基于马尔科夫链种群竞争的贝叶斯有限元模型修正  

Bayesian finite element model updating based on Markov chain population competition

作　　者：叶玲 江宏康 邹雨清 陈华鹏 王力骋 YE Ling;JIANG Hongkang;ZOU Yuqing;CHEN Huapeng;WANG Licheng(State Key Laboratory of Performance Monitoring Protecting of Rail Transit Infrastructure,East China Jiaotong University,Nanchang 330013,China;Jiangxi Transport Investment Consulting Group Co.,Ltd.,Nanchang 330013,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重点实验室,南昌330013 [2]江西交投咨询集团有限公司,南昌330013

出　　处：《机械强度》2025年第2期85-93,共9页Journal of Mechanical Strength

基　　金：国家自然科学基金项目(52008168,52468042);国家重点研发计划项目(2021YFE015600)。

摘　　要：针对传统马尔科夫链蒙特卡洛(Markov Chain Monte Carlo,MCMC)模拟方法在高维问题或后验概率密度复杂时采样效率低且难收敛的缺陷,建立了基于马尔科夫(Markov)链种群竞争的贝叶斯有限元模型修正算法。在基于Metropolis-Hastings(MH)随机游走算法实现MCMC模拟的传统方法基础上,引入差分进化算法,利用种群中Markov链之间不同携带信息的相互作用关系,得到优化建议以快速逼近目标函数,解决了高维参数模型修正过程中采样滞留的缺点;引进竞争算法,通过不断的竞争刺激和内置失败者向胜利者学习的机制,采用较少的Markov链获得较高的精度,提高了模型修正效率与精度;最后,通过一个桁架结构的有限元模型修正数值算例验证了所提算法,并与标准MH算法的结果对比,得出该算法可以快速修正高维参数模型,具有较高的精度,且对随机噪声有良好的鲁棒性,为考虑不确定性的大型结构有限元模型修正提供了一种稳定有效的手段。The traditional Markov chain Monte Carlo(MCMC)simulation method is inefficient and difficult to converge in high dimensional problems and complicated posterior probability density.In order to overcome these shortcomings,a Bayesian finite element model updating algorithm based on Markov chain population competition was proposed.First,the differential evolution algorithm was introduced in the traditional method of Metropolis-Hastings(MH)random walk algorithm.Based on the interaction of different information carried by Markov chains in the population,optimization suggestions were obtained to approach the objective function quickly.It solves the defect of sampling retention in the updating process of high-dimensional parameter model.Then,the competition algorithm was introduced,which has constant competitive incentives and a built-in mechanism for losers to learn from winners.Higher precision was obtained by using fewer Markov chains,which improves the efficiency and precision of model updating.Finally,a numerical example of finite element model updating of a truss structure was used to verify the proposed algorithm.Compared with the results of standard MH algorithm,the proposed algorithm can quickly update the high-dimensional parameter model with high accuracy and good robustness to random noise.It provides a stable and effective method for finite element model updating of large-scale structure considering uncertainty.

关 键 词：模型修正 贝叶斯估计 马尔科夫链蒙特卡洛 种群竞争 

分 类 号：TU311.3[建筑科学—结构工程]