Hierarchical Bayesian model updating using Dirichlet process mixtures for structural damage localization

TL;DR

This paper introduces a hierarchical Bayesian model updating method using Dirichlet process mixtures to effectively localize structural damage across multiple damage states, incorporating damage classification into FE model calibration.

Contribution

It develops a nonparametric Bayesian framework that handles multimodal damage states without predefining the number of damage clusters, improving damage localization accuracy.

Findings

Clusters inferred match observed damage states

Posterior stiffness distributions align with ground truth

Method reduces uncertainty compared to baseline

Abstract

Bayesian model updating provides a rigorous probabilistic framework for calibrating finite element (FE) models with quantified uncertainties, thereby enhancing damage assessment, response prediction, and performance evaluation of engineering structures. Recent advances in hierarchical Bayesian model updating (HBMU) enable robust parameter estimation under ill-posed/ill-conditioned settings and in the presence of inherent variability in structural parameters due to environmental and operational conditions. However, most HBMU approaches overlook multimodality in structural parameters that often arises when a structure experiences multiple damage states over its service life. This paper presents an HBMU framework that employs a Dirichlet process (DP) mixture prior on structural parameters (DP-HBMU). DP mixtures are nonparametric Bayesian models that perform clustering without pre-specifying the number of clusters, incorporating damage state classification into FE model updating. We formulate the DP-HBMU framework and devise a Metropolis-within-Gibbs sampler that draws samples from the posterior by embedding Metropolis updates for intractable conditionals due to the FE simulator. The applicability of DP-HBMU to damage localization is demonstrated through both numerical and experimental examples. We consider moment-resisting frame structures with beam-end fractures and apply the method to datasets spanning multiple damage states, from an intact state to moderate or severe damage state. The clusters inferred by DP-HBMU align closely with the assumed or observed damage states. The posterior distributions of stiffness parameters agree with ground truth values or observed fractures while exhibiting substantially reduced uncertainty relative to a non-hierarchical baseline. These results demonstrate the effectiveness of the proposed method in damage localization.