Multi-objective optimization method for the ATO system using Cellular Automata

Transcription

1 Computers n Ralways XI 173 Mult-objectve optmzaton method for the ATO system usng Cellular Automata J. Xun, B. Nng & K. P. L The Key State Laboratory of Ral Traffc Control and Safety, Bejng Jaotong Unversty, Bejng, People s Republc of Chna Abstract Automatc Tran Operaton (ATO) s one of the most mportant functons for an advanced tran control system n hgh-speed ralway systems. Research on optmzaton methods for ATO has been done before t s mplemented n a tran control system. From a theoretcal pont of vew, t can be formulated as one of the functons of mult-objectve Optmal Control Theory. Ths paper presents a new mult-objectve optmzaton method for an ATO system usng Cellular Automata (CA). A CA model for an ATO system s appled to smulate tran operaton. An optmal method for ATO s proposed. Compared wth actual tran operaton results, the control algorthm can reduce energy consumpton and ensure tran operaton safety such as hgher accuracy of tran stop. Therefore, t can mprove the effcency and safety of the tran operaton. Keywords: Automatc Tran Operaton (ATO), Cellular Automata (CA), optmal method. 1 Introducton ATO system has been known as one of the most effectve methods for savng energy and mprovng the transportaton effcency. Along wth the rapd mprovement of technologes, especally wth the development of CBTC (Communcaton Based Tran Control) system [1], more and more ATO systems have been put n operaton. The control algorthm s the core of ATO system. Many scholars dd a lot of researches on ATO control algorthm. C.S.Chang proposed a novel approach of dfferental evoluton (DE) by ncorporatng the Pareto-optmal set whch s presented for optmzng tran movement through tunng fuzzy membershp functons n mass transt systems [2]. Satosh Sekne do:1.2495/cr8181

2 174 Computers n Ralways XI proposed two-degree-of-freedom fuzzy neural network control systems [3]. Tang Tao presented the basc structure and functons of ATO system [4]. At present, there are several systems wth ATO functon from the dfferent companes n the world. For nstance, TRAINGUARD from Semens has been used n M4 lne and M5 lne n Guangzhou Metro n Chna snce 24. The SELTRAN from Alcatel has been used n lght ral n Wuhan Metro and M3 lne n Guangzhou Metro. URBALIS from Alstom has been used n M2 lne and Arport lne for Bejng Metro. There are also ATO systems from Htach and Westnghouse etc. Some scholars have put Cellular Automata nto analyzng tran movement. L Ke-Png et al. [5] and Nng Bn et al. [6] extended the NaSch model and proposed an mproved model of tran-followng n ral system. Zhou Hua Lang et al. [7] smulated the traffc phenomenon of delay propagaton usng a cellular automaton traffc model for movng-lke block system. In [8], a CA model that extended to the ralway network was proposed. What we present n ths paper s about the researches on a new multobjectve optmzaton method for ATO system usng cellular automata. We smulate some tran trajectores wth dfferent optmal objects and dscuss the nfluence among dfferent optmal objects. 2 Automatc Tran Operaton system Automatc Tran Control system ncludes ATP (Automatc Tran Protecton), ATS (Automatc Tran Supervson) and ATO (Automatc Tran Operaton). ATP s the safety system whch ensures that trans reman a safe dstance and have suffcent warnng to allow them to stop wthout colldng wth another tran. The ATS can help dspatcher supervse and manage tran operaton. ATO (Automatc Tran Operaton) s concerned on the parts of tran operaton related to staton stops and starts, punctualty, comfort and energy savng. It wll receve commands from ATS to adjust tran speed. The runnng speed can not exceed the speed restrcton by ATP. Wthout ATP and ATS, ATO can t work ndependently. The schematc dagram s shown as Fgure 1. ATO On-board Man-Machne Interface ATP On-board Speed Sensor Servce/Emergency Brake Tracton ATO Track-sde ATP Track-sde ATS Fgure 1: The schematc dagram of ATO system.

