基于马尔可夫链的西安市城市公交工况构建

Development of driving cycle of bus in Xi'an city based on Markov chain

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.