基于广义多项式混沌的跨座式单轨车辆随机平稳性分析

Stochastic stationarity analysis of a straddle monorail vehicle using the generalized polynomial chaos method

借助参数化UM(universal mechanism)仿真模型,考虑车辆载重、悬挂参数和轮轨参数的随机性,建立某型跨座式单轨车辆的随机平稳性模型。然后,在有限试验设计样本数限制下,以最佳近似精度为目标,结合低阶交互截断、最小角回归、最小二乘法和留一法交叉验证等实现广义多项式混沌(generalized polynomial chaos,gPC)的自适应稀疏展开。分别基于拉丁超立方抽样(Latin hypercube sampling,LHS)方法和自适应稀疏gPC方法,讨论三种速度等级下单轨车辆平稳性指标的概率分布特征和全局灵敏度。算例表明:相比LHS结果,基于gPC近似模型的随机结果更为准确可靠,尤其是在高阶统计矩方面;同一速度等级下垂向平稳性指标均值要大于横向平稳性指标均值,并且随着速度的增大各平稳性指标的离散性在减小,而75 km/h下的分布特征与正态分布的差异最为明显;车辆载重、走行轮垂向刚度、水平轮径向刚度、空气弹簧垂向阻尼是对平稳性指标方差贡献最主要的随机参数。

With the help of the parameterized universal mechanism(UM)simulation model,the stochastic stationarity model of a straddle monorail vehicle was established considering the randomness of input variables such as vehicle load,vehicle suspension parameters,and wheel-track parameters.Then,aiming at the best approximation accuracy under the limited number of experimental design samples,the adaptive sparse expansion of generalized polynomial chaos(gPC)was realized by combinedly using the low-order interaction truncation,least angle regression,ordinary least squares,and leave-one-out cross-validation.Later,the probability distribution characteristics of the stationarity index and global sensitivity of the monorail vehicle under three speed levels were discussed based on the Latin hypercube sampling(LHS)method and adaptive sparse gPC method respectively.The results show that:compared with the LHS results,the results based on the gPC approximation model are more accurate and reliable,especially in the high-order statistical moments;at the same speed level,the mean value of the vertical stationarity index is greater than that of the lateral stationarity index,and the degree of dispersion of each stationarity index decreases with the increase of speed.The distribution characteristics of the stationarity index at 75 km/h are the most obviously different from those of normal distribution;the vehicle load,vertical stiffness of driving wheel,radial stiffness of horizontal wheel and vertical damping of air spring are the main random parameters contributing to the variance of stationarity index.