Integrating Bayesian Uncertainty into an Explainable AI Framework for CWT-CNN Structural Damage Localization

L. E. Mujica, L. Acho, P. Buenestado, Víctor Fernández-pacheco, José Gibergans, G. Pujol, M. Ruiz

TL;DR: A novel framework that integrates Bayesian Inference into the framework of Explainable AI (XAI) techniques to provide a transparent and reliability-aware diagnostic tool for structural damage localization and demonstrates that the integration of Bayesian uncertainty effectively filters out spurious hot-spots caused by environmental fluctuations.

Precision in damage localization is critical for the safety and maintenance of engineering structures. While previous studies have utilized Convolutional Neural Networks (CNNs) paired with Continuous Wavelet Transform (CWT) scalograms of ultrasonic guided waves to regress damage coordinates, these deterministic approaches often fail to account for predictive noise and model uncertainty. This paper proposes a novel framework that integrates Bayesian Inference into the framework of Explainable AI (XAI) techniques to provide a transparent and reliability-aware diagnostic tool for structural damage localization. Within this framework, standard point estimates for model weights w are replaced by posterior probability distributions p(w D), conditioned on the training dataset D, through the use of Variational Inference. Consequently, the model outputs a predictive mean for the spatial coordinates (x ̂,y ̂) and a corresponding predictive variance σ^2, which serves as a formal measure of localization uncertainty. To interpret these results, we adapt Gradient-weighted Class Activation Mapping (Grad-CAM) to explain not only the predicted location but also the source of the uncertainty. By analyzing the time-frequency representations of the acoustic signals through this lens, we can pinpoint which time-frequency features contribute to high-confidence detections versus those that induce predictive variance, in other words, this allows us to not only say: "sensor A” influenced the damage coordinate prediction, but also "sensor A” is the reason for the high uncertainty in this prediction. The approach is validated using experimental ultrasonic signals from an aluminium plate subjected to variations in temperature at different localizations (hot-spots). Results demonstrate that the integration of Bayesian uncertainty effectively filters out spurious hot-spots caused by environmental fluctuations. Furthermore, the XAI component reveals a physical alignment between high-relevance pixels in the CWT domain and the theoretical Time-of-Flight (ToF) of structural Lamb waves.