ANFIS Based Modeling and Prediction Car Following Behavior in Real Traffic Flow Based on Instantaneous Reaction Delay

Transcription

1 th Internatonal IEEE Annual Conference on Intellgent Transportaton Systems Madera Island, Portugal, September 9-, MC.5 AFIS Based Modelng and Predcton Car Followng Behavor n Real Traffc Flow Based on Instantaneous Reacton Delay Alreza Khodayar, Al Ghaffar, Reza Kazem, and egn Manavzadeh Abstractowadays, car followng models, as the most popular mcroscopc traffc flow modelng, are ncreasngly beng used by transportaton experts to evaluate new Intellgent Transportaton System (ITS) applcatons. Ths paper presents a car-followng model that was developed usng an adaptve neuro fuzzy nference system (AFIS) to smulate and predct the future behavor of a Drver-Vehcle- Unt (DVU). Ths model was developed based on new dea for calculate and estmate the nstantaneous reacton of DVU. Ths dea was used n selecton of nputs and outputs n tran of AFIS model. Integraton of the drvers reacton tme delay and omsson of the necessty of regme classfcaton are consdered whle developng the model. The models performance was evaluated based on feld data and compared to a number of exstng car followng models. The results showed that new model based on nstantaneous reacton delay outperformed the other car-followng models. The model was valdated at the mcroscopc level, and the results showed very close agreement between feld data and model outputs. The proposed model can be recruted n Drer Assstant devces, Safe Dstance Keepng Observers, Collson Preventon systems and other ITS applcatons. I I. ITRODUCTIO TELLIGET Transportaton Systems (ITS) are beng developed and deployed to mprove the effcency, productvty, and safety of exstng transportaton facltes and to allevate the mpact of transportaton on the envronment. These systems explot currently avalable and emergng computer, communcaton, and vehcle-sensng technologes to montor, manage, and control the hghway transportaton system. The success of ITS deployment depends on the avalablty of advanced traffc analyss tools to predct network condtons and to analyze network performance n the plannng and operatonal stages. Many ITS sub-systems are heavly dependent on the avalablty of tmely and accurate wde-area estmates of prevalng and emergng traffc condtons. Therefore, there s a strong need for a Traffc Estmaton and Predcton System (TrEPS) to meet the nformaton requrements of these subsystems and to ad n the evaluaton of ITS traffc Manuscrpt receved Aprl,,. Alreza Khodayar s wth the Mechancal Engneerng Department of K.. Toos Unversty Of Technology, Tehran, Iran; (correspondng author to provde e-mal: arkhodayar(at)dena.kntu.ac.r). Al Ghaffar s wth the Mechancal Engneerng Department of K.. Toos Unversty Of Technology, Tehran, Iran; (e-mal: ghaffar(at)kntu.ac.r). Reza Kazem s wth the Mechancal Engneerng Department of K.. Toos Unversty Of Technology, Tehran, Iran; (e-mal: kazem(at)kntu.ac.r). egn Manavzadeh s wth the Electrcal Engneerng Department of K.. Toos Unversty Of Technology, Tehran, Iran; (e-mal: manavzadeh(at)dena.kntu.ac.r). management and nformaton strateges []. Mcroscopc models are ncreasngly beng used by transportaton experts to evaluate the applcatons of new ITS. A varety of applcatons ncludng car navgaton systems, adaptve cruse control systems, lanes keepng assstance systems and collson preventon systems drectly use the mcroscopc traffc flow models []. Car followng models are among the most popular mcroscopc traffc flow modelng approaches amng to descrbe the process of followng a leader car by a vehcle. As shown n Fg., car followng descrbes the longtudnal acton of a drver when he follows another car and tres to mantan a safe dstance to the leadng car. The majorty of avalable car-followng models assume that the drver of the follower vehcle (FV) responds to a set of varables lke relatve velocty and relatve dstance between the leader vehcle (LV) and the FV, velocty of the FV, and/or desred dstance and/or velocty of the target drver. The response s typcally consdered