Novel ensemble analytic discrete framelet expansion for machinery fault diagnosis1

As the celebrated "mathematical scope", the multi-resolution analyzing capacity of wavelet transform (WT) plays an important role in condition monitoring and fault diagnosis of mechanical equipment. However, it has proven that the effectiveness of WT is hampered by several negative factors, such as shift-sensitiveness, significant energy leakage, and the fixed dyadic "frequency-sale" paving. Especially, the dyadic "frequency-sale" paving creates inevitable deficiency in identifying mechanical signatures located in transition areas of adjacent wavelet scales. A novel "time-sale" analysis methodology, named as derived ensemble analytic framelet (DEAF), based on overcomplete wavelet tight frame, is proposed. The DEAF is developed based on the existing dual tree complex wavelet transform (DTCWT). The DEAF starts from a selected DTCWT basis, and combines it with a hybrid augmented tree-structured filter-bank, which results in quasi analytic wavelet packet decomposition (QAWPD). With the results of QAWPT, an ensemble wavelet packet generating strategy is applied such that an unprecedented implicit wavelet packet tight frame (IWPTF) containing pseudo dyadic wavelet packets is obtained. With the combination of QAWPD and IWPTF, the proposed DEAF can be derived which possesses the "frequency-sale" paving characterized by continued time-frequency refinement of analysis centers. The proposed technique is applied to the mechanical signature analysis of an engineering application to validate its superiority compared with the existing methods.