Algorithm Unrolling Network With Learnable Sparse Regularization for Interpretable Mechanical Anomaly Detection

Sparse representation-based interpretable algorithm unrolling is one of promising techniques for mechanical anomaly detection. In order to enhance the learning and representation capabilities of the algorithm unrolling model, this article proposes a learnable sparse regularization network (LSR-Net). Instead of imposing explicit regularization constraints on the encoding and dictionary during modeling, two subnetworks are designed to learn prior information: $\mathbf{Net}_{\mathbf{X}}$ and $\mathbf{Net}_{\mathbf{D}}$. The model is solved using the half quadratic splitting algorithm, and further unrolls the process of iterative computation into the form of a network. The architecture for encoding learning is structured as input convex neural networks, ensuring LSR-Net can learn meaningful encoding priors. Through the analysis of simulated and experimental data, it has been demonstrated that LSR-Net has strong feature extraction and noise resistance capabilities, and the design of its prior learning architecture is both reasonable and effective. In addition, the visualization of LSR-Net's overall reconstruction and the reconstruction of different dictionary atoms allows for both global and local interpretation of the learning results, thereby providing post hoc interpretability to LSR-Net. The visualization results confirm that LSR-Net is capable of learning features that align with mechanical vibration characteristics.