3 Computers n Ralways XI 175 ATO controller should consder the tran parameters and lne parameters, such as slope and curve etc. Accordng to schedule and real-tme nformaton, t decdes the brake or propulson rate of tran. Under the lmtaton of ATP, ATO controller wll gather the nformaton whch s helpful to ts decson, such as tran speed, programmed stop and dwell tme, and so on. Fgure 2 shows the ATO controller model. Interval wth a seres of next obstacles Programmed Travel Tme Tachometer (Speed) Odometer (Poston) ATP ATO Controller Lmted Speed of Lne Programmed Stop and Dwell Tme Break/Propulson Rate (Handle Poston) Fgure 2: ATO controller model. In the development of ATO, the control algorthms whch have been used can be put nto 4 types [4]: (1) Frst type: PID (Proporton-Integral-Dervatve) Control. Because of ts smple and convenent operaton, the ATO system wth PID control algorthm s frstly put nto subway tran control. Ths method belongs to classcal control method. The core s to compute based on the tracton/brakng character formulae, and then to control tran operaton under dfferent modes of start-up, coastng, tracton and brakng modes. Because of the low demand of traffc at that tme, the ATO system whch s controlled by ths method s put n operaton n several lnes. (2) Second type: Parameter Self-adaptve Control. Snce some of uncertan factors affect ATO system, the control strategy wll be dfferent as the change of work condton. The tradtonal PID control s dffcult to be used to control the complcated operaton. PID control algorthm s mproved, and Parameter Selfadaptve Control Algorthm appears. Ths method adopts adjustment strategy wth adaptve parameters to decrease the nfluence of envronment changng. The core of ths method s the same wth one of classcal PID control. (3) Thrd type: Intellgent Control. As the development of control theores, ntellgent technology s appled to solve control problems. The combnaton of experence and ntellgent control theory brngs a new algorthm: ntellgent control algorthm. Intellgent control system ncludes fuzzy control, expert system, neural network control, and so on. Fuzzy control can effectvely control a system whch s dffcult to buld a mathematcal model and can be controlled wth experence. Expert system can make decson wth commonsense of experenced drver and unque ntellgent behavors. Neural network has the ablty to parallel processng and self-learnng.

4 176 Computers n Ralways XI (4) Fourth type: Integrated Intellgent Control. Along wth ncreasng requrement on ATO, sngle ntellgent control method can t meet the requrement of ATO system. Integrated ntellgent control s under consderaton. Because each ntellgent control algorthm has ts own characterstcs, several ntellgent control algorthms can complement each other and acheve better results. Integraton of several ntellgent control algorthms s the research drecton of ATO control algorthm. ATO s a complex tran control system. ATO control algorthm should consder envronmental factors to decde control parameters. 3 Optmal method wth CA model 3.1 CA model Nagel and Schreckenberg developed a one-dmensonal probablstc CA model (called NaSch model), whch s a model of traffc flow on a sngle-lane [5]. In NaSch model, the road s dvded nto L cells numbered by = 1, 2,, L, and tme s dscrete. Each ste can be ether empty or occuped by a vehcle wth nteger speed V =, 1,, V max, where Vmax s the maxmum speed. X () t s the poston where vehcle s at tme t, and gap ( t) = X + 1( t) X ( t) 1 expresses the gap between vehcle and + 1 at tme t.the underlyng dynamcs of NaSch model s governed by the updated rules appled at dscrete tme steps. All stes are smultaneously updated accordng to four successve steps: (1) Acceleraton: V ( t + 1) mn( V ( t) + 1, Vmax ) (2) Slowng down: V ( t + 1) mn( V ( t), gap ( t) ) ( gap (t) s the number of empty cells n front of the vehcle ). (3) Randomzaton: V ( t + 1) max( V ( t) 1, ) (decrease V by 1 wth randomzaton probablty p f V > ). (4) Movement: X ( t + 1 ) X ( t) + V ( t +1) In the proposed model, the tme nterval between two sequental cellular states s 1 second. And n order to determne stop accuracy, the length of each cell corresponds to 1 cm. 3.2 Optmal control algorthm The basc requrement of ATO s to adjust tran speed n operaton and make tran stop accurately at a staton when the tran approaches the staton. ATO should not only adjust tran speed to reach the requrement of schedule, but also acheve excellent performance n punctualty, comfort and energy savng and so on. The followng ponts are the man ones for the ATO performance. Hgh-Effcency Ths s the orental purpose for usng ATO system. ATO can mprove the effcency of the whole system and ncrease the capacty of lne.

