Stochastic Structural Finite Element Model Updating via Variational Bayesian Monte Carlo

The structural finite element model updating (FEMU) is of great significance in structural health monitoring and condition assessment. However, low accuracy and slow convergence speed are frequently encountered during posterior parameter inference in probabilistic methods, especially when high-dimensional parameter spaces or complex likelihood functions are processed. To address this issue, a probabilistic framework of FEMU is developed using artificial neural networks (ANNs) and variational Bayesian Monte Carlo (VBMC). First, an ANN-based structural surrogate model is obtained by sensitivity analysis and Latin hypercube sampling (LHS). Then, the likelihood function is constructed through the integration of ANN surrogate models and observed data, by which the probability relationship between the prior information of updating parameters and the likelihood functions is established via Bayesian inference. Subsequently, Gaussian models and Monte Carlo methods are employed to approximate the expectation of the joint distribution of the established probability relationship. On this basis, the variational approximate posterior information of the updating parameters is acquired by evidence lower bound (ELBO) maximization, thereby realizing the FEMU. Finally, the effectiveness and superiority of the proposed method are verified numerically by a long-span arch bridge. The results show that the average errors of frequency and displacement response of the updated model have decreased from 4.97% and 10.91% to 0.56% and 1.39%, respectively. Superior accuracy is demonstrated when compared with conventional frequency-based updating methods. Furthermore, compared to other conventional sampling methods, the computation efficiency has been increased by at least 17 times.