Explainability of convolutional neural networks for damage diagnosis using transmissibility functions

Structural health monitoring (SHM) is crucial for ensuring the safety and efficiency of engineering systems. Vibration-based signals have been widely employed in numerous studies for damage detection, localization and quantification, thanks to their high sensitivity to structural damages and versatile applicability across various structures. Among these, transmissibility functions (TFs) have emerged as particularly promising because they can be derived from output-only measurements, making them practical for real-world applications. Vibration-based features, including those captured by TFs, provide a wealth of damage-related information, but extracting these features can be challenging with traditional methods and often requires a priori knowledge. To address this challenge, deep learning has gained significant attention for its capacity to handle intricate patterns and extract hidden features. However, deep learning algorithms are often perceived as black-box models due to their complex and heterogeneous layers, which hinder transparency and raise concerns, especially in critical domains. Although numerous studies have highlighted the diagnostic potential of deep learning in SHM with vibration-based data, there has been limited exploration of the rationale behind using deep neural networks (DNNs) for processing TFs. This paper addresses this gap by introducing explainable artificial intelligence (XAI) methods in two distinct TF-based damage diagnostic case studies: a numerical aluminium structural beam and a large-scale experimental steel frame. In the former, damage is simulated as local stiffness reductions, while in the latter, damage is introduced by loosening joint bolts. In both cases, a convolutional neural network (CNN) is used to process raw TF data for damage detection, localization, and quantification in the beam, and for detection and localization in the frame. Subsequently, an XAI method based on the layer-wise relevance propagation (LRP) algorithm is employed to identify the most relevant input features. A pattern analysis is presented to explain recurrent patterns, and a comparison with other XAI methods is proposed for further validation. The results demonstrate that the CNN provides accurate predictions for both case studies, with its focus on damage-sensitive features aligning closely with findings in the existing literature.