WaveletKernelNet: An Interpretable Deep Neural Network for Industrial Intelligent Diagnosis

Convolutional neural network (CNN), with the ability of feature learning and nonlinear mapping, has demonstrated its effectiveness in prognostics and health management (PHM). However, an explanation on the physical meaning of a CNN architecture has rarely been studied. In this article, a novel wavelet-driven deep neural network, termed as WaveletKernelNet (WKN), is presented, where a continuous wavelet convolutional (CWConv) layer is designed to replace the first convolutional layer of the standard CNN. This enables the first CWConv layer to discover more meaningful kernels. Furthermore, only the scale parameter and translation parameter are directly learned from raw data at this CWConv layer. This provides a very effective way to obtain a customized kernel bank, specifically tuned for extracting defect-related impact component embedded in the vibration signal. In addition, three experimental studies using data from laboratory environment are carried out to verify the effectiveness of the proposed method for mechanical fault diagnosis. The experimental results show that the accuracy of the WKNs is higher than CNN by more than 10%, which indicate the importance of the designed CWConv layer. Besides, through theoretical analysis and feature map visualization, it is found that the WKNs are interpretable, have fewer parameters, and have the ability to converge faster within the same training epochs.