An Interpretable and Calibrated Energy-Based Model for Bearing Fault Diagnosis and Out-of-Distribution Detection

Abstract

Predictive maintenance of rotating machinery in industrial settings requires bearing fault diagnosis that is both accurate and auditable by maintenance engineers. Methods that achieve high classification accuracy typically operate as closed-box deep learning models, while methods that provide interpretability rarely report probability calibration, out-of-distribution (OOD) detection, or pairwise statistical significance. This paper addresses this gap with an Energy-Based Model (EBM) trained via Stochastic Gradient Langevin Dynamics on physics-informed features, in which the energy gradient with respect to each input feature provides intrinsic interpretability without post-hoc surrogates. A single forward pass simultaneously yields classification logits, a calibrated probability output, and a free-energy score for OOD detection. On three benchmark datasets (CWRU, MFPT, Paderborn) under file-level splitting and across five training seeds, the method attains 93.24% accuracy on Paderborn with an Expected Calibration Error of 0.017, less than half that of a Random Forest baseline. The same energy score separates inputs drawn from datasets absent at training time and preserves accuracy under additive feature noise. A leave-one-operating-condition-out evaluation bounds the operating envelope, in which three of four unseen conditions transfer with moderate loss and the lowest-speed condition does not. The results indicate that classification, probability calibration, OOD detection, noise robustness, and feature-level interpretability can be jointly delivered by a single energy-based model on bearing fault diagnosis benchmarks, without auxiliary classifiers or post-hoc explanation modules.