Period-assisted adaptive parameterized wavelet dictionary and its sparse representation for periodic transient features of rolling bearing faults

Accurate extraction of fault-induced periodic transient features from noise interference contain-ing harmonics and large-amplitude random impulses is a key to fault detection of rolling bearings. Therefore, this paper proposes a sparse representation method based on a period-assisted adap-tive parameterized wavelet dictionary to extract periodic transient features of rolling bearing faults. First, considering the influence of noise and vibration transmission paths on impulse response generated by bearing faults, an asymmetric bilateral exponential attenuation wavelet is constructed according to a vibration model of impulse response, which can be more flexible to match impulse features in vibration signals. Meanwhile, an adaptive correlation filtering method and a benchmark atom obtained by a standard K-SVD are utilized to determine optimal param-eters of the constructed wavelet, which is less disturbed by noise and harmonics. On this basis, by introducing a priori knowledge of an impulse period, a method of constructing a period-assisted parameterized wavelet dictionary is proposed to get a dictionary that is suitable to characterize periodic transient features. Finally, a periodic transient signal is recovered using the constructed dictionary and the orthogonal matching pursuit (OMP) algorithm. Comparisons with the K-SVD, a sparse representation method based on a db8 wavelet dictionary, spectral correlation and spectral kurtosis demonstrate that the proposed method can more accurately extract periodic transient features in simulated and experimental vibration signals, which provides an effective analysis tool for rolling bearing fault detection.