基于Kriging模型的多次尝试差分进化贝叶斯有限元模型修正  

Multiple attempts of differential evolution Bayesian finite element model revision based on Kriging model

作　　者：秦世强[1] 李宁 宋任贤 QIN Shiqiang;LI Ning;SONG Renxian(School of Civil Engineering and Architecture,Wuhan University of Technology,Wuhan 430070,China)

机构地区：[1]武汉理工大学土木工程与建筑学院,武汉430070

出　　处：《振动与冲击》2024年第9期204-213,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金(51608408)。

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(multiple-try differential evolution adaptive Metropolis with“ZS”,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试验,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。The standard differential evolution adaptive Metropolis(DREAM)algorithm requires parallel computation of multiple Markov chains,and it suffers from low convergence efficiency and high computational costs.Here,a framework for multiple attempts of differential evolution Bayesian finite element model revision based on Kriging model was proposed.This framework could introduce historical vector differential sampling,snooker updating and multiple attempts of Metropolis sampling based on DREAM,and use Kriging model instead of finite element model for random sampling to realize fast exploration of multi-dimensional revised parametric posterior distribution with a very small number of parallel chains.Consolidated steel plate beam model tests were used to compare revision effects of DREAM and the proposed framework.The results showed that the proposed framework can realize fast convergence of Markov chains,its convergence efficiency is 3.42 times higher than that of DREAM,and the accuracy and stability of the revision results are improved;Kriging model can significantly reduce computational costs;the proposed framework can provide a new idea for solving problems of low convergence efficiency and high computational costs in revising multi-parameter uncertain models.

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 

分 类 号：TU311[建筑科学—结构工程]