脱轨系数数字特征求解的同分布概率演化法

Identically Distributed Probability Evolution Method for Numerical Characteristic Solution of Derailment Factors

为探究高速铁路列车的脱轨系数统计特性,提出同分布概率演化法研究其数字特征(均值与标准差)、阈值、概率分布和服从该分布的前提条件。采用该方法求得脱轨系数均值和标准差与横、竖向轮轨力数字特征的关系;本文方法证明脱轨系数满足高斯分布的数学条件;采用Monte Carlo法对脱轨系数的数字特征进行验证,并比较不同方法的计算效率;提出采用阈值估计法求脱轨系数的阈值。基于该方法,以动车组通过3跨桥梁为例,研究不同轨道谱、列车速度和桥梁动挠度等工况下的列车脱轨系数。计算结果表明:对常用高速铁路桥梁而言,脱轨系数具有高斯特性;本文计算方法能准确地求得不同工况下列车脱轨系数的数字特征,计算效率较高;脱轨系数的尾部分布不是高斯分布,不同工况需要采用相应的阈值估计法才能达到高斯分布3σ法则的置信水平。

In order to explore the statistical characteristics of derailment factors of high-speed trains,the identically distribution probability evolution method was proposed to study the numerical characteristics(mean and standard deviation)and threshold of derailment factors,probability distribution and the preconditions of obeying the distribution.The relationship between the mean and standard deviation of derailment factors and numerical characteristics of lateral and vertical wheel-rail contact forces was obtained by using this method.The mathematical condition of derailment factor approximately following Gaussian distribution was verified by using this method.The Monte Carlo method was used to verify the numerical characteristics of the derailment factors,to compare the computational efficiency of different methods.Finally,the threshold of derailment factors was obtained by threshold estimation method proposed in this paper.Based on this calculation method and the case of EMU passing through a 3-span bridge,the derailment coefficients of trains under different track spectra,train speeds and bridge dynamic deflection conditions were studied.The calculation results show that:for common high-speed railway bridges,the derailment factor has Gaussian characteristics.The proposed method in this paper can accurately obtain the numerical characteristics of the derailment factors under different working conditions,with high calculation efficiency.The tail distribution of derailment factor is not the Gaussian distribution,and the corresponding threshold estimation method needs to be used for different working conditions to achieve the confidence level of the 3σrule of the Gaussian distribution.