Driving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d
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1 Interntionl Industril Informtics nd Computer Engineering Conference (IIICEC 15) Driving Cycle Construction of City Rod for Hybrid Bus Bsed on Mrkov Process Deng Pn1,, Fengchun Sun1,b*, Hongwen He1, c, Jinkun Peng1, d 1 tionl Engineering Lbortory for Electric Vehicles, Beijing Institute of Technology, Beijing 81, Chin hdpndeng@163.com, sunfch@bit.edu.cn, hwhebit@bit.edu.cn, d pengjinkun87719@163.com b c Keywords: Driving cycle; Mrkov processes; Grdient; Hybrid Bus Abstrct. By using the relevnt theory of Mrkov chin, the ctul driving dt re compressed nd reconstructed, nd then the city rod driving cycle is constructed bsed on chrcteristic prmeters such s velocity, ccelertion nd grdient. In the process of constructing the driving cycle, corresponding stte division principle nd the evlution criteri of chrcteristic prmeters re designed ginst hybrid bus. The comprison results show tht the driving cycle constructed using Mrkov processes cn reflect the rel driving chrcteristics on city rods. Introduction Driving cycle is velocity-time trce tht describes driving chrcteristics of specific vehicle in specific environment. Driving cycle hs been n importnt prmeter to estimte rel-world vehicle emissions nd fuel consumption which re evlution criterions of power chin design. [1,2] When vehicle is in motion, the driver chnges the output power of vehicle s power chin nd finlly chnges vehicle velocity. The vehicle stte in the next second is only relted with current rod condition. Then we could sy tht this rndom vrible follows Mrkov process. [3] Compred with trditionl construction method, the Mrkov driving cycle method better reflects the nture of velocity chnge. Rndom selection in trditionl method is substituted by selection bsed on Mrkov trnsition mtrix, nd the ccurcy of construction is improved. [4] 2 The originl driving dt collection The required prmeters of the originl driving dt collection re velocity, ccelertion nd grdient. This pper dopts the OXTS Inertil+ to mesure velocity, ccelertion nd grdient of vehicle. These prmeters re combined mesured by Stellite-bsed Globl Positioning System (GPS) nd Inertil vigtion System. OXTS Inertil+ mesurement ccurcy is shown in tble 1. Tble 1Mesurement ccurcy of the experimentl equipment Position Accurcy Velocity Accurcy Roll/Pitch 2cm 1σ.5 km/hrms.3 1σ Bis mm/s² 1σ Accelertion Linerity Scle Fctor.1%.1% 1σ Rnge m/s² 3 Dt Preprocessing The dt preprocessing is consists of four steps: division, stte cluster division, estimtion of the trnsition mtrix nd nlysis of chrcteristic prmeters. 3.1 Frgment Division The s, which re the minimum unit of the driving cycle construction, re divided from the originl driving dt ccording to specific rules. These s will be used to nlyze the chnge regultion of velocity The selection of velocity threshold The object of this study is hybrid electric bus. The pure electric mode is often pplied when the vehicle velocity is low. So if the vehicle velocity is lower thn the selected velocity threshold, this 15. The uthors - Published by Atlntis Press 1159
2 smpling point should be divided into the which we clled stop. Anlyze ll of smpling points, whose velocity is below 4Km/h, nd the sttisticl dt is shown in tble 2 Tble 2 Probbility distribution of smpling points in low velocity velocity rnge(km/h) ~.4.4~.7.7~1 1~ ~2 2~ ~3 3~ ~4 Probbility distribution.1% 17.32% 9.36% 7.85% 4.7% 3.36% 2.8% 2.42% 2.