High-fidelity fault signature extraction of rolling bearings via nonconvex regularized sparse representation enhanced by flexible analytical wavelet transform

Diagnosing the bearing fault, especially incipient fault is important for equipment health management while is still a challenge in which high-fidelity extraction of the fault signature is expected. A method termed flexible analytical wavelet transform (FAWT)-enhanced sparse representation with nonconvex regularization is proposed in this research. FAWT enjoys flexible covering along both the frequency and time axis as well as tunable oscillation property and is adopted to well match the fault impulses after parameters optimization. In the fabricated FAWT-enhanced sparse model with generalized minimax-concave regularization, an index termed harmonic-to-noise energy ratio of envelope spectrum (ES-HNER) is proposed which is found effective and robust for quantitative assessment of the richness of fault signature and could be automatically evaluated from the envelope spectrum, based on which the parameters for constructing the FAWT basis and threshold are optimized via maximizing the ES-HNER in the candidate parameters space. The sparse decomposition signals are further obtained via solving the FAWT-enhanced sparse model, upon which the bearing fault signature is expected to be exhibited on the envelope spectrum. The performance of the proposed method has been validated via analysis of both simulation and experiment signals as well as comparison with other methods.