Fractal Lifting Wavelets for Machine Fault Diagnosis

Fault diagnosis is of vital importance in safety and reliable operations of modern electromechanical systems. Advanced signal processing techniques are indispensable for extracting incipient features from measured dynamical signals. For discrete wavelet analysis, shift-invariance and proper frequency-scale configuration are both necessary for effective investigation of incipient fault features. In this paper, a novel fractal lifting scheme is proposed based on redundant second generation wavelet packet decomposition (RSGWPD). Implicit wavelet packets (IWPs), generated via fractal lifting scheme, can realize a novel centralized multiresolution. It is demonstrated that each IWP inherits the property of exact shift-invariance originated from redundant lifting scheme. In addition, a novel concept of nested centralized wavelet packet cluster is introduced for explaining merits provided by sets composed of IWPs. The numerical simulations were employed to validate the benefits of exact shift-invariance in a multiscale analysis of discrete time series. RSGWPD and IWPs are combined to conduct multiscale expansion of vibration measurement. To further explore optimal features, an indicator of spatial-spectral ensemble kurtosis is utilized to select optimal analysis parameters. The proposed technique was successfully applied to case studies of gearbox fault diagnosis as well as bearing fault diagnosis. The comparisons were made between results by the proposed technique and those provided by some other mainstream adaptive signal decomposition methodologies. It is verified that the combination of exact shift-invariance and centralized multiresolution significantly enhances the performance of incipient fault feature extraction of nonstationary vibration signals.