基于马尔可夫链的西安市城市公交工况构建
|
摘要
汽车行驶工况是汽车在实际路况下运行状态的反映,是车辆参数匹配和控制策略优化的基础。本文将行驶工况看作随时间变化的马尔可夫过程,通过采集西安市某城市公交运行工况的实际数据,采用特征值将分割的运动学片段划分为不同状态,以极大似然估计法确定了状态转移概率矩阵;通过不同时间尺度下的车速相关性,验证了在小时间尺度下,采样的汽车运行工况数据具备马尔可夫性;基于马尔可夫链构建了西安市城市公交线路备选工况,以平均车速、平均运行车速等10个特征参数为评价指标,筛选出与总体误差最小的备选工况作为典型工况。数理统计分析表明:本文构建的工况与验证数据的特征值误差分别为8.92%和8.43%,速度、加速度和速度-加速度联合概率分布均与验证数据一致。与V-A法构建的工况相比,基于马尔可夫链构建的工况与验证数据的特征值误差、速度概率分布平均误差、加速度概率分布平均误差、速度-加速度联合概率分布平均误差及比功率分布均方根误差都要更小,更能真实有效地反映出实际工况特征。
The vehicle driving cycle is the reflection of the state of the vehicle running under the actual road condition and it is the basis for parameters matching and control strategy optimization.In this study,the vehicle driving cycle can be treated as a Markov process changing with time.The datas of driving cycle about a line of city bus running in Xi'an city were collected.By using eigenvalues,the kinematic segments are divided into different states,and the state transition matrix was determined by the maximum likelihood estimation method.According to the speed correlation at different time scales,it was proved that the data of the vehicle's driving cycle has Markov property in a small times scale.Based on Markov chain method,the alternative driving cycles of Xi'an typical city bus were constructed.With ten characteristic parameters such as average speed as the evaluation index,the driving cycle with the minimum deviation degree of the total data was selected as the typical driving cycle.Analysis of mathematical statistics showed that the error of characteristic value between the driving cycle and the two sizes of validation data are 8.92% and 8.43%.The probability distributions of velocity,acceleration and velocity-acceleration were in accordance with the validation data.Compared with the velocity-acceleration(V-A)method,the errors of eigenvalue,velocity and acceleration probability distribution,the joint probability distribution of velocity and acceleration and the root mean square error of the vehicle specific power distribution between the driving cycle based on Markov chain and the validation data were all smaller,and it can effectively reflect the actual driving cycle.
The vehicle driving cycle is the reflection of the state of the vehicle running under the actual road condition and it is the basis for parameters matching and control strategy optimization.In this study,the vehicle driving cycle can be treated as a Markov process changing with time.The datas of driving cycle about a line of city bus running in Xi'an city were collected.By using eigenvalues,the kinematic segments are divided into different states,and the state transition matrix was determined by the maximum likelihood estimation method.According to the speed correlation at different time scales,it was proved that the data of the vehicle's driving cycle has Markov property in a small times scale.Based on Markov chain method,the alternative driving cycles of Xi'an typical city bus were constructed.With ten characteristic parameters such as average speed as the evaluation index,the driving cycle with the minimum deviation degree of the total data was selected as the typical driving cycle.Analysis of mathematical statistics showed that the error of characteristic value between the driving cycle and the two sizes of validation data are 8.92% and 8.43%.The probability distributions of velocity,acceleration and velocity-acceleration were in accordance with the validation data.Compared with the velocity-acceleration(V-A)method,the errors of eigenvalue,velocity and acceleration probability distribution,the joint probability distribution of velocity and acceleration and the root mean square error of the vehicle specific power distribution between the driving cycle based on Markov chain and the validation data were all smaller,and it can effectively reflect the actual driving cycle.
引文
[1]高建平,丁伟,孙中博,等.基于道路工况优化的混合动力公交车控制策略[J].浙江大学学报(工学版),2017,51(11):2265-2275.GAO Jianping,DING Wei,SUN Zhongbo,et al.Control strategy of hybrid electric bus based on road driving cycle optimization[J].Journal of Zhejiang University(Engineering Science),2017,51(11):2265-2275.(in Chinese)
[2]OU Shiqi,ZHOU Yafu,LIAN Jing,et al.Development of hybrid city bus’s driving cycle[C]∥International Conference on Electric Information and Control Engineering.Wuhan:IEEE,2011:12072030.
