上海交通大学学报

上海交通大学学报

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基于改进MCMC方法和代理模型的结构仿真模型更新（网络首发）

  

  1. 1. 上海交通大学土木工程系2. 上海市公共建筑和基础设施数字化运维重点实验室
  • 基金资助:
    上海市科技创新项目（21DZ1204600）；

Structural simulation model updating based on improved MCMC method and surrogate model

  1. （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）

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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，并利用改进马尔科夫链蒙特卡洛（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%，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, 马尔科夫链蒙特卡洛, 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 combining 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 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 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, Whale Optimization Algorithm, surrogate model

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