基于马尔科夫链种群竞争的贝叶斯有限元模型修正

叶玲; 江宏康; 邹雨清; 陈华鹏; 王力骋

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基于马尔科夫链种群竞争的贝叶斯有限元模型修正

更新时间：2024-06-26

- 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
- 机械强度 2024年页码：1-9
- 作者机构：
  
  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，南昌 330013
  2.Jiangxi Transport Investment Consulting Group Co.，Nanchang 330013，China
- 作者简介：
  
  YE Ling，E-mail： 58718070@qq.com
- 基金信息：
  
  The project supported by the National Natural Science Foundation(52008168);the Jiangxi Department of Education Foundation(GJJ200662);the National Key Research and Development Program of China(2021YFE015600)
- DOI：
  中图分类号： TU311.3
- 网络出版日期：2024-06-26，
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叶玲,江宏康,邹雨清等.基于马尔科夫链种群竞争的贝叶斯有限元模型修正[J].机械强度,

YE Ling,JIANG HongKang,ZOU YuQing,et al.BAYESIAN FINITE ELEMENT MODEL UPDATING BASED ON MARKOV CHAIN POPULATION COMPETITION[J].Journal of Mechanical Strength,
叶玲,江宏康,邹雨清等.基于马尔科夫链种群竞争的贝叶斯有限元模型修正[J].机械强度, DOI：10.16579/j.issn.1001-9669...001.

YE Ling,JIANG HongKang,ZOU YuQing,et al.BAYESIAN FINITE ELEMENT MODEL UPDATING BASED ON MARKOV CHAIN POPULATION COMPETITION[J].Journal of Mechanical Strength, DOI：10.16579/j.issn.1001-9669...001.

摘要

针对传统马尔科夫链蒙特卡罗（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。在基于随机游走（Metropolis-Hastings，MH）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。

Abstract

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 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 in this paper.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罗种群竞争

Keywords

Model updatingBayesian estimationMarkov Chain Monte CarloPopulation competition

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