An Interpretable Multiplication-Convolution Sparse Network for Equipment Intelligent Diagnosis in Antialiasing and Regularization Constraint

As deep learning (DL) with its powerful fitting representation ability is increasingly applied in intelligent fault diagnosis of mechanical equipment, the interpretability of networks directly affects the credibility and universality of the models with the mechanism of equipment signal characteristic ignored. In order to solve those issues, this study proposes a multiplication-convolution sparse network (MCSN) with interpretable sparse kernels, which contains a simple three layers, including feature separator, feature extractor, and logic classifier. Inspired by signal modulation mechanism, the raw spectrum signals are first processed by a feature separator with multiple learnable multiplication filtering kernels (MFKs). The feature separator can effectively separate fault features from complex spectrum in a comprehensible way. Then, feature extractor with convolutional process is also used to mine the sequential characteristics and those features are finally input into the logic classifier. It should be noted that the combination of the multiplication process and the convolution process aims to achieve efficient feature mining of the signal. In particular, the addition of antialiasing constraint and
$L^{1}$
regularization constraint in the training process makes the multiplication filtering kernel parameters sparse and learn as much fault feature information distributed in different frequency bands as possible, which is conducive to the visualization of the spectrum information extraction and thus enhances the interpretability and reliability of the multiplication filtering kernels. The interpretability of the proposed MCSN is verified by a two-class task experiment, and the visualizations of the learned multiplication filtering kernel illustrate a clear and accurate representation related to the fault features. Compared with other six open-source network models, including WaveletKernelNet (WKN), LeNet, convolutional neural network (CNN), ResNet18, AlexNet, and BiLSTM, the proposed MCSN has the highest fault recognition accuracy, with an average recognition accuracy of 99.65% for gear faults and 99.83% for bearing faults. Ablation experiments on CNN indicate the benefit of the proposed feature separator in feature enhancement with an average recognition accuracy improvement of 1.59%.