to be as acceleraton or velocty changes of the followng vehcle []. Fgure. Car followng behavor (LV and FV). Hghly nonlnear nature of car followng behavor necesstates the development of ntellgent algorthms to descrbe, model and predct ths phenomenon. Fuzzy logc can be a potental method dealng wth structural and parametrc uncertantes n the car followng behavor. Addtonally, artfcal neural networks can be favorable tools provdng the possblty of explotng real observed data whle developng the models. euro-fuzzy models, such as AFIS, are combnatons of artfcal neural networks and fuzzy nference systems, smultaneously usng the advantages of both methods. Integraton of human expert knowledge expressed by lngustc varables, and learnng based on the data are powerful tools enablng neuro fuzzy models to deal wth uncertantes and naccuraces []. In ths paper an nnovatve AFIS model based nstantaneous reacton delay s proposed for modelng and predcton of DVU behavor n car followng scenaros //$6. IEEE 599

2 II. BRIEF REVIEW OF CAR-FOLLOWIG MODELS Humans play an essental role n the operaton and control of humanmachne systems such as drvng a car. Modelng drver behavor has transferred human sklls to ntellgent systems, e.g., the adaptve cruse control (ACC) system, ntellgent speed adapton (ISA) system, and autonomous vehcles. Human drvng models are also ndspensable for the performance evaluaton of transportaton systems. Wth advances n emergng vehcle-based ITS technologes, t becomes even more mportant to understand the normatve behavor response of drvers and changes under new systems []. Based on Rasmussenmachne model as shown n Fg. [4], drver behavor can also be separated nto a herarchcal structure wth three levels: the strategc, tactcal, and operatonal level. At the hghest or strategc level, goals of each drver are determned, and a route s planned based on these goals. The lowest operatonal level reflects the real actons of drvers, e.g., steerng, pressng pedal, and gearng. In the mddle tactcal level, certan maneuvers are selected to acheve short-term objectves, e.g., nteractons wth other road users and road nfrastructures. The behavor at ths level s domnated by the most recent stuatons but s also nfluenced by drvers goals at the hgher level. Fgure. Rasmussenmachne model To develop mcroscopc traffc smulaton of hgh fdelty, researchers are often nterested n mtatng human wthout descrbng the detaled drver actons, DVUs n the smulaton are modeled to replcate ther states n realty,.e., the profles of vehcle poston, velocty, acceleraton, and steerng angle. Fg. shows the model structure of a DVU n whch the detaled drver actons become nternal. Fgure. Structure of a DVU model [] Although more factors mght be nvolved n the follower varables above show strong correlaton to the drver decson and are relatvely easy to observe usng modern equpment. Car followng behavor, whch descrbes how a par of vehcles nteracts wth each other, s an mportant consderaton n traffc smulaton models. A number of factors have been found to nfluence car-followng behavor, and these nclude ndvdual dfferences of age, gender, and rsk-takng behavor []. Regardng lteratures, car-followng models can be classfed nto 4 groups as follows: Gazs-Herman-Rothery [5], collson avodance/safe dstance [6], lnear model/ Helly [7], acton pont [8], fuzzy logc-based model [9], desred spacng [], capacty drop and hysteress theory [], neural network [], optonal velocty [], adaptve neural fuzzy nference system [4], emotonal learnng fuzzy nference system [5], local-lnear neural fuzzy [6], local quadratc neural fuzzy [7] and genetc algorthm based optmzed least squares support vector machne [8]. All models presented for car followng behavor are evaluated based on ther ablty to predct or estmate of ncrease or decrease of FV acceleraton. In a general classfcaton, car followng behavor mcroscopc models can be dvded nto groups: mathematcal equaton-based and nput-output based. The most mportant pont n mathematcal models s calculaton and obtanng model parameters. Therefore, these parameters can be