[3]SALEH W,KUMAR R,KIRBY H,et al.Real world driving cycle for motorcycles in Edinburgh[J].Transportation Research Part D:Transport and Environment,2009,14(5):326-333.
[4]孙宏图,宋希庚,王天灵.改进的城市公交循环工况开发方法[J].大连理工大学学报,2009,49(6):837-841.SUN Hongtu,SONG Xigeng,WANG Tianling.Improved method of driving cycle construction for urban bus[J].Journal of Dalian University of Technology,2009,49(6):837-841.(in Chinese)
[5]FOTOUHI A,MONTAZERIGH M.Tehran driving cycle development using the k-means clustering method[J].Scientia Iranica,2013,20(2):286-293.
[6]刘炳姣,石琴,仇多洋,等.基于改进蚁群算法的行驶工况构建及精度分析[J].合肥工业大学学报(自然科学版),2017,40(10):1297-1302.LIU Bingjiao,SHI Qin,QIU Duoyang,et al.Driving cycle construction based on improved ant colony optimization algorithm and precision analysis[J].Journal of Hefei University of Technology(Natural Science),2017,40(10):1297-1302.(in Chinese)
[7]高建平,孙中博,丁伟,等.车辆行驶工况的开发和精度研究[J].浙江大学学报(工学版),2017,51(10):2046-2054.GAO Jianping,SUN Zhongbo,DING wei,et al.Development of vehicle driving cycle and accuracy of research[J].Journal of Zhejiang University(Engineering Science),2017,51(10):2046-2054.(in Chinese)
[8]李忠玉,苟琦智,任田园,等.基于变步长V-A矩阵法的西安市某公交线路工况构建[C]∥第19届亚太汽车工程年会暨2017中国汽车工程学会年会论文集.上海:中国汽车工程学会,2017:1365-1371.LI Zhongyu,GOU Qizhi,Ren Tianyuan,et al.Driving cycle construction of Xi’an bus line based on V-A and variable step analysis[C]∥Nineteenth Annual Conference of the Asia Pacific automobile engineering and the annual conference of the 2017China Auto Engineering Society.Shanghai:Society of Automotive Engineers of China,2017:1365-1371.(in Chinese)
[9]赖瑾璇,于雷,宋国华,等.基于比功率分布的公交车行驶周期建立方法研究[J].交通运输系统工程与信息,2014,14(1):209-214,228.LAI Jinxuan,YU Lei,SONG Guohua,et al.Establishing method of driving cycles for transit buses based on VSP distributions[J].Journal of Transportation Systems Engineering&Information Technology,2014,14(1):209-214,228.(in Chinese)
[10]GONG Quanyi,MIDLAM-MOHLER S,MARANOV,et al.An iterative Markov chain approach for generating vehicle driving cycles[J].SAE International Journal of Engines,2011,4(1):1035-1045.
[11]曹骞,李君,刘宇,等.基于马尔科夫链的长春市乘用车行驶工况构建[J].吉林大学学报(工学版),2018,48(5):1366-1373.CAO Qian,LI Jun,LIU Yu,et al.Construction of driving cycle based on Markov chain for passenger car in Changchun city[J].Journal of Jilin University(Engineering and Technology Edition),2018,48(5):1366-1373.(in Chinese)
[12]李耀华,刘鹏,杨炜,等.西安市纯电动城市客车行驶工况研究[J].中国科技论文,2016,11(7):754-759.LI Yaohua,LIU Peng,YANG Wei,et al.Research on Xi’an pure electric bus driving cycle[J].China Sciencepaper,2016,11(7):754-759.(in Chinese)
[13]邵攀登,任田园,李忠玉,等.基于短行程V-A矩阵法的西安市某公交线路工况构建[C]∥第19届亚太汽车工程年会暨2017中国汽车工程学会年会论文集.上海:中国汽车工程学会,2017:1394-1397.SHAO Pandeng,REN Tianyuan,LI Zhongyu,et,al.Construction of a bus line in Xi’an based on short trip V-A matrix[C]∥Nineteenth Annual Conference of the Asia Pacific automobile engineering and the annual conference of the 2017 China Auto Engineering Society.Shanghai:Society of Automotive Engineers of China,2017:1394-1397.(in Chinese)
[14]BRADY J,O’MAHONY M.Development of a driving cycle to evaluate the energy economy of electric vehicles in urban areas[J].Applied Energy,2016,177:165-178.
