Adaptive k-Sparsity-Based Weighted Lasso for Bearing Fault Detection

Vibration monitoring is widely used for machinery fault detection as one of the most effective and common methods. However, it is difficult to extract fault features from the vibration signals. In this paper, adaptive k-sparsity-based weighted Lasso (Ada-KWLasso) is proposed to extract fault features of vibration signals for bearing fault diagnosis. A sparse regularization term, i.e., weighted
${l}_{1} $
-norm is adopted in Ada-KWLasso for promoting the signal sparsity due to its good anti-noise property. The adaptive parameter setup is proposed based on the integration of the k-sparsity and forward–backward splitting algorithm, which makes the regularization term parameter-free and then improves applicability of Ada-KWLasso in real-world cases. Finally, the simulation signal and bearing fault signals are used to demonstrate the effectiveness of Ada-KWLasso for bearing fault diagnosis. In the simulation signal analysis, Ada-KWLasso is compared with the conventional sparse representation methods under different regularization parameters. Moreover, energy rate (ER) value of filtered signal for Ada-KWLasso is 4.81% and the highest ER values of Lasso and overlapping group shrinkage (Ogs) under different regularization parameters are 3.16 and 4.68%, respectively. The testing results show that the proposed method is more effective for extracting fault features from those noised vibration signals in comparison with other conventional methods.