Fault signature extraction of rolling bearings under variable speed via time–frequency overlap group sparse representation

The high-fidelity extraction of the nonperiodic fault transients of rolling bearings under variable speed is of significant importance, while still a challenge for early-stage fault diagnosis of major equipment such as aero engines and wind turbines. A method termed continuous symmetric Laplace wavelet transform (CSLWT) enhanced time–frequency overlap group sparse (OGS) representation is proposed in this paper. A symmetric Laplace mother wavelet function is proposed which could satisfy the admissibility condition of wavelet decomposition and reconstruction, upon which the CSLWT is fabricated and adopted as the sparse representation dictionary to match the nonperiodic fault transients. Since the decomposition coefficients of nonperiodic fault impulses via the CSLWT exhibit group sparsity on the time–frequency plane with unknown intervals, the time–frequency OGS model is adopted and then solved for extraction of the nonperiodic fault transients. Moreover, a data driven, multi-objective optimization strategy is presented for determining the hyper-parameters of the sparse model. The correlated kurtosis of angular envelope signal (CK-AE) and harmonic-to-noise energy ratio of the order spectrum (HNR-OS) are introduced as the optimization objectives, and the Pareto front is solved based on the NSGA-II algorithm, upon which the acceptable solutions set is chosen from the Pareto front, and the proper hyper-parameters are further determined via proposed normalized solutions distance density sorting of the acceptable solutions set. The performance of the proposed method is validated via processing both simulated and experimental vibration signals, as well as compared with some tradition fault diagnosis methods.