Unrolled sparse coding via lifting wavelet for interpretable intelligent fault diagnosis

Interpretable intelligent fault diagnosis is one of the key technologies in prognostic and health management. Algorithm unrolling emerges as a systematic method for constructing interpretable networks. To further enhance prior knowledge and improve performance in fault diagnosis, we unroll sparse coding via lifting wavelet into a network named LWU-Net. A learnable lifting wavelet dictionary is introduced, capable of representing the fault features accurately and efficiently with fewer parameters. Its natural perfect reconstruction property makes it suitable for algorithm unrolling. To maintain the wavelet properties and align with signal features throughout the training process, a set of dictionary-specific loss functions is proposed. Subsequently, the lifting wavelet sparse denoising model is proposed. Within the algorithm unrolling framework, the model is solved and unrolled into LWU-Net with learnable lifting wavelet dictionaries. The construction process of LWU-Net is interpretable, resulting in each component of LWU-Net possessing a clear physical meaning. Furthermore, taking into account the physical meaning of dictionary atoms and codes from a wavelet perspective, a set of visualization methods are developed to understand LWU-Net's decision-making process. Therefore, LWU-Net has both ad hoc and post hoc interpretability. To assess the performance of LWU-Net, a series of fault experiments were conducted. The results revealed that compared to other popular networks, such as ResNet, WavekernelNet and ML-ISTA, LWU-Net has the superior diagnostic accuracy, fastest convergence speed, minimized parameter size, low data dependency. The visualizations indicate that LWU-Net focuses on different frequency bands for different faults and similar frequency bands for different severities. It effectively explains LWU-Net's decision-making process.