LW-Net: an interpretable network with smart lifting wavelet kernel for mechanical feature extraction and fault diagnosis

Deep learning has been applied in mechanical fault diagnosis. Hereinto, the convolutional neural network (CNN) has the shallow convolution operation, supporting the function of feature learning. However, the interpretability of CNN has always been an urgent problem to be solved. Due to the advantages of lifting wavelets and their transforms for impact fault diagnosis, an interpretable network called LW-Net with smart lifting wavelet kernels is proposed for mechanical feature extraction and fault diagnosis. Different from the traditional CNN, the shallow layer of the net is designed to be the lifting layer, concluding split, prediction and update sublayers by the natural convolution operation of lifting wavelet transforms. The smart lifting wavelet kernels are constructed by the mathematic constraints of lifting wavelets, resulting in the nice properties of signal processing. Meanwhile, the kernels with only two parameters are learned from the input data and updated by the back-propagation process. The lifting layer is suitable to accurately extract the impact fault features, improving the effective fault diagnosis of LW-Net. Moreover, the interpretability of LW-Net to achieve shallow feature extraction is verified and discussed by the repeatable simulations. The underlying logic and physical meaning of the lifting layer is revealed to be the adaptive waveform matching and learning based on the inner product matching principle. LW-Net is applied to the engineering diagnostic cases of the Case Western Reserve University dataset and planetary gearbox dataset to verify the effectiveness. The results show the method outperforms the classical and popular methods on the converge speed, classification accuracy and feature extraction.