Sparsity promoted dictionary using topological fractal multi-resolution and its applications in mechanical fault detection

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (6) : 210-219.

CAO Xincheng1,CHEN Binqiang1,YAO Bin1,HE Wangpeng2

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Abstract

Multiresolution dictionary is an important tool to decouple the multitude of vibration modes with weak spectral coherence in vibration measurement.However, there is lack of systematic theory that enables continuous spectral refinements around fixed analyzing center.To address this problem, a novel theory of topology fractal multi-resolution (TFMR) was proposed based on the nearly analytic wavelet theory.With the concept of nested centralized wavelet packet space (NCWPS), the amazing capability of simultaneous multi-object tracking with respect to mechanical fault features was ensured.Mathematically, it is proved that: ① Any NCWPS is a topology space of the original spectral domain; ② All NCWPSs share the self-similar fractal property.The research reveals the important intrinsic relation between the classical dyadic multiresolution and TFMR, that is, any dyadic wavelet packet uniquely belongs to a NCWPS.In the sense of augmented NCWPS, the wavelet packet space is regarded as a subset to the theory of TFMR.Combining the technique of TFMR with the component damage model, a novel sparsity promoted learning dictionary for repetitive transient features due to mechanical damages was proposed.The algorithm has been applied to analyze signals from the mechanical system with rub-impact fault, and the periodic impact features in the form of mono-component were successfully extracted in the presence of strong background noises.Compared to the methods represented by fast kurtogram and periodic group sparse optimization, the enhanced noise resistibility of the proposed method was validated.

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mechanical fault diagnosis / topology fractal theory / multiresolution analysis / nested centralized wavelet space cluster / roller element bearing

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CAO Xincheng1,CHEN Binqiang1,YAO Bin1,HE Wangpeng2. Sparsity promoted dictionary using topological fractal multi-resolution and its applications in mechanical fault detection[J]. Journal of Vibration and Shock, 2020, 39(6): 210-219

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