Abstract The Bayesian approach offers a systematic framework for updating finite element (FE) models and quantifying the remaining uncertainty given measured data. However, an inappropriate formulation of the probabilistic model can compromise accuracy. This paper presents an improved hierarchical Bayesian method for FE model updating by formulating the likelihood function in a fully probabilistic manner and incorporating time-varying stiffness parameters. A key methodological novelty lies in latent variable treatment of unmeasured mode shapes within the Bayesian hierarchy, yielding the joint inference of structural parameters and modal quantities in a fully generative manner without explicit eigenvalue decomposition. Furthermore, the geometric nature of mode shapes is rigorously respected by constraining them to the unit hypersphere using a Bingham distribution. A Metropolis-within-Gibbs sampling algorithm is developed to approximate the posterior distribution, with QR and Cholesky decompositions ensuring computational efficiency and accuracy. Three case studies, including synthetic, lab, and field test data, validate the effectiveness of the proposed approach. The updated model can be used as a reference model for structural damage detection and condition assessment in structural health monitoring.
Chen et al. (Thu,) studied this question.