Acoustic signals-based probabilistic fault diagnosis for expansion joints of small and medium bridges using Bayesian ensemble learning

Premature failures of in-service bridge expansion joints (BEJs) have become increasingly prevalent due to fatigue, traffic load, and environmental influences. The condition assessment of BEJs usually relies on the temperature-displacement correlation models using structural health monitoring (SHM) data for long-span bridges. However, such approaches are less applicable to small and medium bridges (SMBs), where the temperature–displacement relationship is not dominant, and the implementation of SHM systems is economically constrained. Consequently, routine assessment for SMBs remains largely dependent on manual inspection, which is labor-intensive and subjective. Acoustic-based monitoring is a promising and cost-effective solution for assessing damage severity and localization in BEJs, but its application to SMBs still remains limited. Moreover, existing studies mostly focus on deterministic models failing to quantify uncertainty, which is essential for trustworthy diagnostics under noise and variability. To address these limitations, this study proposes a probabilistic fault diagnosis framework based on convolutional neural networks with Bayesian deep ensemble (CNN-BDE) for BEJs of SMBs using acoustic signals. It incorporates an adaptive inter-class variance regularization term to enhance feature discrimination under noisy conditions. A Bayesian deep ensemble strategy is developed to quantify predictive uncertainty and improve the reliability of diagnostic results. Real-world acoustic data from in-service BEJs of SMBs are used to illustrate the feasibility of the proposed CNN-BDE. Compared to representative baseline methods under various working conditions, the results indicate that the proposed model achieves the highest diagnosis accuracy and best ability in uncertainty estimation.