Impulsive components separation using minimum-determinant KL-divergence NMF of bi-variable map for bearing diagnosis

In vibration-based monitoring techniques, the periodic impulse response is a typical manifestation of the localized failure of rolling element bearings (REBs). Cyclic spectral help reveal the cyclostationarity of such signals by bridging the carrier frequency and the cyclic frequency, which are represented in bi-variable maps. By integrating the components within the optimal band over the carrier axis, the Enhanced Envelope Spectrum (EES) or Squared Envelope Spectrum (SES) can be obtained and provide attractive analysis tools for the bi-variable map. In this paper, as a complement of integration analysis of the bi-variable map, Non-negative Matrix Factorization is adopted to separate the cyclic components in bi-frequency map. In addition to using KL-divergence as the fidelity term, the minimum determinant regularization term is crafted to enforce the sparseness, uniqueness, and identifiability of the solution. With numerical simulation and bearing fault experiments, the result shows that the number of cyclic components is estimated correctly and that the periodic impulsive components are separated and enhanced from the bi-variable map, especially in the cases that cyclic interferences mask the fault feature.