5 Computers n Ralways XI 177 Punctualty Ths pont s an mportant character for ralway traffc, especally for urban mass transport. Trans run under the schedule. When a tran s delayed, t needs ATO to adjust tran s speed and prevent tran from dsordered operaton. Energy-Savng The energy cost of the manual operaton s usually more than automatc operaton. Therefore, energy-effcent tran control for ATO s an mportant approach to savng energy. The mnmum of energy cost s the optmalty crteron. We obtan the optmalty crteron: () t mn J = mn F S = mn M a ds (1) Because of the dscrete model, eqn. (1) can be presented n a dscrete form: D V ( t) V ( t 1) mn J = mn M s t T D ( V () t V ( t 1) ) V ( t) = mn M (2) 1 Where J s energy consumpton whch does not nclude auxlary power needed by tran, F s tracton force, M s tran weght, a (t) s the acceleraton at tme t, V (t) s the tran velocty at tme t, D s the total length of lne and T s the tran travel tme. Comfort In order to mprove comfort, the change of acceleraton and deceleraton should be nfrequent and the value should be small. The total number and the maxmum of acceleraton and deceleraton durng a trp s the optmalty crteron. Stop-Accuracy For urban mass transport, stop-accuracy s also an mportant character, especally for statons wth PSD (Platform Screen Door). Inaccurate stop wll obstruct passengers takng on and off. It s mportant to tune the ATO accordng to the above ponts and also dffcult snce the trade-off among the above ponts. So the ATO system s a multobjectve control system. We can buld up the objectve set ncludng Effcency(OB_Eff), Punctualty(OB_Punc), Comfort(OB_Comf), Stop Accurancy(OB_SA) and Energy Savng(OB_ES) as follows: ObjectveS et Effcency (OB_Eff), Punctualt y(ob_punc) Comfort(OB _Comf) Stop Accurancy( OB_SA) Energy Savng(OB_ ES)

6 178 Computers n Ralways XI Start End Intalze Tran Condton Optmal Speed Profle found Select Lne Condton Smulate tran speed profle by CA model < I Tune Calculate Smulaton Results Update optmal set Compare Run Tme wth Schedule Tme Compare wth the solutons n the exstng optmal set Fgure 3: The flow chart of optmal algorthm. It may be necessary to emphasze tme schedule when n flat-out run optmzaton, or to emphasze effcency n optmal tran-coast run, and so on. Before tran starts, t should be decded whch s the most mportant object. The detaled steps of the proposed method wth CA model are lsted below: Step 1. Frstly, ntalze tran and lne condton and set = 1, where s the ndex of teraton. Step 2. Then generate a soluton accordng to the weghts of each object. Step 3. Smulate tran speed profle wth CA model and calculate the travel tme, stop accuracy, the value of energy consumpton, total number and maxmum of acceleraton and deceleraton durng ths trp. Step 4. Check whether the travel tme of ths soluton s smaller than the schedule tme. If yes compare wth the solutons n the exstng optmal set. If the new soluton domnates any one n the set, then replace the old one and update the set. If no, keep the optmal set unchanged. Step 5. Tune ths soluton to decrease the travel tme and smulate agan. Step 6. Repeat Step 2 to 5 untl > I where I s the presettng number of teraton. Step 7. If > I, termnate calculaton and output the results. 4 Smulaton results and ts analyss In order to prove the valdty of proposed CA model, a track n a test lne between two statons NS (the North Staton) and SS (the South Staton) s chosen for an nterstaton optmzaton. The total length s 87.29m and the maxmum safety speed s 5 km/h. There are two cvl speed lmtatons of 35 km/h from m to 6m and from m to m. The effect caused by the slope and curve of ralway secton s gnored.

7 Computers n Ralways XI 179 Parameters n ths method are chosen as follows: 1) The maxmum acceleraton and deceleraton a_max = 1 m/s 2 ; 2) The length of the tran s 6 m (3 Carrages); 3) The weght of the tran s 9 t (3 Carrages); 4) The deceleraton caused by ar resstance and frcton between track and wheel s consdered as.4 m/s 2 ; 5) The scheduled tme runtme s 1 s. Three cases wth dfferent optmal subjects are studed n the smulaton. The data of frst three cases n Table 1 are obtaned from smulaton and the data of the fourth case are actual tran runnng results (Energy Consumpton s computed by equaton (2) and not actual tran runnng energy cost). The results n Table 1 show that the tran performance has been much mproved after optmzng wth the proposed method. In case 2, the proposed method not only mproves the comfort of passengers but also ensures that the tran fnshes ts trp on tme. Assume all the regenerated energy s fully absorbed by other tran, the tran n case 2 performs the optmal object n Energy-Savng and Comfort. Otherwse, the tran n case 3 reaches the destnaton wth the shortest travel tme. In case 2 and 3, the dstance between actual stop and the stop sgn s only.2m. It s a great ncrease compared wth actual expermental stop accuracy n case 4. The effect of communcaton between tran and tracksde wll be mproved and the tran safety wll be strengthened. Table 1: Comparson of tran performances. Acceleraton Energy Travel Total Maxmum Consumpton(MJ) Tme(s) 2 Count ( m / s ) Case ID Stop Accuracy(m) Case 1: typcal condton (Fg. 4a-4b) Compared wth the case 2 and 3, the present case s well balanced n terms of all the objectves. For example, t use less energy, mprove the passenger comfort and runs only slghtly slower than the flat-out run condton (92 seconds to complete the trp). Compared wth the case 2, t greatly decreases the travel tme wth the energy consumpton ncreasng. Ths s a typcal case taken from the fnal optmal set. Case 2: least energy condton (Fg. 4c-4d) When the tran accelerates close to the cvl speed lmt, t wll cut off the tracton and start to coast. Then tran wll coast for a few seconds untl t has to take breakng to stop at the staton SS. The energy consumpton durng ths trp s the least n all cases.