always obtaned by average of values or regardng them as a fx value of DVU. Because these parameters are as a functon of tme, results of these models are proper for test cases and are not relable. In nput-output models, by consderng the fxed DVU reacton tme, output values are appled to nput. Snce the DVU reacton tme s not actually fxed, other parameters vary wth tme. So an error n modelng s appeared because of the dfference between real data and data used for modelng. III. EW AFIS CAR FOLLOWIG MODEL DESIG In ths secton, consderng a proposed dea, an nputoutput model s presented to estmate FV acceleraton. Usng ths method, DVU nstantaneous reacton tme as nput for system s calculated and then other nputs and outputs are chosen accordng to DVU reacton delay. DVU reacton delay n subsequent moments s not the same, so nput and output must be chosen as a functon of the proper and correct reacton tmes. In fact, the stmulus and reacton should be consdered as an nput and output wth respect to accurate nstantaneous reacton tme. So the prevous models n whch DVU reacton tme was consdered as a constant value can be modfed by ntroducng ths proposed dea. Reacton delay s a common characterstc of humans n operaton and control, such as drvng a car. The operatonal coeffcents and delay characterstc of humans can vary rapdly due to changes of factors such as task demands, motvaton, workload and fatgue. However, estmaton of these varatons s almost mpossble n the classcal paradgms. Therefore, an assumpton of a fxed reacton delay n a certan regme stll cannot be completely crcumvented. Drver reacton tme was defned as the summaton of percepton tme and foot movement 6

3 tme by earler car-followng research. In psychologcal studes, the drver reacton process s further represented n four states: percepton, recognton, decson and physcal response. Although research on car followng models has been hstorcally focused on exploraton of dfferent modelng frameworks and varables that affect ths behavor, t has been recognzed that the reacton delay of each drver s an ndspensable factor for the dentfcaton of car followng models [8]. Many studes have estmated the reacton tme based on ndoor experments and drvng smulators. To estmate drver reacton delays from real data, several approaches have been proposed. Fg. 4 ndcates how the DVU nstantaneous reacton delay can be calculated by usng the proposed dea. Ths dea s based on the fact that the delay tme s the tme between the varaton of relatve velocty and acceleraton of FV whch s the concept of the stmulus and reacton. Varatons n relatve velocty and FV acceleraton are the maxmums or mnmums of velocty trajectory or FV acceleraton, respectvely. DVU nstantaneous reacton s the tme dfference between two subsequent varatons: relatve velocty as stmulus and FV acceleraton as reacton. dataset s used to tran the AFIS predcton model []. In June 5, a dataset of trajectory data of vehcles travellng durng the mornng peak perod on a segment of Interstate hghway n Emeryvlle (San Francsco), Calforna has been made usng eght cameras on top of the 54m tall Unversal Cty Plaza next to the Hollywood Freeway US-. On a road secton of 64m, as shown n Fg. 5, 6 vehcle trajectores have been recorded n three consecutve 5-mnute ntervals. Ths dataset has been publshed as the - Dataset conssts of detaled vehcle trajectory data on a merge secton of eastbound US-. The data s collected n. second ntervals. Any measured sample n ths dataset has 8 features of each drver-vehcle unt n any sample tme, such as longtudnal and lateral poston, velocty, acceleraton, tme, number of road, vehcle class, front vehcle and etc. Fgure 4. calculaton DVU nstantaneous reacton delay ow ntroduces the bascs of the AFIS network archtecture appled for the car-followng predcton system. A detaled coverage of AFIS can be found n [9, ]. AFIS enhances fuzzy controllers wth selflearnng capablty for achevng optmal control objectves. An adaptve network s a multlayer feedforward network where each node performs a partcular node functon on ncomng sgnals. It s characterzed