基于模块化贝叶斯推理的随机非线性模型修正

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (2) : 79-88.

论文

王未寅1，王佐才1,2，辛宇1,3，丁雅杰1

作者信息 +

Stochastic nonlinear model updating based on modular bayesian inference

WANG Weiyin1，WANG Zuocai1,2，XIN Yu1,3，DING Yajie1

Author information +

文章历史 +

摘要

为同时考虑多种不确定因素对非线性结构模型修正的影响，提出了一种基于模块化贝叶斯推理的随机非线性模型修正方法。为了描述具有时变特性的非线性动力响应，提取结构动力响应主分量的瞬时加速度幅值作为非线性指标，基于贝叶斯方法，将整个模型修正过程分为三个相互独立的模块：首先建立非线性模型的高斯过程替代模型记为模块一；同时，为考虑模型误差对非线性结构随机模型修正的影响，将设计变量作为输入，模型误差作为输出，建立关于模型误差的高斯过程替代模型，记为模块二；最后，结合贝叶斯推理方法，结合模块一和模块二中的高斯过程模型，利用过渡马尔可夫链蒙特卡罗（Transitional Markov Chain Monte Carlo, TMCMC）随机采样方法估计待修正参数后验概率密度函数，实现基于模块化贝叶斯推理的随机非线性模型修正研究。采用三跨连续梁桥数值算例来验证所提出的随机非线性模型修正方法的准确性，并对比了不同噪声水平、不同程度模型误差条件下的模型修正结果，研究结果表明，基于模块化贝叶斯推理的随机非线性模型修正方法能够有效地实现非线性结构的随机模型修正，并具有较好的鲁棒性。

Abstract

To simultaneously consider the effects of multiple uncertainties on nonlinear structural model updating, a stochastic nonlinear model updating method based on modular Bayesian inference is proposed. In this study, the instantaneous acceleration amplitude of the main component of the structural dynamic response is extracted as the nonlinear indicator. Based on the proposed approach, the nonlinear model updating is divided into three modules. Firstly, a Gaussian process alternative model of the nonlinear model is established as module 1; meanwhile, to consider the influence of the model uncertainties on nonlinear model updating, a Gaussian process model is further constructed in module 2, in this model, the design variables are assigned as input and the model error is designed as output. Finally, combing with the modules 1 and 2, the posterior probability density function of the nonlinear model parameter is estimated by using the Transitional Markov Chain Monte Carlo (TMCMC) Random sampling method. Numerical simulation on a three-span continuous girder bridge is used to verify the accuracy of the proposed stochastic nonlinear model updating method, and the updating results under different noise levels and different model uncertainties are investigated. The results show that the proposed method is effective for stochastic nonlinear model updating with a better robustness.

导出引用

王未寅1，王佐才1,2，辛宇1,3，丁雅杰1. 基于模块化贝叶斯推理的随机非线性模型修正[J]. 振动与冲击, 2023, 42(2): 79-88

WANG Weiyin1，WANG Zuocai1,2，XIN Yu1,3，DING Yajie1. Stochastic nonlinear model updating based on modular bayesian inference[J]. Journal of Vibration and Shock, 2023, 42(2): 79-88

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