Bayesian inference has been widely used for updating structural finite element models.
However, the high computational cost of evaluating the posterior distribution in
conventional Bayesian model updating (BMU) frameworks significantly limits their applicability.
In this study, a novel fast variational Bayesian inference method is introduced
to reduce the computational cost of BMU. The core of the method is to decouple the
joint optimization problem of model parameters and noise parameter, and accomplishes
the optimization through the iterative solution of two analytically tractable subproblems.
Specifically, an explicit update equation for the optimal parameter distribution is
derived by linearizing the structural response with a first-order Taylor expansion, thus
avoiding the need for expensive Monte Carlo sampling. The accuracy and efficiency of
the proposed method are validated through numerical case studies on an 18-story steel
frame and an arch bridge structure. The results demonstrate significant improvements
of the proposed method in both parameter identification accuracy and computational
efficiency compared to conventional methods such as Gibbs sampling and Laplace approximation.
This establishes the proposed method as an efficient and practical solution
for structural model updating.

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