wth a set of parameters pertanng that node. To reflect dfferent adaptve capabltes, both square and crcle node symbols are used. A square node (adaptve node) has parameters, whle a crcle node (fxed node) has none. The parameter set of an adaptve network s the unon of the parameter sets assocated to each adaptve node. To acheve a desred nputoutput mappng, these parameters are updated accordng to gven tranng data and a recursve least square (RLS) based learnng procedure. In order to desgn an AFIS predcton system, a dataset of car followng behavor s needed. So, real car followng data from US Federal Hghway Admnstraton Fgure 5. A segment of Interstate hghway n Emeryvlle, San Francsco, Calforna. The trajectory data seems to be unfltered and exhbts some nose artefacts, so we have appled a movng average flter to all trajectores before any further data analyss. Comparson of unfltered and fltered data s shown n Fg. 6. 6

4 A c c e l e r a t o n ( m /s ) Real Data Fltered Data Fgure 6. Comparson of unfltered and fltered data. To desgn AFIS model shown n Fg. 6, t s assumed that the fuzzy nference system appled for predcton model has four nputs and one output, whch nputs are nstantaneous reacton delay, relatve speed, relatve dstance and velocty of FV, and output s acceleraton of FV. There are three dsgmf membershp functons for each nput. The rule base contans 8 fuzzy f-then rules of Takag-Sugeno] and hybrd algorthm s used to tran ths model. In the development of AFIS predcton model, the avalable data are usually dvded nto two randomly selected subsets. The frst subset s known as the tranng and testng data set. Ths data set s used to develop and calbrate the model. The second data subset (known as the valdaton data set), whch was not used n the development of the model, s utlzed to valdate the performance of the traned model. For ths paper, 7% of the master data set was used for tranng and testng purposes. The remanng % was set asde for model valdaton. based on the nstantaneous reacton delay dea; two AFIS estmator systems wth constant delay and three nputs are desgned and smulated..s and.s are assumed for constant delay. Also to tran and test the performance of these systems, same real traffc data are used as nput and output. Fg. 8 shows the performance results for AFIS estmator for DVU car followng behavor based on nstantaneous reacton delay as nput to estmate the FV acceleraton. As seen n ths fgure, the trajectores of real drver and AFIS model are qute same. A cce le ra to n(m /s ) - - Real Model Fgure 8. Results for AFIS estmator based on nstantaneous reacton delay Fg. 9 shows the performance of AFIS estmator for DVU n car followng behavor based on the constant delay of.s. Fg. shows the performance of AFIS estmator for DVU n car followng behavor based on the constant delay of.5s. A c c e le ra to n (m /s ) - Real Model Fgure 9. Results for AFIS estmator based on constant reacton delay. sec Real Model A c c e le ra t o n (m /s ) - Fgure 7. Desgned AFIS model for car followng behavor. IV. DISCUSSIO AD RESULTS To evaluate the competence of AFIS estmator system Fgure. Results for AFIS estmator based on constant reacton delay.5 sec 6

5 To examne the performance of developed models, varous crtera are used to calculate errors. The crteron mean absolute percentage error (MAPE), accordng to equaton (), shows the mean absolute error can be consdered as a crteron for model rsk for usng t n real world condtons. Root mean squares error (RMSE), accordng to equaton (), s a crteron for comparng error dmenson n varous models. Standard devaton error (SDE), accordng to equaton (), ndcates the persstent error even after calbraton of the model. In these equatons, x shows the real value of the varable beng modeled (observed data), x shows the real value of varable modeled by the model and x s the real mean value of the varable and s the number of test observatons. x x MAPE x RMSE ( x x ) SDE x x MAPE x () () () Errors n modelng wth consderng MAPE, RMSE and SDE are summarzed n Table I. TABLE I RESULT OF ERROR FOR AFIS CAR FOLLOWIG