为可靠地评估列车运行的安全性与平稳性，基于多体动力学理论和概率统计方法，对随机轨道不平顺激励作用下列车加速度响应最大值的分布规律进行分析。采用多体动力学软件Simpack建立列车–轨道耦合模型，通过三角级数法模拟得到轨道不平顺作为随机输入激励，基于Monte-Carlo方法计算得到了列车在行驶过程中加速度响应的样本序列。将列车加速度响应样本序列的最大值作为随机变量进行统计分析，通过构建基于高斯混合模型的列车振动加速度响应最大值的概率密度分布函数，并结合期望最大化算法对概率模型参数进行最大似然估计，从而对列车加速度响应最大值分布的统计规律以及响应样本数量的选取开展研究。结果表明：采用高斯混合模型能够有效地拟合列车加速度响应最大值的分布规律；此外，随着车速的增加，列车加速度响应最大值分布的离散性增强。

In order to reliably evaluate the safety and stability of running train during operation, the distribution of maximum acceleration response of the running train under random track irregularity excitation is analyzed, based on the theory of multi-body dynamics and the theory of probability statistics. To this end, the train-track coupling model is established using the multi-body dynamics software Simpack. As the internal source excitation of the train-track coupling model, the track irregularity is simulated through trigonometric series method. In addition, the Monte-Carlo method is used to obtain multiple samples of the train’s acceleration response under random track irregularity. Subsequently, the maximum value of each sample (time history of train’s acceleration responses) is obtained and treated as a random variable for statistical analysis. The distribution of the train’s maximum acceleration response is fitted by the Gaussian Mixture Model, in which the fitting parameters are obtained through expected maximum algorithm and maximum likelihood estimation. Meanwhile, the reasonable number of samples to derive appropriate distribution model is also discussed. The results show that the Gaussian Mixture Model can accurately model the distribution of the train’s maximum acceleration response. Additionally, it is found that the variation of the train’s maximum acceleration response increases with higher vehicle speed.

U270.1

国家自然科学基金（51708470）；国家杰出青年科学基金（51525804）；国家重点研发计划项目（2018YFC1507802）；西南石油大学科研“启航计划”项目（2017QHZ025）；西南石油大学桥梁安全评估青年科技创新团队（2018CXTD07）