Dynamic Bayesian wavelet transform: New methodology for extraction of repetitive transients

Visualization of the dynamic Bayesian wavelet transform: (a) the mixture of simulated repetitive transients caused by a bearing defect, two low-frequency components and noises; (b) the informative frequency band detected by using the fast kurtogram; (c) frequency spectrum of an initial wavelet filter; (d) frequency spectrum of the mixed signal processed by the initial wavelet filter; (e) the temporal waveform of the filtered signal and its kurtosis; (f) a prior wavelet parameter distribution; (g) extrapolations of the kurtosis of the filtered signal and production of artificial observations; Visualization of the dynamic Bayesian wavelet transform: (h) to (k) posterior wavelet parameter distributions at iterations from 0 to 201; (l) predicted observations (kurtosis) and their convergence to a stable level; (m) frequency spectrum of the posterior wavelet filter at iteration k=201; (n) frequency spectrum of the filtered signal at iteration k=201; (o) repetitive transients extracted by the optimal wavelet transform (the temporal waveform of Fig. 1 (n)).245