基于Kriging模型的多次尝试差分进化贝叶斯有限元模型修正

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摘要标准差分进化自适应Metropolis(differential evolution adaptive Metropolis，DREAM)算法需进行多条马氏链并行计算，存在收敛效率低和计算成本高的问题。为此，提出一种基于Kriging模型的多次尝试差分进化贝叶斯有限元模型修正(MT-DREAM(ZS))框架。该框架在DREAM的基础上引入历史向量差分采样、斯诺克更新以及多次尝试Metropolis抽样，并利用Kriging模型代替有限元模型进行随机抽样，实现利用极少数并行链便可快速探索多维修正参数后验分布。利用固结钢板梁模型实验，比较了DREAM和MT-DREAM(ZS)的修正效果。结果表明：MT-DREAM(ZS)可实现马尔科夫链的快速收敛，其收敛效率较DREAM提升了3.42倍，且修正结果精度和稳定性有提升；Kriging模型可大幅度降低计算成本。所提框架为解决多参数不确定模型修正中的收敛效率低和计算成本高等问题提供了一种新思路。

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	秦世强
	李宁
	宋任贤

关键词 ：有限元模型修正, 贝叶斯估计, 多次尝试Metropolis抽样, 差分进化自适应Metropolis(DREAM), Kriging模型

Abstract：The standard Differential Evolution Adaptive Metropolis (DREAM) algorithm requires parallel computing with multiple Markov chains, which suffers from low convergence efficiency and high computational costs. To address these challenges, this study proposes a novel framework called MT-DREAM(ZS), based on the Kriging model, for multiple-try differential evolution Bayesian finite element model updating. This framework extends the DREAM algorithm by introducing historical vector differential sampling, Snooker update, and multiple-try Metropolis sampling. Furthermore, it utilizes the Kriging model as a surrogate for the finite element model to enable efficient random sampling, allowing for rapid exploration of high-dimensional posterior distributions of correction parameters using a minimal number of parallel chains. To validate the effectiveness of the proposed MT-DREAM(ZS) method, this study conducts the experiment on a consolidated steel plate beam model and compare the updating performance with the standard DREAM algorithm. The results demonstrate that MT-DREAM(ZS) achieves fast convergence of the Markov chains, improving the convergence efficiency by a significant factor of 3.42 compared to DREAM. Moreover, the updating accuracy and stability are enhanced. Additionally, the utilization of the Kriging model substantially reduces computational costs. The proposed framework provides a new approach to address the challenges of low convergence efficiency and high computational costs in the updating of multi-parameter uncertain models.

Key words： Finite element model updating Bayesian estimation Multiple-try Metropolis sampling Differential Evolution Adaptive Metropolis (DREAM) Kriging model

收稿日期: 2023-07-10 出版日期: 2024-05-15

引用本文:

秦世强，李宁，宋任贤. 基于Kriging模型的多次尝试差分进化贝叶斯有限元模型修正[J]. 振动与冲击, 2024, 43(9): 204-213.
QIN Shiqiang, LI Ning, SONG Renxian. Multiple attempts of differential evolution Bayesian finite element model revision based on Kriging model. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(9): 204-213.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2024/V43/I9/204

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