Use of generalized Gaussian cyclostationarity for blind deconvolution and its application to bearing fault diagnosis under non-Gaussian conditions

Blind deconvolution (BD) methods can extract fault signatures from noisy observations. Among all the BD methods, maximum second-order cyclostationarity blind deconvolution (CYCBD) is an effective method for extracting weak periodic impulses related to bearing faults. CYCBD is done by maximizing the second-order cyclostationarity of a signal through the indicator of second-order cyclostationarity (ICS2, which can be calculated using the squared envelope spectrum, SES). The effectiveness of the SES is under the assumption that signals are Gaussian distributed. However, SES, ICS2 and CYCBD can be ineffective when signals are corrupted by highly leptokurtic noise. A recent study separates the detection of non-stationarity from non-Gaussianity by releasing the hypothesis of Gaussianity to generalized Gaussianity. The indicator IGGCS/GGS can detect the cyclostationarity of a signal corrupted by highly impulsive noise. In addition, it can be approximated by the β-power envelope spectrum (PES). Inspired by the relationship between IGGCS/GGS and ICS2, a blind deconvolution method by maximizing the generalized Gaussian cyclostationarity (CYCBDβ) is proposed in this study. Compared with CYCBD, the robustness of CYCBDβ against strong non-Gaussian noise increases. However, the original shape parameter estimation method has two limitations, which introduces difficulties in using IGGCS/GGS as the criterion for BD. (1) The fault period must be known in advance. (2) The fault period should be an integer for the synchronous average. In addition, a serious problem of CYCBD is that the used cyclic frequencies must match fault frequencies. Otherwise, the performance of CYCBD can be severely compromised. To better incorporate the shape parameter estimation into the BD method, the GGCS model using fault frequencies for synchronous average is proposed. In addition, a fault frequencies estimation approach has been added to the generation of the weighting matrix of CYCBDβ. Benefiting from these improvements, the proposed CYCBDβ has two advantages compared with CYCBD: (1) the robustness of CYCBDβ against strong non-Gaussian noise is higher, and (2) CYCBDβ can extract fault features when fault frequencies are unknown. The effectiveness and robustness of the method are validated using simulations and real vibration datasets.