OW-NISTA: Bridging Orthogonal Wavelets and Algorithm Unrolling in an Interpretable Way

Deep Neural Networks (DNNs) have achieved significant success in various fields. However, in the field of mechanical fault diagnosis, interpretability is particularly important due to the significant safety issue and property loss mechanical fault diagnosis relates to, which is lacking in traditional DNNs. To address this, DNNs based on wavelets and algorithm unrolling have been separately developed, each providing interpretability for diagnosis. However, to the best of my knowledge, there has been no attempt to integrate the two. In this paper, we propose a Hybrid Orthogonal Wavelet Nested Iterative Soft Thresholding Algorithm by organically combining the Mallat algorithm of orthogonal wavelets for signal decomposition with the Nested Iterated Soft Thresholding Algorithm (NISTA) for solving multi-layer convolutional sparse coding problems, enhancing the interpretability of network from a structural perspective. Additionally, through the design of various visualization methods for network features and results, the interpretability of the network is further increased from a post-analysis perspective. Finally, by classifying data from two public datasets, the XJTU-SY dataset and the German Paderborn bearing dataset, the classification performance of the model is validated compared with some other widely used methods.