Physics-guided learnable wavelet filtering network for small-sample fault diagnosis with application to band saw blades

Abstract Intelligent fault diagnosis of metal band saw blades is challenged by the intricate entanglement of fault patterns in industrial scenarios, where limited samples impede deep networks from learning class-specific discriminative boundaries, and black-box decision mechanisms preclude the traceability of misdiagnosis origins. To address the coupling of multi-fault categories and the deficiency of interpretability, a physics-guided learnable wavelet filtering attention network is proposed, in which physical prior knowledge is leveraged to guide adaptive feature extraction and fault decoupling. Specifically, an adaptive Morlet wavelet filter is designed to explicitly extract fault-related physical features through time–frequency impact, thereby endowing the feature extraction process with interpretability. Subsequently, an adaptive residual hybrid wavelet network is constructed, wherein a dual-path architecture of discrete wavelets and convolutions is adopted to deeply mine multi-scale features and alleviate the information bottleneck induced by physical filtering. Furthermore, a cross-category filtering strategy is incorporated, by which the multi-class classification task is implicitly decoupled through category competition mechanisms, compelling the network to learn discriminative feature representations. Experiments demonstrate that the proposed method achieves significantly superior diagnostic accuracy under small-sample conditions compared to existing approaches, yielding an average fault diagnosis accuracy of 96.8% on the gearbox dataset and 89.92% on the band saw blade dataset, while its generalization capability and full-process interpretability are validated through the physical semantic analysis of filter parameters and feature visualization.