列车动力响应的平稳性和各态历经性分析

研究列车动力响应的平稳性和各态历经性对寻求列车动力响应随机过程的统计规律具有重要意义。基于多体动力学理论,采用多体动力学分析软件Simpack建立国内某高速列车动车车辆的多体动力学模型。采用三角级数法模拟得到的轨道不平顺作为随机输入激励计算得到列车以不同速度行驶不同距离的动力响应时程样本序列。进一步运用平稳性检验方法中的逆序数检验法和单位根检验法对列车动力响应随机过程的平稳性进行检验。运用Monte-Carlo方法并结合随机过程的相关理论,计算1 500个在随机轨道不平顺激励下列车以200 km/h速度行驶1 km工况的动力响应时程样本序列的集合均值和集合相关函数,时间均值和时间相关函数,对列车动力响应的平稳性和各态历经性进行了证明。研究结果表明,列车以200 km/h的速度行驶1 km工况的动力响应可近似为具有各态历经性的平稳随机过程,即可采用一个时程响应样本来反映列车动力响应总体的统计规律。随着列车动力响应样本个数的增加,列车动力响应的平稳性和各态历经性都将更加稳定。

Analysis of stationarity and ergodicity of train dynamic response

It is of great significance to study the stationarity and ergodicity of train dynamic response,usually regarded as a stochastic process,in order to reveal the statistics of the train dynamic response.Firstly,a three-dimensional multi-body dynamics model of a high-speed passenger rail vehicle was established based on the multi-body dynamics theory in the multi-body dynamics analysis software Simpack.Secondly,the stochastic track irregularities were simulated using the trigonometric series method and used as the internal excitation for the established rail vehicle numerical model,with which the train dynamic responses under different running speeds and distances were obtained.Subsequently,the stationarity of the train dynamic responses was examined by both the Inverse Ordinal Number test and the Augmented Dickey-Fuller test.Finally,Monte-Carlo approach was employed to obtain 1500 samples of train dynamic responses travelling over a distance of 1 km at a speed of 200 km/h.In order to validate the stationarity and ergodicity of train dynamic responses,the statistics of the 1500 samples,i.e.,ensemble means,ensemble related functions,time-average values and time-related functions,were calculated based on the stochastic process theory.The statistical results show that the dynamic response of the train travelling over a distance of 1 km at a speed of 200 km/h can be regarded as a stationary and ergodic process.This suggests that the statistical information of one sample of the train dynamic response can be used to reflect the overall statistical law of the train dynamic response.It is also found that the stationarity and ergodicity of train dynamic response will be more stable with more samples.