基于改进MCMC算法和代理模型的结构仿真模型更新

doi:10.16183/j.cnki.jsjtu.2023.584

上海交通大学学报 ›› 2025, Vol. 59 ›› Issue (8): 1114-1122.doi: 10.16183/j.cnki.jsjtu.2023.584

基于改进MCMC算法和代理模型的结构仿真模型更新

缪季¹, 段立平¹^,²(), 刘吉明¹, 林思伟¹, 赵金城¹^,²

1.上海交通大学土木工程系, 上海 200240
2.上海市公共建筑和基础设施数字化运维重点实验室, 上海 200240

收稿日期:2023-11-17 修回日期:2024-03-18 接受日期:2024-04-25 出版日期:2025-08-28 发布日期:2025-08-26
通讯作者: 段立平 E-mail:duanliping@sjtu.edu.cn
作者简介:缪季(1999—),硕士生,主要从事建筑结构损伤识别研究.
基金资助:
上海市科技创新项目(21DZ1204600)

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

MIAO Ji¹, DUAN Liping¹^,²(), LIU Jiming¹, LIN Siwei¹, ZHAO Jincheng¹^,²

1. Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
2. Shanghai Key Laboratory for Digital Maintenance of Buildings and Infrastructure, Shanghai 200240, China

Received:2023-11-17 Revised:2024-03-18 Accepted:2024-04-25 Online:2025-08-28 Published:2025-08-26
Contact: DUAN Liping E-mail:duanliping@sjtu.edu.cn

摘要/Abstract

摘要：

为提高有限元模型仿真精度,提出了一种基于贝叶斯理论的模型更新框架,并利用改进马尔可夫链蒙特卡罗(MCMC)算法和代理模型提升了更新效率.以待更新参数为输入、有限元模型模态响应为输出构建径向基函数(RBF)代理模型,将鲸鱼优化算法(WOA)引入MCMC算法,更新有限元模型的不确定参数.最后,通过一例简支梁数值算例和三层钢框架的试验研究证明了该算法的准确性.结果表明,WOA可以明显改善MCMC算法的采样平稳性和收敛速度,更新效率最高可提升13.9%,基于鲸鱼优化的Metropolis-Hastings(WO-MH)算法更新的简支梁模型和三层钢框架模型最大频率误差分别为0.009%和2.41%.所提模型更新方法在二维输入和八维输入的情况下均能有效提升有限元模型的仿真精度,为建筑结构的精益化仿真和优化设计提供技术参照.

关键词: 模型更新, 贝叶斯理论, 马尔可夫链蒙特卡罗, 鲸鱼优化算法, 代理模型

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

中图分类号:

TU311

缪季, 段立平, 刘吉明, 林思伟, 赵金城. 基于改进MCMC算法和代理模型的结构仿真模型更新[J]. 上海交通大学学报, 2025, 59(8): 1114-1122.

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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参考文献 20

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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

基于改进MCMC算法和代理模型的结构仿真模型更新

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

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Metrics

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模态	频率/Hz
模态	实测值	初始值	MH 更新值	WO-MH 更新值
X方向一阶	12.761	18.707	13.088	13.069
Y方向一阶	13.381	19.207	13.615	13.474
X方向二阶	49.370	61.607	47.878	49.385
Y方向二阶	50.508	62.051	48.545	49.864

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