Uncertainty-Aware Structural Anomaly Detection under Varying Environmental Conditions Based on Bayesian Nonparametric Density Estimation–Guided Probabilistic Damage Index

Abstract

This paper presents a novel structural anomaly detection method that combines a truncation-free variational inference (VI)-based Dirichlet process Gaussian mixture model (DPGMM) with a Mahalanobis squared distance (MSD)-based damage index (DI). The DPGMM, serving as a Bayesian nonparametric density estimator, characterizes the distribution of normal condition data, and the truncation-free VI efficiently approximates the posterior distribution of the DPGMM. By harnessing the adaptability of the truncation-free VI-DPGMM in adjusting the component number (model complexity) based on observed data, the method adeptly captures the multimodal distribution of normal condition data, which reflects diverse patterns of structural behavior influenced by various uncertainties, through establishing a baseline distribution based on the variational posterior of the DPGMM. Subsequently, a MSD-based DI is devised to assess the discordancy of a test sample to this baseline, which addresses the limitations of MSD resulting from its implicit Gaussian assumption and provides a systematic framework for uncertainty quantification through its empirical variance. The effectiveness of the proposed method is verified using the Z24 Bridge data set, demonstrating superior performance in accuracy and robustness compared with several existing methods. Additionally, it explicitly quantifies the overall uncertainty inherent in structural anomaly detection, thereby facilitating a more informed decision-making process.