Traceable Algorithm Unrolling Network: An Interpretable Deep Sparse Representation Model for Mechanical Fault Diagnosis

In mechanical fault diagnosis (MFD), intelligent fault diagnosis (IFD) methods perform excellently regarding diagnosis accuracy. However, those methods are generally constructed with an excessive number of unprincipled parameters, resulting in uninterpretable architecture, ambiguity in the diagnosis process, and unclear decision-making basis. Thus, a traceable algorithm unrolling (TAU) network for interpretable MFD is proposed to overcome the above limitations. First, a mechanism-driven feature extractor (FE) is constructed by unrolling the iterative algorithm of sparse coding, aiming at encoding interpretable features from vibration signals. Second, a theory-based feature clustering (FC) algorithm is executed through the dynamic routing mechanism of the capsule network (CN), where the inner product serves as a measure for the association between input and output features. Finally, a post hoc interpretability strategy based on the coupling matrix is introduced to investigate how the TAU generates diagnostic results from the learned features and to verify whether these features are associated with faults, thereby enhancing the credibility of the diagnosis results. In addition, the simulation and experiment are designed to verify the decision-making mechanism and diagnostic performance of TAU. The results demonstrate that TAU makes diagnostic decisions based on the high-dimensional feature mapping associated with fault characteristic frequencies. Meanwhile, TAU outperforms the compared methods in fault diagnosis performance.