The processing of resonances excited by gear faults using continuous wavelet transform with adaptive complex Morlet wavelet and sparsity measurement

Abstract

This paper explores an improved technique for detection and characterisation of excited resonances by gear faults using the redundant information of continuous wavelet transforms (CWT) and sparsity measurement (SM) as a criterion for selecting the optimal parameters. The proposed method is conducted in two steps. First, the CWT is calculated with a scale vector that covers the medium and high frequency range of the inspected signal, with 0.1 increments. The wavelet coefficients at the resonance scale have the form of a pulse train with the same resonance characteristics and large amplitude. Away from the scales resonance value, the resemblance with the pulse train decreases continuously until it becomes noise. Thus, the scales of the excited resonances with higher signal-to-noise ratio are revealed clearly by sparsity measurement maximisation (SMM). The proposed SM-based scale selection method allows to select more than one or two resonance frequency bands. Second, the signal is band-pass filtered around each located resonance in order to detect the fault-contained frequency band. The bandwidths are obtained by adjusting the shape factor values of the Complex Morlet Wavelet. The optimal band where the SNR is the highest can be deduced using the SMM. This technique makes it possible to locate accurately all scales of resonances present in a signal, including those with low energies, and the optimal filter band of each resonance. The effectiveness of the proposed method has been verified by numerical simulations and by fault vibration signals from a gear with three types of local faults: broken tooth, hunting tooth defect and flaking defect tooth. The results show that the proposed method allows an accurate identification and location of a single or even multiple defects.