轨道梁参数随机的磁悬浮列车-轨道梁系统概率密度演化分析  

Probability Density Evolution Analysis of Maglev Train-Guideway System with Random Guideway Parameters

作　　者：余志武[1,2] 张鹏 丁叁叁 YU Zhiwu;ZHANG Peng;DING Sansan(School of Civil Engineering,Central South University,Changsha 410075,China;National Engineering Laboratory for High Speed Railway Construction,Changsha 410075,China;CRRC Qingdao Sifang Co.,Ltd.,Qingdao 266111,China)

机构地区：[1]中南大学土木工程学院,湖南长沙410075 [2]高速铁路建造技术国家工程实验室,湖南长沙410075 [3]中车青岛四方机车车辆股份有限公司,山东青岛266111

出　　处：《铁道学报》2023年第12期138-147,共10页Journal of the China Railway Society

基　　金：国家自然科学基金(U1934217,51578549,51708558);2019年湖南省研究生科研创新项目(CX20190129);湖南创新省份建设专项(2022JJ10075)。

摘　　要：为研究轨道梁随机参数对磁悬浮系统动力响应的影响,建立磁悬浮车辆-控制器-轨道梁时变随机动力分析模型,考虑轨道梁弹性模量、质量密度和阻尼比的随机性,采用数论选点法构造S维代表点集,运用Voronoi区域剖分概率空间并赋予点集初始概率,进而建立响应的概率密度演化方程。采用Newmark-β法和带TVD(total variation diminishing)格式的双边差分法求解概率密度函数、标准差、均值和满足99.75%概率保证率的响应最大值。首先采用文献结果和随机模拟法验证了模型的计算精度和效率,然后研究轨道梁随机参数和车速对车桥动力响应的影响。结果表明:基于概率密度演化理论的随机模型高效准确,与随机模拟法相比计算效率提高1~2个数量级;考虑轨道梁随机参数影响的车桥响应呈现明显的随机演化特征,响应的敏感程度为:轨道梁跨中加速度>轨道梁跨中位移>车体位移>电磁悬浮力;车桥随机响应受车速影响较大;随机弹性模量对车辆竖向振动有主导作用,随机阻尼比和质量密度的影响很小但不容忽略。To study the influence of random guideway parameters(RGPs)on the dynamic responses of maglev system,a time-varying stochastic dynamic model for maglev vehicle-controller-guideway coupling was established.Considering the randomness of elastic modulus,mass density,and damping ratio of the guideway,the number theory method was used to construct the S-dimensional representative point sets.Based on the Voronoi cells to divide the probability space and determine the initial probability of the point sets,the probability density evolution equations of the responses were established.The Newmark-βmethod and the bilateral difference method with total variation diminishing(TVD)format were utilized to solve the probability density function,mean value,standard deviation,and the maximum responses satisfying 99.75%probability guarantee rate.Firstly,the literature results and Monte Carlo simulation(MCS)were employed to verify the accuracy and efficiency of the model.Meanwhile,the influence of the RGPs and the vehicle speed on the train-guideway dynamic responses was analyzed.The results show that the stochastic model based on probability density evolution method is efficient and accurate,with the computational efficiency being increased by 1~2 orders of magnitude compared with MCS.Moreover,considering the dynamic responses under RGPs exhibiting obvious random evolution characteristics,the sensitivities of the responses are in the order of mid-span guideway acceleration>mid-span guideway displacement>carbody displacement>electromagnetic levitation force.The random vehicle and guideway responses are remarkably affected by the train speed.The random elastic modulus plays a leading role in the vertical vehicle vibration,while the influence of random damping ratio and mass density is minor but cannot be ignored.

关 键 词：磁悬浮列车 随机结构参数 概率密度演化 随机动力分析 车桥耦合振动 

分 类 号：U24[交通运输工程—道路与铁道工程] U271[机械工程—车辆工程]