Structural Simulation Model Updating Based on Improved MCMC Algorithm and Surrogate Model

doi:10.16183/j.cnki.jsjtu.2023.584

Abstract

Abstract:

To enhance the accuracy of finite element model simulation, a model updating method based on Bayesian theory is proposed, and the updating efficiency is improved by integrating improved Markov chain Monte Carlo (MCMC) algorithm and surrogate model. A radial basis function (RBF) surrogate model is constructed using the parameters to be updated as inputs and the finite element model modal responses as outputs. Whale optimization algorithm (WOA) is introduced into the MCMC algorithm and the uncertain parameters are updated. Finally, a numerical study on a simply supported beam and an experimental study on a three-story steel frame are conducted to verify the accuracy of the proposed method. The results show that WOA can significantly improve the stability and convergence speed of the MCMC algorithm, the updating efficiency can be improved by 13.9% at most, and the maximum frequency errors of the simply supported beam model and the three-story steel frame model updated by the WO-MH algorithm are 0.009% and 2.41%, respectively. The proposed model updating method can effectively enhance the simulation accuracy of the finite element model under both two-dimensional and eight-dimensional inputs, which provides technical reference for lean simulation and optimal design of building structures.

Key words: model updating, Bayesian theory, Markov chain Monte Carlo (MCMC), whale optimization algorithm (WOA), surrogate model

CLC Number:

TU311

MIAO Ji, DUAN Liping, LIU Jiming, LIN Siwei, ZHAO Jincheng. Structural Simulation Model Updating Based on Improved MCMC Algorithm and Surrogate Model[J]. Journal of Shanghai Jiao Tong University, 2025, 59(8): 1114-1122.

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代理模型	e_RMSE	R²
RBF	0.000 8	0.999 9
Kriging	0.001 3	0.999 9
RF	0.198 4	0.998 6

模型	弹性模量/ GPa	弹性模量相对误差/%	质量密度/ (kg·m^-3)	质量密度相对误差/%
真实值	206.000	0	7 850	0
初始值	160.000	22.330	6 500	17.197
MH-RBF	206.293	0.142	7 856	0.076
WOMH-RBF	206.012	0.006	7 850	0

模态	真实频率/Hz	更新前		更新后
模态	真实频率/Hz	频率/Hz	误差/%	频率/Hz	误差/%
一阶	28.381	27.487	3.150	28.381	0
二阶	108.71	105.29	3.146	108.72	0.009
三阶	229.46	222.24	3.147	229.47	0.004

模态	频率均值/Hz	方差/Hz²
X方向一阶	12.761	0.760
Y方向一阶	13.381	0.484
X方向二阶	49.370	0.219
Y方向二阶	50.508	0.233

代理模型	e_RMSE	R²
RBF	0.070 1	0.998 9
Kriging	0.087 1	0.998 3
RF	0.308 4	0.947 0