layer; is the variance of the Gassian fnction. The activation fnction reflects the activation condition of neron by the discrepancy of Eclidean distance instead of linear activation fnctions. So the otpt elements vales shold be 1 y x c h j kj exp( ) i k (3) i1 k Where yj O, j 1,,, n; kj is the connection weights between the neron k in hidden layer and the neron j in the otpt layer. Actally, the process to train the RBFNN is to calibrate c k, k, and kj. The learning algorithm of RBFNN can be fond in reference (L, Sndararajan, Saratchandran, 1998)... RBFNN Used in Bs Arrival Time Forecasting It was demonstrated by Jeong (Jeong and Rilett, 004) that there are relationships among bs travel time, dwell time, the nmber of passengers getting on or off, delay, and the distance between two stops. Additionally, dring the experiment, we fond that the travel speed of bs reflects the congestion level of road to some extent, and the congestion sitation shold affect the travel time of bs, while the correlation between travel time and this factor is not clear. Linear regression shows the linear dependences are not strict, so that nonlinear relationships are spposed. Giving the relationships assmptions between inflence factors and travel time as follows: D T T P S Cong 1/ V Delay D T P, S, Delay, Cong (4) (5) (6) (7) (8) So that Y T D F( S, P, Delay, V ) (9)

5 Lei Wang et al. / Procedia - Social and Behavioral Sciences 138 ( 014 ) Where T is the travel time from stop to stop 1; stop to stop 1 ; on off P max{ p, p },where D is the dwell time at stop ; S is the distance from P is the nmber of passengers getting on or off at stop, sally setting on p represents the nmber of passengers getting on and Delay is the overall delay from stop to stop 1; off p represents the nmber of V is the travel speed from stop to passengers getting off; stop 1 ; Cong is the congestion index between stop and 1 ; Y means the time interval between bs arriving at stop and stop 1. With sch kind of complicated nonlinear approximation problem, RBFNN are good enogh at dealing. It is qite convenient to gather the historical data of T, D, S, P, Delay, and V, and conseqently to organize them as samples set. Afterwards, the RBFNN model can be trained and resed. D, S, P, Delay, and V are all statistical independent variables which can be provided by real-time bs operation data. In this phase, original data and prepared data cold be offline, and once the mapping had been approximated, the mapping model can express almost entire relationship of sorce data, which is qite more simplified than doing analysis throgh enormos databases. By giving a set of these factors, we can export an reslt of T, which is so called baseline data for the next phase. ˆ 3. Adjstment Model Using Online Data Baseline data exported from the first phase is a time period parameter which actally means the travel time dring stop to stop 1. When sers are reqesting for arrival time of a specific bs, generally the bs shold be on the rote in most cases than at a stop. So a conclsion can be drawn that offline prediction method cannot acqire the instant position of the bs in order to give an exact arrival time. In the second phase, we will give a method to adjst the baseline data sing the online operating parameters Using of Kalman Filter The instant speed of vehicle cold be available to indicate the real-time operation stats, which cold be sefl for baseline adjstment. As recording the instant speed by continos time step, time series can be gotten. Set vt ( ) t as system stats variable with the meaning of instant speed, and t as time point, where the length of t is determined by the time step size l, a method of instant speed prediction sing Kalman Filter can be offered as following (Kalman, 1960): Withot inpt vector to the system, system stats transforming eqation and system covariance transforming iteration eqation as In which Kalman Gain is defined as vt ( t1) vt ( 1 t 1) (10) Pt ( t1) Pt ( 1 t1) Q (11) v( ) t t v( t t1) Kg()( t v () t v( t t 1)) (1) r Pt ( ) t (1 Kgt ()) Pt ( t 1) (13) Pt ( t1) Kg() t Pt ( t1) R (14)