[15]潘登.混合动力汽车城市循环工况构建及运行工况多尺度预测[D].北京:北京理工大学,2015.PAN Deng.Study on urban driving cycle construction and its multi-scale prediction for hybrid electric vehicles[D].Beijing:Beijing Institute of Technology,2015.(in Chinese)
[16]苗强,孙强,白书战,等.基于聚类和马尔可夫链的公交车典型行驶工况构建[J].中国公路学报,2016,29(11):161-169.MIAO Qiang,SUN Qiang,BAI Shuzhan,et al.Construction of typical driving cycle of bus based on clustering and Markov chain[J].China Journal of Highway and Transport,2016,29(11):161-169.(in Chinese)
[17]姜平,石琴,陈无畏.基于马尔科夫的城市道路行驶工况构建方法[J].农业机械学报,2009,40(11):26-30.JIANG Ping,SHI Qin,CHEN Wuwei.Driving cycle construction methodology of city road based on Markov process[J].Transactions of The Chinese Society of Agricultural Machinery,2009,40(11):26-30.(in Chinese)
[18]张岩.面向混合动力汽车能量管理策略的汽车运行工况多尺度预测方法[D].长春:吉林大学,2013.ZHANG Yan.Multi-scale prediction method of driving cycle for HEV energy management strategy[D].Changchun:Jilin University,2013.(in Chinese)
[19]姜平.城市混合道路行驶工况的构建研究[D].合肥:合肥工业大学,2011.JIANG Ping.Study on development of driving cycle of urban mixed road[D].Hefei:Hefei University of Technology,2011.(in Chinese)
[20]LIU Li,HUANG Chaosheng,LU Bingwu,et al.Study on the design method of time-variant driving cycles for EV based on Markov process[C]∥Vehicle Power and Propulsion Conference.Seoul:IEEE,2012:1277-1281.
[21]何朕,王毅,孟范伟,等.马尔可夫跳变系统的蒙特卡罗仿真[J].电机与控制学报,2008,12(1):80-83.HE Zhen,WANG Yi,MENG Fanwei,et al.Monte Carlo simulation of Markovian jump system[J].Electric Machines and Control,2008,12(1):80-83.(in Chinese)
[22]张曼,施树明.典型汽车运行工况的状态转移特征分析[J].吉林大学学报(工学版),2018,48(4):1008-1015.ZHANG Man,SHI Shuming.Analysis of state transition characteristics for typical vehicle driving cycles[J].Journal of Jilin University(Engineering and Technology Edition),2018,48(4):1008-1015.(in Chinese).
[23]张昕,王松涛,张欣,等.基于马尔可夫链的混合动力汽车行驶工况预测研究[J].汽车工程,2014,36(10):1216-1220,1236.ZHANG Xin,WANG Songtao,ZHANG Xin,et al.Aresearch on driving condition prediction for HEVs based on Markov chain[J].Automotive Engineering,2014,36(10):1216-1220,1236.(in Chinese)
[24]SHI Shuming,LIN Nan,ZHANG Yan,et al.Research on Markov property analysis of driving cycles and its application[J].Transportation Research Part D:Transport and Environment,2016,47:171-181.
[25]LAI Jinxuan,YU Lei,SONG Guohua,et al.Development of city-specific driving cycles for transit buses based on VSP distributions:case of Beijing[J].Journal of Transportation Engineering,2013,139(7):749-757.
[26]郝艳召,于雷,宋国华,等.基于比功率参数的北京市柴油公交车行驶和排放特征研究[J].汽车工程,2010,32(2):103-109.HAO Yanzhao,YU Lei,SONG Guohua,et al.Astudy on driving and emission features of diesel buses in Beijing based on VSP parameter[J].Automotive Engineering,2010,32(2):103-109.(in Chinese)
[2]OU Shiqi,ZHOU Yafu,LIAN Jing,et al.Development of hybrid city bus’s driving cycle[C]∥International Conference on Electric Information and Control Engineering.Wuhan:IEEE,2011:12072030.
