Multiband weights-induced periodic sparse representation for bearing incipient fault diagnosis

Faulty impulses from incipient damaged bearings are typically submerged in harmonics, random shocks, and noise, making incipient fault diagnosis challenging. The prerequisite to this problem is the robust estimation of faulty impulses; thus, this paper proposes a multiband weights-induced periodic sparse representation (MwPSR) method. Firstly, a multiband weighted generalized minimax-concave induced sparse representation (MwGSR) approach is presented to accelerate the sparse approximation process and eliminate the interference components. A new indicator, coined the frequency-weighted energy operator spectrum's kurtosis-to-entropy ratio, is defined to construct the MwGSR's weights to accentuate faulty impulses. Secondly, to enhance the periodicity of the estimated impulses, a fault period decision strategy with an improved periodic target vector is developed and embedded into MwGSR to form MwPSR eventually. Detailed simulations and experiments demonstrate that MwPSR can achieve periodic sparsity with high accuracy and robustness and is reliable for incipient bearing fault diagnosis.