MODEL AFIS CAR FOLLOWIG MODEL Error Crtera MAPE RMSE SDE Based on nstantaneous reacton delay Based on reacton delay =. sec Based on reacton delay =.5 sec AFIS car followng model based on nstantaneous reacton delay has a lower error value comparng wth models regardng fxed reacton delay n all crtera. Ths result shows that ths new model has a strong capablty wth respect to other models. V. COCLUSIO In ths paper, a new AFIS model for DVU n car followng was studed. Ths model s based on nstantaneous reacton delay dea for DVU as a nput and also choosng sutable other nputs and outputs wth respect to nstantaneous reacton delay. In ths model, the stmulus and reacton should be consdered as an nput and output wth respect to accurate nstantaneous reacton tme. Satsfactory performance of the proposed model s demonstrated through comparsons wth real traffc data and also the results of AFIS models regardng fxed reacton delay. The smulaton results show the effcency of the proposed model n drver modelng and predcton of the drver's actons comparng wth others AFIS based model. The proposed method can be recruted n drver assstant devces, safe dstance keepng observers, collson preventon systems and other ITS applcatons. REFERECES [] X. Ma, I. Andr, Behavor Measurement, Analyss, and Regme Classfcaton n Car Followng IEEE Transactons on Intellgent Transportaton Systems, vol. 8, no.,pp , 7. [] S. Panwa, H. Da, Followng Models IEEE Transactons on Intellgent Transportaton Systems, vol. 8, no., pp. 67, 7. [] B. Kosko, eural etworks and Fuzzy Systems, Prentce-Hall, 99. [4] J. Rasmussen, Informaton Processng and HumanMachne Interacton: An Approach to Cogntve Engneerng ew York: Elsever, 986. [5] K. I. Ahmed, behavor Technology, Department of Cvl and Envronmental Engneerng, Cambrdge, Massachusetts, 999. [6] R. Tatchkou, S. Bswas, F. Don, Avodance usng Inter-vehcle Packet Forwardng Telecommuncatons Conference, GLOBECOM'5, vol. 5, pp , 5. [7] T. H. Yang, C. W. Zu, -followng model Ffth World Congress on Intellgent Control and Automaton, WCICA4, vol. 6, pp. 5-56, 4. [8] W. Wang, W. Zhang, D. L, K. Hrahara, K. Ikeuch, Improved acton pont model n traffc flow based on drver's cogntve mechansm- 45, 4. [9] P. Zheng, M. McDonald, Car-Followng Behavor Analyss Scence, Sprnger, book: Fuzzy Systems and Knowledge Dscovery, vol. 6/5, pp , 5. [] P. Hdas, of mergng and weavng Emergng Technologes, vol., no., pp. 76, 5. [] Z. L, F. Lu, Y. Lu, -Followng Model of Traffc Flow and umercal Tests on Automaton and Logstcs, pp. 6-, 7. [] S. Panwa, H. Da, -Based eural etwork Car Followng Model Conference on Intellgent Transportaton Systems, pp. 75-8, 5. [] M. Kana, K. shnar, T. Tokhro, model and ts long-lved metastabltyphys. Rev. E, vol. 7, no., 5. [4] S. L, Smulaton of car-followng decson usng fuzzy neural networks systemieee Intellgent Transportaton Systems, vol., pp. 4-45,. [5] A. Ghaffar, R. Zarrnghalam, M. Abdollahzade, Modelng and Predcton of Drver-Vehcle-Unthavor n Real Traffc Flow Intellgence (n press),. [6] A. Ghaffar, R. Zarrnghalam, M. Abdollahzade, Future States of a Vehcle n a Car-Followng Scenaro Usng Locally Lnear euro-fuzzy Models and LOLIMOT Learnng Algorthm IEEE Internatonal Conference on Intellgent Systems, Varna, Bulgara, September 6-8, 8. [7] R. Zarrnghalam, Flow Regardng the Drveror n Mechancal Engneerng, K.. Toos Unversty of Technology, Iran, 8. [8] A. Ghaffar, R. Zarrnghalam, M. Abdollahzade, -LSSVM: an nventve method and ts applcaton n smulaton and predcton of mcroscopc traffc flow ever, Smulaton Modellng Practce and Theory (n press), 9. [9] J. Mar and F. Ln, -Followng Collson Preventon System, IEEE Transactons on Vehcular Technology, vol. 5, no. 4, pp. 6,. [] A. Khodayar, A. Ghaffar, R. Kazem,. Manavzadeh, Behavor n Real Traffc FlowIEEE Internatonal Conference on Cybernetcs and Intellgent Systems (CIS), Sngapore,. [] US Department of Transportaton, ext Generaton Smulaton,ngsm.fhwa.dot.gov, 9. 6

6 [] J. S. R. Jang, C.-T. Sun, and E. Mzutan, -Fuzzy and Soft Computng: A Computatonal Approach to Learnng and Machne Intellgence, Prentce Hall,