蒲珍华 吴梦雪 唐德发 朱金 李永乐

摘 要：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。

关键词：列车轨道耦合系统;随机振动;加速度响应;高斯混合模型;期望最大化算法

Abstract： 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 the sample sequence of the trains acceleration response under random track irregularity. Subsequently， the maximum value of each sample （time history of trains acceleration responses） is obtained and treated as a random variable for statistical analysis. By constructing the probability density distribution function of the maximum train vibration acceleration response based on the Gaussian mixture model， and combining with the expectation maximization algorithm， the maximum likelihood estimation of the probability model parameters is carried out.The statistical law of the maximum distribution of train acceleration response and the selection of the number of response samples are studied. The results show that the Gaussian mixture model can accurately model the distribution of the trains maximum acceleration response. Additionally， it is found that the variation of the trains maximum acceleration response increases with higher vehicle speed.

Keywords： train-track coupling system; random vibration; acceleration response; Gaussian mixture model; expectation maximization algorithm

轨道不平顺是引起列车轨道或列车桥梁耦合系统振动的重要激励源之一。在车辆参数确定的情况下，轨道不平顺对列车运行的安全性与平稳性有很大的影响[1]。文献[2]探讨了列车荷载作用下不同轨道不平顺样本对桥梁结构动力响应的影响规律，结果表明，桥梁结构的动力响应随轨道不平顺样本的不同而变化，且有较大的离散性和随机性。……