% It is obvious from tble 2 tht the smpling points whose velocity is less thn.7km/h ccount for 67.32% of ll the smpling points. After comprehensive considered,.7km/h is selected s the velocity threshold of stop The selection of ccelertion threshold The ccelertion threshold selection is s sme s the velocity threshold. When vehicle trvels t uniform velocity, the vehicle s ccelertion fluctuted in smll rnge. Tble 3 Probbility distribution of smpling points in stop s bsolute ccelertion ~.5.5~.1.1~.15.15~.2.2~.25.25~.3.3~.35 >.35 Probbility distribution 82.9% 9.92% 2.59% 1.23%.75%.6%.49% 2.33% As we cn see from tble 3, bout 94.6% of ccelerometer redings of the smpling points re between nd.15 when the vehicle is sttionry. And it is cceptble tht the ccelertion threshold should be set to Bsis of division The bsis of division is shown in Fig. 1. The originl test dt Velocity.7km/h Y Acclertion.15m/s 2 Y Acclertion -.15m/s 2 Stop Accelertion Decelertion Y Uniform Figure 1 Bsis of Frgment Division 3.2 Stte cluster division Clcultion for the rode power nd the nominl velocity To completely descript the driving condition, the rod power is introduced s n importnt bsis of stte cluster division. Rod power, clculted in Eq. 1, cptures the combined effects of rolling resistnce, erodynmic resistnce, ccelertion resistnce nd grdient resistnce. 3 1 Gfu (.15) ( Giu CDAu P = + + ),.15 ηt (1) 3 1 Gfu (.15) ( Giu CDAu d mu du P = ), > >.15 ηt dt Rod power is not direct prmeter to divide the originl dt, nd we need velocity prmeter to be the division criterion. ominl velocity, clculted in Eq. 2, is good choice. where u is the vehicle nominl velocity. 116
3 3 1 Gfu C (.15) ( D Au P = + ) = P (.15),.15 ηt C Au P(.15) = + + = P (.15) > > > ηt dt 3 1 Gfu ( D dmu du ), Stte cluster division According to the vehicle nominl velocity discussed bove, the verge nominl velocity of ech cn be clculted. According to the verge velocity, ll the s re lbeled by 7 stte clusters: (-,5],[5,15],[15,25],[25,35],[35,45],[45,55],[55, ]. The stte clusters re collections of s with similr verge velocity chrcteristics. 3.3 Estimtion of the trnsition mtrix Vehicle s driving condition trnsltes from one stte to nother long with the time. The trnsition mtrix is estimted by counting the trnsltion of stte in the originl dt. The expression of elements in the trnsition mtrix is shown in Eq. 3. (2) T = p ij ij = ij j (3) where ij is the number of individuls in stte i t time t-1 nd j t time t. The clcultion results T, 7 7 mtrix, is shown below: 3.4 Clcultion for PM PM (Performnce Mesure) chrcterize the difference between the originl dt nd lterntive driving cycles tht hve been constructed. We define the finl representtive cycle to be the one tht hs the lowest vlue of PM. The clcultion for PM is consists of three steps: (1) We obtin n 16 mtrix, denoted by M, by counting chrcteristic prmeters of every lterntive driving cycle. And then denote M s the chrcteristic prmeters mtrix of the originl dt. The prmeters, shown in tble 4, typiclly describe the chrcteristics of the verge driving behvior in term of velocity, ccelertion nd rod power, etc. [5] Tble 4 Chrcteristic prmeters of the originl dt Chrcteristic Prmeters sttistic Chrcteristic Prmeters sttistic 1 Proportion of stop time 24.9% 9 Mximum ccelertion Proportion of uniform velocity 19.91% Accelertion stndrd devition Proportion of ccelertion.31% 11 Minimum grdient -4.59% 4 Proportion of decelertion 25.69% 12 Mximum grdient 5.61% 5 Velocity stndrd devition Averge grdient.54% 6 Mximum velocity Minimum rod power Averge velocity Mximum rod power Minimum ccelertion Averge rod power (2) ote tht in tble 4, the rnges of chrcteristic prmeters re totlly different. Without normliztion, the PM vlue would be dominted by one or two chrcteristic prmeter tht hs lrge vlue rnge. The expression is shown in Eq
4 T pm = M ( ) ( 1,1, 1 16 ) ( 1 ) M n n ( 1 16 ) pm( ki, ) pmi min PM (, ) =, k 1, n i 1,16 ki pmimx pmimin ( ), ( ) (3) The finl PM of the kth lterntive driving cycle is obtined by integrting elements of row k in mtrix PM. 4 Driving Cycle Construction In this study, the entire driving cycle is divided into three prts: strting prt, middle prt nd ending prt. According to the theory of Mrkov chin, the probbility of the current stte s t depends only on the previous stte s t-1. In the strting prt nd the ending prt, however, the movement trend of vehicle hs been determined, nd the method bsed on Mrkov theory is not pplicble. Figure 2 The selected strting prt 4.1 Selection of strting