基于多链竞争差分进化算法的无砟轨道结构有限元模型修正  

Finite element model correction for ballastless track structure based on multi-chain competition based differential evolution algorithm

作　　者：叶玲 江宏康 陈华鹏 冯宇轩 王力骋 YE Ling;JIANG Hong-kang;CHEN Hua-peng;FENG Yu-xuan;WANG Li-cheng(State Key Laboratory of Performance Monitoring and Protecting of Rail Transit Infrastructure,East China Jiaotong University,Nanchang 330013,Jiangxi,China;Jiangxi Transport Investment Consulting Group Co.,Ltd.,Nanchang 330108,Jiangxi,China)

机构地区：[1]华东交通大学轨道交通基础设施性能监测与保障国家实验室,江西南昌330013 [2]江西交投咨询集团有限公司,江西南昌330108

出　　处：《交通运输工程学报》2024年第2期112-124,共13页Journal of Traffic and Transportation Engineering

基　　金：国家自然科学基金项目(52008168)。

摘　　要：为获得更接近真实情况的轨道结构模型,提出了一种基于多链竞争差分进化算法的无砟轨道结构有限元模型修正方法;以频率振型模态为响应建立了适用于无砟轨道结构的目标函数和似然函数,以标准马尔科夫链蒙特卡罗算法为基础,引入多链差分进化算法来解决高维参数模型效率低和收敛难的问题;引进竞争算法,利用竞争决出的失败者向胜利者学习的机制,不断迭代修正钢轨模型以提高修正精度;在此基础上,通过一个无砟轨道结构有限元模型修正数值算例验证所提方法的高效性。分析结果表明:采用Metropolis-Hastings算法和延缓拒绝自适应Metropolis算法修正后,单元参数与真实值间的最大相对误差分别为4.75%和1.35%,而采用多链竞争差分进化算法修正后,单元参数与真实值间的最大相对误差为0.28%,且模态振型向量之间的相关性接近1,说明多链竞争差分进化算法的修正精度优于另外2种算法;在分别加噪5%、10%和15%的噪声测试中,采用Metropolis-Hastings算法和延缓拒绝自适应Metropolis算法修正后,参数误差达到了9%左右,而采用多链竞争差分进化算法模型修正后,参数误差均在5%以内,进一步证明了多链竞争差分进化算法良好的鲁棒性。由此可见,多链竞争差分进化算法可以为解决复杂环境导致测试信息不完备的无砟轨道结构有限元模型修正提供一种新手段。To obtain a more realistic track structure model,a finite element model correction method for the ballastless track structure based on a multi-chain competition based differential evolution algorithm was proposed.The objective function and likelihood function suitable for the ballastless track structure were established according to the response of frequency vibration mode.Based on the standard Markov Chain Monte Carlo algorithm,a multi-chain differential evolution algorithm was introduced to solve the problems of low efficiency and difficult convergence in high-dimensional parameter models.Then,the competitive algorithm was introduced,and the mechanism of learning from the winners by the losers determined by the competition was utilized,so as to continuously iteratively correct the track model and thus improve the correction accuracy.On this basis,the efficiency of the proposed method was verified by a numerical example of the finite element model correction of the ballastless track structure.Analysis results show that after correction using the Metropolis-Hastings algorithm and the delayed rejection adaptive Metropolis algorithm,the maximum relative errors between the corrected unit parameters and the true values are 4.75%and 1.35%,respectively.However,the maximum relative error between the corrected unit parameters and the true values is 0.28%,after correction using the multi-chain competition based differential evolution algorithm.In addition,the correlation between vibration mode vectors is close to 1,indicating that the correction accuracy of the multi-chain competition based differential evolution algorithm is better than the other two algorithms.In the noise tests with 5%,10%,and 15%noise,respectively,the parameter errors reach about 9%after corrected by the Metropolis-Hastings algorithm and the delayed rejection adaptive Metropolis algorithm,while those corrected by the multi-chain competition based differential evolution algorithm are all within 5%.It further proves the good robustness of the multi-chai

关 键 词：轨道交通 轨道结构模型修正 多链竞争差分进化算法 无砟轨道 结构健康监测 

分 类 号：U239.5[交通运输工程—道路与铁道工程]