Fractal geometry of wavelet decomposition in mechanical signature analysis

Abstract Multiple modes of vibration are usually incorporated in a single record of vibration measurement in condition monitoring of rotating machinery. Wavelet transform is an effective tool to detect and isolate transient fault features from other interfering modes. The conventional dyadic wavelet transform decomposes the signal into wavelet subspaces with distinct central frequencies and specific frequency bandwidths. In this paper, we propose a novel theory of centralized multiresolution analysis (CMR) and reveal the implicit fractal geometry properties in CMR. A concept of nested centralized wavelet packet space (NCWPS) is introduced to describe the self-similarity phenomenon in CMR. Within the theoretical framework, the classical dyadic wavelet packet is assimilated as a subordinated proper-subset of the augmented NCWPS. Moreover, the generalized CMR characterized by tunable and flexible frequency-scale topology configuration is established using harmonic wavelet transform. The CMR can be regarded as an improved transient signature dictionary. Therefore, the CMR is combined with an improved stationary signature dictionary to ensure enhanced performance in fault feature extraction in multiple modes coupled vibration measurements. The effectiveness of the proposed method is validated using numerical simulations, a rub-impact experiment, and a case study of vibration signal analysis in steel making industry.