A Sparse Representation Method Based on Multiobjective Optimization for the Extraction of Nonperiodic Fault Features of Rolling Bearing Under Variable Speed

Fault signature extraction of rolling bearings under variable speed conditions is crucial while still a challenge due to the nonperiodic features of the fault impulses. A sparse representation method based on multiobjective optimization (MOO) is proposed to extract the nonperiodic fault impulses with high fidelity, in which the sparse representation with the generalized minimax concave (GMC) regularization based on flexible analytic wavelet transform (WT) enhanced is adopted. Moreover, a MOO model based on the angular domain correlated kurtosis (AD-CK) and the harmonic-to-noise ratio of envelope order spectrum (HNR-EOS) is constructed for adaptive parameters optimization of the sparse representation model, upon which a density estimation strategy is proposed to determine the optimal parameters from the Pareto front originally obtained via NSGA-II algorithm. The nonperiodic fault impulses can thus be extracted with the fault signature further identified from the envelope order spectrum. The method is validated by analyzing simulation and experiment signals.