[3]SALEH W,KUMAR R,KIRBY H,et al.Real world driving cycle for motorcycles in Edinburgh[J].Transportation Research Part D:Transport and Environment,2009,14(5):326-333.
[4]孙宏图,宋希庚,王天灵.改进的城市公交循环工况开发方法[J].大连理工大学学报,2009,49(6):837-841.SUN Hongtu,SONG Xigeng,WANG Tianling.Improved method of driving cycle construction for urban bus[J].Journal of Dalian University of Technology,2009,49(6):837-841.(in Chinese)
[5]FOTOUHI A,MONTAZERIGH M.Tehran driving cycle development using the k-means clustering method[J].Scientia Iranica,2013,20(2):286-293.
[6]刘炳姣,石琴,仇多洋,等.基于改进蚁群算法的行驶工况构建及精度分析[J].合肥工业大学学报(自然科学版),2017,40(10):1297-1302.LIU Bingjiao,SHI Qin,QIU Duoyang,et al.Driving cycle construction based on improved ant colony optimization algorithm and precision analysis[J].Journal of Hefei University of Technology(Natural Science),2017,40(10):1297-1302.(in Chinese)
[7]高建平,孙中博,丁伟,等.车辆行驶工况的开发和精度研究[J].浙江大学学报(工学版),2017,51(10):2046-2054.GAO Jianping,SUN Zhongbo,DING wei,et al.Development of vehicle driving cycle and accuracy of research[J].Journal of Zhejiang University(Engineering Science),2017,51(10):2046-2054.(in Chinese)
[8]李忠玉,苟琦智,任田园,等.基于变步长V-A矩阵法的西安市某公交线路工况构建[C]∥第19届亚太汽车工程年会暨2017中国汽车工程学会年会论文集.上海:中国汽车工程学会,2017:1365-1371.LI Zhongyu,GOU Qizhi,Ren Tianyuan,et al.Driving cycle construction of Xi’an bus line based on V-A and variable step analysis[C]∥Nineteenth Annual Conference of the Asia Pacific automobile engineering and the annual conference of the 2017China Auto Engineering Society.Shanghai:Society of Automotive Engineers of China,2017:1365-1371.(in Chinese)
[9]赖瑾璇,于雷,宋国华,等.基于比功率分布的公交车行驶周期建立方法研究[J].交通运输系统工程与信息,2014,14(1):209-214,228.LAI Jinxuan,YU Lei,SONG Guohua,et al.Establishing method of driving cycles for transit buses based on VSP distributions[J].Journal of Transportation Systems Engineering&Information Technology,2014,14(1):209-214,228.(in Chinese)
[10]GONG Quanyi,MIDLAM-MOHLER S,MARANOV,et al.An iterative Markov chain approach for generating vehicle driving cycles[J].SAE International Journal of Engines,2011,4(1):1035-1045.
[11]曹骞,李君,刘宇,等.基于马尔科夫链的长春市乘用车行驶工况构建[J].吉林大学学报(工学版),2018,48(5):1366-1373.CAO Qian,LI Jun,LIU Yu,et al.Construction of driving cycle based on Markov chain for passenger car in Changchun city[J].Journal of Jilin University(Engineering and Technology Edition),2018,48(5):1366-1373.(in Chinese)
[12]李耀华,刘鹏,杨炜,等.西安市纯电动城市客车行驶工况研究[J].中国科技论文,2016,11(7):754-759.LI Yaohua,LIU Peng,YANG Wei,et al.Research on Xi’an pure electric bus driving cycle[J].China Sciencepaper,2016,11(7):754-759.(in Chinese)
[13]邵攀登,任田园,李忠玉,等.基于短行程V-A矩阵法的西安市某公交线路工况构建[C]∥第19届亚太汽车工程年会暨2017中国汽车工程学会年会论文集.上海:中国汽车工程学会,2017:1394-1397.SHAO Pandeng,REN Tianyuan,LI Zhongyu,et,al.Construction of a bus line in Xi’an based on short trip V-A matrix[C]∥Nineteenth Annual Conference of the Asia Pacific automobile engineering and the annual conference of the 2017 China Auto Engineering Society.Shanghai:Society of Automotive Engineers of China,2017:1394-1397.(in Chinese)
[14]BRADY J,O’MAHONY M.Development of a driving cycle to evaluate the energy economy of electric vehicles in urban areas[J].Applied Energy,2016,177:165-178.
