Pseudo non-dyadic second generation wavelet tight frame for machine fault diagnosis

This paper investigates a novel wavelet tight frame (WTF) constructing strategy for obtaining pseudo second generation bases with non-dyadic time-frequency partition grids. The proposed constructing strategy starts with a known second generation wavelet basis and applies it in an undecimated filterbank. Via forward and inverse transformation procedure, an input signal is decomposed into a set of dyadic wavelet packets. By introducing a systematic way of wavelet packet reordering and ensemble wavelet generating method, another corresponding set of non-dyadic wavelet packets are generated. It is demonstrated that the derived pseudo non-dyadic second generation wavelet packets (PNSGW) are associated with well-defined band-pass filters, which ensure good time-frequency localizability and exact shift-invariance. The PNSGW strategy is combined with spectral kurtosis to detect incipient faults in mechanical systems. The processing results show that the proposed technique is a well complement to conventional dyadic wavelet transform in investigating transient impulse responses caused by faulty mechanical components.