Bayesian finite element model updating based on Markov chain population competition

YE Ling; JIANG Hongkang; ZOU Yuqing; CHEN Huapeng; WANG Licheng

doi:10.16579/j.issn.1001.9669.2025.02.011

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Bayesian finite element model updating based on Markov chain population competition

·Optimization·Reliability· | 更新时间：2025-02-28

- Bayesian finite element model updating based on Markov chain population competition
- Journal of Mechanical Strength Vol. 47, Issue 2, Pages: 85-93(2025)
- 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重点实验室，南昌 330013
  2.江西交投咨询集团有限公司，南昌 330013
- 作者简介：
  
  YE Ling, E-mail: 58718070@qq.com
- 基金信息：
  
  National Natural Science Foundation of China(52008168;52468042);National Key Research and Development Program of China(2021YFE015600)
- DOI：10.16579/j.issn.1001.9669.2025.02.011
  CLC： TU311.3
- Received：24 May 2023，
  
  Revised：17 July 2023，
  
  Published：15 February 2025
- 稿件说明：
移动端阅览
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，2025，47（2）：85-93.

YE Ling，JIANG Hongkang，ZOU Yuqing，et al.Bayesian finite element model updating based on Markov chain population competition［J］. Journal of Mechanical Strength，2025，47（2）：85-93.
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，2025，47（2）：85-93. DOI： 10.16579/j.issn.1001.9669.2025.02.011.

YE Ling，JIANG Hongkang，ZOU Yuqing，et al.Bayesian finite element model updating based on Markov chain population competition［J］. Journal of Mechanical Strength，2025，47（2）：85-93. DOI： 10.16579/j.issn.1001.9669.2025.02.011.

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。

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 (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.

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references

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