[15]潘登.混合动力汽车城市循环工况构建及运行工况多尺度预测[D].北京:北京理工大学,2015.PAN Deng.Study on urban driving cycle construction and its multi-scale prediction for hybrid electric vehicles[D].Beijing:Beijing Institute of Technology,2015.(in Chinese)
[16]苗强,孙强,白书战,等.基于聚类和马尔可夫链的公交车典型行驶工况构建[J].中国公路学报,2016,29(11):161-169.MIAO Qiang,SUN Qiang,BAI Shuzhan,et al.Construction of typical driving cycle of bus based on clustering and Markov chain[J].China Journal of Highway and Transport,2016,29(11):161-169.(in Chinese)
[17]姜平,石琴,陈无畏.基于马尔科夫的城市道路行驶工况构建方法[J].农业机械学报,2009,40(11):26-30.JIANG Ping,SHI Qin,CHEN Wuwei.Driving cycle construction methodology of city road based on Markov process[J].Transactions of The Chinese Society of Agricultural Machinery,2009,40(11):26-30.(in Chinese)
[18]张岩.面向混合动力汽车能量管理策略的汽车运行工况多尺度预测方法[D].长春:吉林大学,2013.ZHANG Yan.Multi-scale prediction method of driving cycle for HEV energy management strategy[D].Changchun:Jilin University,2013.(in Chinese)
[19]姜平.城市混合道路行驶工况的构建研究[D].合肥:合肥工业大学,2011.JIANG Ping.Study on development of driving cycle of urban mixed road[D].Hefei:Hefei University of Technology,2011.(in Chinese)
[20]LIU Li,HUANG Chaosheng,LU Bingwu,et al.Study on the design method of time-variant driving cycles for EV based on Markov process[C]∥Vehicle Power and Propulsion Conference.Seoul:IEEE,2012:1277-1281.
[21]何朕,王毅,孟范伟,等.马尔可夫跳变系统的蒙特卡罗仿真[J].电机与控制学报,2008,12(1):80-83.HE Zhen,WANG Yi,MENG Fanwei,et al.Monte Carlo simulation of Markovian jump system[J].Electric Machines and Control,2008,12(1):80-83.(in Chinese)
[22]张曼,施树明.典型汽车运行工况的状态转移特征分析[J].吉林大学学报(工学版),2018,48(4):1008-1015.ZHANG Man,SHI Shuming.Analysis of state transition characteristics for typical vehicle driving cycles[J].Journal of Jilin University(Engineering and Technology Edition),2018,48(4):1008-1015.(in Chinese).
[23]张昕,王松涛,张欣,等.基于马尔可夫链的混合动力汽车行驶工况预测研究[J].汽车工程,2014,36(10):1216-1220,1236.ZHANG Xin,WANG Songtao,ZHANG Xin,et al.Aresearch on driving condition prediction for HEVs based on Markov chain[J].Automotive Engineering,2014,36(10):1216-1220,1236.(in Chinese)
[24]SHI Shuming,LIN Nan,ZHANG Yan,et al.Research on Markov property analysis of driving cycles and its application[J].Transportation Research Part D:Transport and Environment,2016,47:171-181.
[25]LAI Jinxuan,YU Lei,SONG Guohua,et al.Development of city-specific driving cycles for transit buses based on VSP distributions:case of Beijing[J].Journal of Transportation Engineering,2013,139(7):749-757.
[26]郝艳召,于雷,宋国华,等.基于比功率参数的北京市柴油公交车行驶和排放特征研究[J].汽车工程,2010,32(2):103-109.HAO Yanzhao,YU Lei,SONG Guohua,et al.Astudy on driving and emission features of diesel buses in Beijing based on VSP parameter[J].Automotive Engineering,2010,32(2):103-109.(in Chinese)