6 7 Lei Wang et al. / Procedia - Social and Behavioral Sciences 138 ( 014 ) Where, vr () t is the observed instant speed of the bs; Pt ( ) t stands for the calclating covariance; Q is the covariance dring the system transforming; R is the observing covariance. Combination of Baseline and Instance We adopt a weighting arithmetic to combine the baseline data with instant speed. Firstly, trn the baseline travel time T to travel speed v ˆ by For the speed variable v S / Tˆ (15) ax v we call it axiliary speed, constrct the weighting method as v ax avtt ( ) bv a b (16) f where a and b are weights; set a S which means the length of section that has been passed throgh between l stop and 1; set b S which means the length of section that has not been passed throgh between stop and 1. So it can be modified as S v( ) t t S v f l ax f l S S v (17) Where we can discover that by adopting variable weights can different dependence be given to the axiliary speed: when the bs is more close to the stop, v depends on v more, while the bs is more close to the stop 1, ax ax v depends on vt ( ) t more. Seqentially, when the bs is on the segment between stop 0 1 and 0, the predicting travel time T pred from the real-time location to stop 1 shold be given as T pred S S l ax ax D (18) v0 1 0v System Designing In this research, we developed a set of compter software system prototype based on the bs arrival time forecasting approach proposed above. The strctre of the system is shown in Fig.4. A brief introdction to each component is as follows: Server Scope - Data Collecting Server: handles the large amont of data flow from vehicle devices with database. - Web Server: response the qery or reqest from sers clients or browsers and handles other basic information qery reqests. - Processing Server: sing the data in database to train the model atomatically and to do the online prediction for any reqest. Vehicle Scope - Collecting bs vehicle operating data and sending data back to the Data Collecting Server in real-time. User Scope - Several kind of interfaces are reserved to satisfy the reqest for the specific bs arrival time prediction information throgh SMS, smartphone applications, or web browsers, which are handled by Web Server.

7 Lei Wang et al. / Procedia - Social and Behavioral Sciences 138 ( 014 ) Fig. 4. System Strctre Designing 5. Experimental Stdy We chose the bs No. 1 in Dalian as the experimental rote to collect basic data. Becase the bs operating monitoring data interface was not open to the pblic, we tentatively applied the vehiclar devices of this system to the sample vehicles instead. One week s data was stored and reserved in the database, which was sed to train the RBFNN models. We sed 3 smartphones which had installed the bs arrival time predicting and releasing software to verify the predictive effect. 90 sets of random prediction reqests were processed and the reslts of forecast travel time were given. By recording the real operating time from the nspecified location, where the prediction reqests were sent and the response of prediction reslts were received, to the specific stop arriving at, the effectiveness of this approach cold be evalated by residal error and relative error of each reqests. The accracy measrement of each approach is Mean Absolte Percentage Error (MAPE). Additionally, Mltiple Linear Regression model, BP Neral Networks and RBFNN withot online adjstment are sed as comparisons. The prediction error of RBFNN withot online adjstment approach is shown in Fig.5., and the prediction error of RBFNN with online adjstment approach is shown in Fig.6., in which abscissa represents observed traveling time both in (a) and (b), ordinate represents predicted traveling time in (a) and residal error in (b). Observing Fig.5.(a), we can find that points disperse from the diagonal, while points in Fig.6.(a) are mch more matching with the diagonal. As shown in (b) both of Fig.5. and Fig.6., the residal errors of nadjsted RBFNN distribte from -100 to 100, while of adjsted RBFNN distribte within -50 to 50. These indicate that adjsted RBFNN model has a better accracy than RBFNN withot adjstment. We did a contrast of MLR, BPNN, RBFNN withot online adjstment, and RBFNN with online adjstment by relative error (shown in Fig.7.) and MAPE (shown in table 1.). For approaches withot online adjstment, the travel time from instant position of bs to next stop was calclated by interpolation method. From an overall perspective as

