Total Variation Denoising with Fusing L1 Norm and Overlapping Group Sparsity and Its Application to Analyze Variable Speed Faulty Bearing Signals

As a core transmission component, the health status of rolling bearings is critical to equipment safety. Under variable speed conditions, bearing failures produce non-periodic shock features that are masked by complex signals and noise, leading to diagnostic difficulties. The total variation denoising with overlapping group sparsity (GSTVD) algorithm, although effective in identifying and extracting non-periodic fault shock impulses in the vibration shock signals of rolling bearing failures, ignores the sparsity of the signals themselves. Therefore, this paper proposes a total variation denoising with fusing L1 Norm and overlapping group sparsity (FGSTVD), which combines the sparse characteristics of the signal and its first-order differential, controls the signal sparsity in the non-shock region through L1 norm, enhances the characteristics of faulty shock pulses by using the total variation denoising with overlapping group sparsity penalty term, and solves the sparse model through the alternating direction method of multipliers (AMDD) algorithm. Simulation verification shows that the method can extract the non-periodic fault pulse in the variable speed signal with high fidelity, which provides a new effective means for rolling bearing fault diagnosis and is of great significance to ensure the safe and stable operation of the equipment.