Stochastic nonlinear model updating based on modular bayesian inference

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (2) : 79-88.

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

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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.

Key words

Nonlinear model updating / Modular Bayes / Model error / Measurement error / Gaussian process model

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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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