Bayesian nonparametrics for structural model updating and damage localization

Bayesian finite element model updating provides a rigorous probabilistic framework for estimating structural parameters (e.g., stiffness), enabling both damage localization and uncertainty quantification. Recently, hierarchical Bayesian approaches have attracted increasing attention due to their ability to address ill-posed and ill-conditioned problems. However, most existing hierarchical formulations assume unimodal prior distributions for the structural parameters, limiting their applicability when the dataset contains multiple damage states. This study introduces a hierarchical Bayesian model updating framework that employs Dirichlet process mixture model (DPMM) priors to effectively capture multimodality in structural parameters without pre-specifying the number of clusters. The proposed approach probabilistically infers structural parameters and automatically separates distinct damage states in the parameter space while reducing uncertainty within each cluster. Both numerical and experimental examples on steel moment frames with dynamic strain measurements demonstrate that the proposed method accurately identifies stiffness decreases at beam ends and distinguishes multiple damage scenarios without prior knowledge of the number of damage states present in the dataset.