The automatic selection of an optimal wavelet filter and its enhancement by the new sparsogram for bearing fault detection: Part 2 of the two related manuscripts that have a joint title as "Two automatic vibration-based fault diagnostic methods using the novel sparsity measurement-Parts 1 and 2"

Rolling element bearings are the most important components used in machinery. Bearing faults, once they have developed, quickly become severe and can result in fatal breakdowns. Envelope spectrum analysis is one effective approach to detect early bearing faults through the identification of bearing fault characteristic frequencies (BFCFs). To achieve this, it is necessary to find a band-pass filter to retain a resonant frequency band for the enhancement of weak bearing fault signatures. In Part 1 paper, the wavelet packet filters with fixed center frequencies and bandwidths used in a sparsogram may not cover a whole bearing resonant frequency band. Besides, a bearing resonant frequency band may be split into two adjacent imperfect orthogonal frequency bands, which reduce the bearing fault features. Considering the above two reasons, a sparsity measurement based optimal wavelet filter is required to be designed for providing more flexible center frequency and bandwidth for covering a bearing resonant frequency band. Part 2 paper presents an automatic selection process for finding the optimal complex Morlet wavelet filter with the help of genetic algorithm that maximizes the sparsity measurement value. Then, the modulus of the wavelet coefficients obtained by the optimal wavelet filter is used to extract the envelope. Finally, a non-linear function is introduced to enhance the visual inspection ability of BFCFs. The convergence of the optimal filter is fastened by the center frequencies and bandwidths of the optimal wavelet packet nodes established by the new sparsogram. Previous case studies including a simulated bearing fault signal and real bearing fault signals were used to show that the effectiveness of the optimal wavelet filtering method in detecting bearing faults. Finally, the results obtained from comparison studies are presented to verify that the proposed method is superior to the other three popular methods. (C) 2013 Elsevier Ltd. All rights reserved.