8 74 Lei Wang et al. / Procedia - Social and Behavioral Sciences 138 ( 014 ) shown in table 1., adjsted RBFNN method has better accracy than others. The adjsted RBFNN approach trns ot to be the best option relatively by lower relative errors and MAPE. (a) Scatter of Observed Time and Practical Time (b) Residal Error Fig. 5. Prediction Error of RBFNN withot Online Adjstment (a) Scatter of Observed Time and Practical Time (b) Residal Error Fig. 6. Prediction Error of RBFNN with Online Adjstment Fig. 7. Contrast among MLR, BPNN, RBFNN, and RBFNN with Online Adjstment Table 1. Contrast of these Approaches by MAPE MLR BPNN RBFNN Adjsted RBFNN MAPE.87% 17.41% 15.98% 7.59% 6. Conclsions This paper proposed a bs arrival time predicting approach with two phases those are RBFNN and online adjstment model. In the first phase, RBFNN model is trained by the factors of the dwell time at stop, the nmber of passengers getting on or off, delay, distance, and travel speed between two stops, and the baseline data can be

9 Lei Wang et al. / Procedia - Social and Behavioral Sciences 138 ( 014 ) exported. In the second phase, we developed an online filter method to import the instant speed in real-time condition to enhance the adaptability of this approach. Moreover, a strctre of system designing is given for implementing the bs arrival information system. Frthermore, adjsted RBFNN by online data approach is tested by deploying this system on bs No.1 in Dalian then contrasted with other approaches, and was demonstrated to be the better method relatively. As a part of giding information techniqes, offering and releasing accrate and reliable bs arrival time information is significantly sefl of planning overall travel time and relieving the impatience when waiting for passengers. Althogh a new kind of forecasting approach has been proposed with an accracy analysis in this paper, the reliability both of prediction reslts and bs operation stats, which can tell passengers whether to trst or not, have not been stdied frther. Ultimately, we sppose an integrated bs information system which comprehensively incldes bs arrival time prediction, bs operation monitoring, bs rote and transfer information qery as sbsystems, which will be a sefl and niqe modle on the rban transportation information platform. References Biagioni, J., Gerlich, T., Merrifield, T., & Eriksson, J. (011). Easytracker: atomatic transit tracking, mapping, and arrival time prediction sing smartphones. In Proceedings of the 9th ACM Conference on Embedded Networked Sensor Systems (pp ). ACM. Jeong, R., & Rilett, R. (004). Bs arrival time prediction sing artificial neral network model. In Intelligent Transportation Systems, 004. Proceedings. The 7th International IEEE Conference on (pp ). IEEE. Kalman, R. E. (1960). A new approach to linear filtering and prediction problems. Jornal of basic Engineering, 8, Lin, Y., Yang, X., Zo, N., & Jia, L. (013). Real-Time bs arrival time prediction: A case stdy for Jinan, China. Jornal of Transportation Engineering, 139, Lin, W. H., & Zeng, J. (1999). Experimental stdy of real-time bs arrival time prediction with GPS data. Transportation Research Record: Jornal of the Transportation Research Board, 1666, L Y.W., Sndararajan N., & Saratchandran P. (1998). Performance evalation of a seqential minimal radial basis fnction (RBF) neral network learning algorithm. Neral Networks, IEEE Transactions on, 9, Park, J., & Sandberg, I. W. (1991). Universal approximation sing radial-basis-fnction networks. Neral Comptation, 3, Y, B., Lam, W. H., & Tam, M. L. (011). Bs arrival time prediction at bs stop with mltiple rotes. Transportation Research Part C: Emerging Technologies, 19, Y, B., Yang, Z. Z., & Zeng, Q. C. (008). Bs arrival time prediction model based on spport vector machine and kalman filter. China Jornal of Highway and Transport, 1, Zho, P., Zheng, Y., & Li, M. (01). How long to wait?: Predicting bs arrival time with mobile phone based participatory sensing. In Proceedings of the 10th international conference on Mobile systems, applications, and services (pp ). ACM. Zh, T., Ma, F., Ma, T., & Li, C. (011). The prediction of bs arrival time sing global positioning system data and dynamic traffic information. InWireless and Mobile Networking Conference (WMNC), 011 4th Joint IFIP(pp. 1-5). IEEE.