Interpretable adaptive multiwavelet kernel-driven two-dimensional convolutional neural network for mechanical fault diagnosis

Abstract

Despite extensive research on convolutional neural networks (CNNs) for intelligent fault diagnosis, several challenges remain, including the limited effectiveness of one-dimensional CNNs, susceptibility to noise, and lack of interpretability. To address these issues, an interpretable adaptive multiwavelet kernel-driven two-dimensional convolutional neural network model called MWKN has been designed for mechanical fault diagnosis in this paper. Specifically, a newly designed adaptive natural convolutional layer based on two-dimensional multiwavelet transform is embedded as a feature extraction module in the shallow layer of a two-dimensional CNN model. Crucially, this novel multiwavelet convolutional layer is jointly optimized with the entire network, enabling the adaptive optimization of its intrinsic multiwavelet convolutional kernel. Additionally, this model incorporates a specifically designed embedded two-dimensional neighboring coefficient shrinkage module to address the issue of CNN susceptibility to strong noise. This study investigates the interpretability of the MWKN model through simulated fault experiments, addressing interpretability deficits observed in CNN. The results demonstrate that the embedded multiwavelet kernel and the inclusive WMKN model as a whole possess synchronized learning and matching rules, substantiating that the learning process of the multiwavelet kernel is neither isolated nor random but follows an inherent adaptive learning mechanism based on the principle of error minimization. Finally, the excellent fault identification capability and robust noise resistance of MWKN are validated through experimental cases of variable speed bearing faults and pump circulation bearing faults under strong noise background. In addition, the industrial applicability and interpretability of the method were further validated in an industrial scenario case.