prt The selection of strting prt is divided into 2 steps. First, ccording to specific rules, select ll lterntive strting prt from the originl dt. The durtion of ech lterntive strting prt lst 6s-1s. Second, clculte the PM vlue of ech prt, nd the prt hving the lowest PM vlue will be chosen s the finl strting prt. According to the relted literture t home nd brod, the durtion of strting prt is set to 75s. The selection rules re shown below: (1) Set the checkpoint is t time t. All velocities of smpling points in the rnge of (t-5,t) re less thn velocity threshold (.7 Km/h). (2) All velocities of smpling points in the rnge of (t,t+) re more thn velocity threshold (.7 Km/h). (3) When two criteri bove re met, record this checkpoint nd select ll smpling points in the rnge of (t-5,t+69) s the lterntive strting prt. Figure 3 The selected middle prt (4) 6 8 1, 1162
5 4.2 Construction of middle prt The construction of middle prt is typicl process solved by Monte Crlo method. Once is selected, its stte s well s terminl velocity re identified. A rndom number is generted to determinte the next s stte bsed on the probbility of the corresponding row in the trnsition mtrix. Before clculting the PM vlue, the lterntive middle prt should be combined with the selected strting prt. The one who hs the lowest PM vlue will be chosen s the finl middle prt. Figure 4 The selected ending prt 4.3 Selection of ending prt The ending prt selection method is s sme s the strting prt s. The selection rules re shown below: (1) Set the checkpoint is t time t. All velocities of smpling points in the rnge of (t-, t) re more thn velocity threshold (.7 Km/h). (2) All velocities of smpling points in the rnge of (t, t+5) re less thn velocity threshold. (3) When two criteri bove re met, record this checkpoint nd select ll smpling points in the rnge of (t-114, t+5). (4) Check ll smpling points in the rnge of (t-114, t+5). If there is such point tht the velocity of this point is very close to the terminl velocity of middle prt, record this point, note it by t, nd select ll smpling points in the rnge of (t, t+5) s the lterntive ending prt. Finlly, clculte the PM vlue of ech lterntive ending prt, nd choose the cycle tht hs the lowest PM vlue to be the finl ending prt. Figure 5 The finl driving cycle for hybrid bus 4.4 Construction of driving cycle Construct the finl driving cycle by combining the strting prt, the middle prt nd the ending prt selected bove to be complete velocity-time curve. 5 Conclusions , 1, 1 The mthemticl sttistics theories relted with Mrkov chin re used to construct driving cycle of city rod for hybrid bus. And new method to divide vehicle stte clusters is proposed during the construction process. 2 A specil method for PM clcultion, which elimintes differences cused by non-uniform unit between different chrcteristic prmeters, gurntees the resonbility of prt selection. 1163
6 Acknowledgments This work ws supported by the tionl High Technology Reserch nd Development Progrm of Chin (13BAG5B) in prt, the Progrm for ew Century Excellent Tlents in University (CET ) nd Beijing Institute of Technology Post Grdute Students Innovtion Foundtion in prt. The uthor would lso like to thnk the reviewers for their corrections nd helpful suggestions. References [1] Jing Pin, Shi Qin. A Reserch on the Construction of City Rod Driving Cycle Bsed on Wvelet Anlysis[J]. Automotive Engineering, 11(V1.33) o.1 (in Chinese) [2] Jie Lin. Mrkov Process Approch to Driving cycle Development. [D]. University of Cliforni 2. [3] He Xioqun.Multivrite Sttisticl Anlysis[M]. Beijing: Chin Renmin University Press, 4. [4] Yingyu Yng. Reserch of the City Bus Driving Cycle Bsed on Chrcteristics of Urbniztion Development in Chin [D].Beijing Institute of Technology 11.(in Chinese) [5]Jing Pin, Shi Qin. Driving Cycle Construction Methodology of City Rod Bsed on Mrkov Process[J].Trnsctions of the Chinese Society for Agriculturl Mchinery. 9, (11): 26~. (in Chinese) 1164
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