8 Computers n Ralways XI 1 8 A-T Curve.5 Dstance(m) 6 4 D-T Curve -.5 Acceleraton(m/s ) 2-1 (a) Tme(s) (b) Dstance(m) 5 D-T Curve A-T Curve Acceleraton(m/s ) -.5 (c) Tme(s) (d) A-T Curve.5 Dstance(m) 6 4 D-T Curve -.5 Acceleraton(m/s ) 2-1 (e) Tme(s) (f) Fgure 4: The result of smulaton wth dfferent object. Case 3: flat-out condton (Fg. 4e-4f) The tran s seen to run at the hghest possble speed wth the velocty profle very close to the cvl speed lmt. It takes only 91 seconds to fnsh the entre travel wth average speed reachng a maxmum value of km/h. The comparson between the smulaton results and the actual tran operaton results s shown n Fgure 5. The sold lne denotes the smulaton values usng the proposed method, and the dotted lne denotes the actual tran values ganed from tachometer. From Fgure 5, we can see that the smulaton values are close to the actual values. At acceleraton regon, the smulaton results and actual

9 Computers n Ralways XI 181 results are nearly equal. There s a margn at deceleraton regon and the smulaton values exceed the actual values. These results demonstrate the dependablty and avalablty of the method. Fgure 5: The comparson between smulaton data and actual expermental data. 5 Conclusons An ATO system can not only adjust tran speed n operaton but also acheve excellent performance n punctualty, comfort and energy savng and so on. Ths paper proposes a new mult-objectve optmzaton method for ATO system usng cellular automata. The smulaton results demonstrate that the tran performances are really mproved after optmzng wth the proposed method. The comparson between actual tran operaton results and smulaton results s also dscussed. Fnally the dependablty and avalablty of the method s proved ntally. The proposed method s prelmnary and the smulaton results are proved to be effectve. However snce t does not consder slope and curve of the lne, the future research should focus on mprovng the proposed method by consderng the effect caused by more parameters such as slope, curve and so on. The method wll be further perfected. Acknowledgements The project s supported by the Natonal Natural Scence Foundaton of Chna under Grant No , the Key Project of Chnese Mnstry of Educaton under Grant No. 177 and Bejng Area Key Laboratory Urban Ral Transport Automaton and control.

10 182 Computers n Ralways XI References [1] Nng Bn, Tang Tao, Qu Kuan Mn and Gao Chun Ha CBTC(Communcaton Based Tran Control): system and development Computers n Ralways Ⅹ WIT Press pp July 26, Compral 26, Prague, Crech Republc. [2] C.S.Chang, D.Y.Xu and H.B.Quek Pareto-optmal set based multobjectve tunng of fuzzy automatc tran operaton for mass transt system IEE Proc- Electr. Power Appl., Volume 146, No. 5, September 1999, pp [3] Sekne, S., Imasak, N. and Endo, T. Applcaton of fuzzy neural network control to automatc tran operaton and tunng of ts control rules Fuzzy Systems, Internatonal Jont Conference of the Fourth IEEE Internatonal Conference on Fuzzy Systems and the Second Internatonal Fuzzy Engneerng Symposum., Proceedngs of 1995 IEEE Internatonal Conference on, Volume 4, 1995, pp [4] Tang Tao and Huang Lang-j A Survey of Control Algorthm of Automatc Tran Operaton Journal of the Chna ralway Socety, Volume 25, No.2, 23 pp [5] L Ke-Png,Gao Z-You and Nng Bn Cellular automaton model for ralway traffc Journal of Compute Physcs, Volume 29, 25, pp [6] Nng Bn, L Ke-Png and Gao Z-You Modelng fxed-block ralway sgnalng system usng cellular automata model Internatonal Journal of Modern Physcs, Volume16, 25, pp [7] Zhou Hua-Lang, Gao Z-You and L Ke-Png Cellular automaton model for movng-lke block system and study of tran s delay propagaton Acta Phys. Sn., Volume 55, 26, pp [8] Xun Jng, Nng Bn and L Ke-Png Network-based tran-followng model and study of tran s delay propagaton Acta Phys. Sn., Volume 56, September 27, pp