Sparsity Enhanced Topological Fractal Decomposition for Smart Machinery Fault Diagnosis

Automatic fault feature extraction-based smart fault diagnosis is becoming more and more popular, as it does not require excessive expertise of on-site staff. Advanced signal processing techniques are of significant importance in order to ensure efficient and effective fault feature analysis. Multi-resolution analysis is an effective tool utilized to decouple multiple signal modes within the measured vibration signal. However, current multi-resolution analyzing methods still cannot enable continuous spectral refinements around fixed analyzing frequencies. To address this problem, a novel theory of topological fractal multi-resolution analysis (TFMRA) is proposed. With the concept of nested centralized wavelet packet cluster (NCWPC), TFMRA is equipped with the ability to extract multiple fault features simultaneously. Mathematically, we prove that: 1) each NCWPC is a topology subset of spectral domain of the investigated signal and 2) all sets of NCWPC share a common self-similar fractal property in geometry. This paper reveals an important intrinsic relation between classical dyadic multi-resolution analysis and TFMRA. That is, each dyadic wavelet packet can be uniquely associated with an NCWPC according to the definitions of TFMRA, and classical wavelet packet spaces are regarded as proper subsets of the proposed NCWPCs. Combining signal decomposition using TFMRA and damage information of a mechanical system, we propose an improved sparsity promoted vibration signature analyzing methodology to investigate repetitive transient fault features. This method was applied to extract abnormal vibration signatures from an experimental rotor test rig with rub-impact faults. Processing results demonstrate that nano-components of transient vibrations, which are produced by rub-impact faults, were successfully identified. These results are compared with those of some other comparison techniques based on sparse representation. It is verified that the proposed fault diagnosis method possesses more robust noise resisting capability.