Sparse signal representations attract much attention in the community of signal processing because only a few coefficients are required to represent a signal and these coefficients make the signal understandable. For bearing faults’ diagnosis, bearing faults signals collected from transducers are often overwhelmed by strong low-frequency periodic signals and heavy noises. In this paper, a joint signal processing method is proposed to extract sparse envelope coefficients, which are the sparse signal representations of bearing fault signals. Firstly, to enhance bearing fault signals, particle swarm optimization is introduced to tune the parameters of wavelet transform and the optimal wavelet transform is used for retaining one of the resonant frequency bands. Thus, sparse wavelet coefficients are obtained. Secondly, to reduce the in-band noises existing in the sparse wavelet coefficients, an adaptive morphological analysis with an iterative local maximum detection method is developed to extract sparse envelope coefficients. Simulated and real bearing fault signals are investigated to illustrate how the sparse envelope coefficients are extracted. The results show that the sparse envelope coefficients can be used to represent bearing fault features and identify different localized bearing faults.
Sparse signal representations using the tunable Q-factor wavelet transform