Minimum correlated generalized Lp/Lq deconvolution for recovering repetitive impacts from a vibration mixture

Repetitive impact detection (RID) is a core topic in bearing fault detection. The deconvolution-based method is an effective method in RID. Many deconvolution algorithms have been developed for this purpose. Simplified sparse filtering (SSF) is a typical deconvolution-based method, which has been successfully applied in RID due to its remarkable performance and fast computing speed. SSF generates an inverse filter by minimizing the generalized Lp/Lq (G- Lp/Lq ) norm. The performance of SSF depends on the properties of G- Lp/Lq . However, G- Lp/Lq cannot characterize the periodicity of a specific period. Therefore, SSF cannot effectively detect multiple fault components at the same time and achieve compound fault detection. Additionally, when the signal-to-noise ratio (SNR) of the fault signal is extremely low, SSF might not recover the repetitive impacts from the measured signals. In order to improve these two shortcomings of SSF, we extend the G- Lp/Lq norm from time domain to signal correlation domain, and propose a correlated generalized Lp/Lq norm (CG- Lp/Lq ). The proposed CG- Lp/Lq norm uses the enhanced periodicity which is obtained by calculating the correlation of repetitive impacts to realize the characterization of repetitive impacts with a specific period. Based on the proposed CG- Lp/Lq , a new deconvolution algorithm, the minimum correlated generalized Lp/Lq deconvolution (MCG- Lp/Lq -D) algorithm, is designed. The superiority of the proposed MCG- Lp/Lq -D is validated by both simulated and experimental data. The results demonstrate that MCG- Lp/Lq -D can recover the repetitive impacts, submerged in heavy noise, from the vibration mixture, and it can achieve compound fault detection.