An overlapping group sparse variation method for enhancing time-frequency modulation bispectrum characteristics and its applications in bearing fault diagnosis

Rolling bearings are essential for machines and their faults can cause significant losses. Extracting pulse components from vibrations is difficult due to complicated working conditions. In this paper, a two-dimensional overlapping group sparse variation method based on non-convex function for enhancing time-frequency modulation bispectrum characteristics (OGSVMB) to identify bearing faults is proposed. The time-frequency modulation bispectrum (TFMB) demodulates signals into bispectra, highlighting the relationship between resonance band and modulation frequency. A mathematical model is established with a non-convex penalty term to constrain the distribution of two-dimensional reconstructed signal. The optimization-minimization method is used to find an optimal solution, producing a bispectrum with clearer modulation characteristics and a high SNR by reducing noise and irrelevant components while preserving the group sparsity of TFMB. The modulation Gini index is introduced to adaptively determine group size. Finally, the optimal enhanced envelope spectrum is calculated through slice optimization to identify fault characteristics. The effectiveness of the proposed method in diagnosing rolling bearing faults is verified through simulation and experiments. Compared to MSB, original TFMB, Fast Kurtogram, and Autogram, the OGSVMB method is better at identifying bearing fault characteristics.