基于gPC理论的不确定参数电动汽车脉冲响应研究

Impulse responses of an electric vehicle with uncertain parameters based on the generalized polynomial chaos theory

基于广义多项式混沌(gPC)理论和汽车系统动力学,建立了考虑电机参振的不确定参数电动汽车的平顺性分析模型,并与蒙特卡洛法对比,验证了模型的正确性。以某型电动乘用车为例,分别在整车和电机总成两类参数不确定(10%~30%变异系数)条件下,计算了汽车以10~60 km/h车速通过脉冲型路面时的平顺性指标和电机振动响应的均值、方差、变异系数、概率密度和分布以及超限概率等统计指标,分析了不同变异系数下两类参数不确定对各自振动响应的影响程度和规律。结果表明:gPC理论能快速给出参数不确定对各统计指标的影响程度和规律,且该影响十分显著;在所分析速度域内,随参数不确定程度的增加,各均值响应最大值基本不变,但其方差、变异系数和分布范围均不断增大,超限概率的变化规律存在多样性。当不确定参数变异系数为30%和车速为60 km/h时,车体加速度、悬架压缩量、轮胎载荷、电机加速度和悬置压缩量响应最大值的变异系数最大,分别可达34%,47%,42%,15%和51%;不同参数变异系数和车速条件下,以上各响应最大值超越给定限值的最大概率分别达53%,36%,30%,75%和68%,车轮离地最大概率则达到64%。

Based on the generalized polynomial chaos(gPC)theory and automobile system dynamics,a vertical dynamics model of an electric vehicle considering electric motor vibration with uncertain parameters was established,and compared with the Monte Carlo method in which the correctness of the model was verified.Take a certain type electric vehicle as an example,under two kinds of parametric uncertainties(variation coefficient of 10%-30%)which result from the whole vehicle and the motor assembly respectively,the statistical indicators,such as the mean,variance,coefficient of variation,probability density and distribution,and overrun probability of the vehicle ride index and motor vibration were calculated,when the car runs over a pulse type pavement in the speed range of 10-60 km/h.Under different variation coefficient of the above two kinds of parameter uncertainties,the degree and rule of influence on respective vibration responses were analyzed.The results show that the degree and rule of influence of parametric uncertainty on their statistical indices can be obtained efficiently by the generalized polynomial chaos method,and the influences are significant.In the analyzed speed domain,the maximum values of each mean response are basically unchanged with the increase of the parameters’uncertain degree,but the variances,variation coefficients and distribution ranges are all increasing,the changing rules of overrun probabilities have diversity.When the variation coefficient of uncertain parameters and vehicle speed are set to 30%and 60 km/h,respectively,the variation coefficients of the peaks of the vehicle body acceleration,suspension compression,tire load,motor acceleration and mount compression responses reach their maximums which are 34%,47%,42%,15%,and 51%,respectively.Under different parametric variation coefficients and vehicle speeds,the largest probabilities of the above response peaks exceeding the given limits are 53%,36%,30%,75%,and 68%respectively,and the biggest liftoff probability of the wheel is up to 64%.