机械故障特征提取的拓扑集分形稀疏字典

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摘要多尺度字典是实现机械动态信号中频域弱相干成分解耦的重要方法，但目前还欠缺围绕固定频率进行分辨率持续细化的系统性理论。基于近似解析小波变换构建了全新的拓扑集分形多分辨理论。提出了中心嵌套子空间簇，它随分析尺度深化实现了机械故障特征多目标同时追踪细化，在频域上表现为围绕一系列固定中心频率进行严格的二进细化。在数学上严格证明了：①任意中心嵌套子空间簇都是动态信号频域的拓扑空间; ②各中心嵌套子空间簇按分析尺度具有严格自相似的分形特性。另外研究还揭示了二进制多分辨理论与拓扑集分形的深刻同构关联，即任意二进小波包唯一从属于某个中心嵌套子空间簇。其次，在扩展中心嵌套子空间诱导下，经典小波包变换可以化归成拓扑集分形的真子集。将拓扑集分形与旋转机械部件损伤动态模型结合提出了一种新的机械故障特征提取方法。该方法通过周期性成分稀疏测度优化和中心嵌套子空间搜索对冲击性机械故障特征的周期、瞬时动力学参数进行优化提取, 从而提取物理意义更显著的单分量信息。将该方法应用于滚动轴承的故障诊断中，在含强噪声的振动信号中准确提取了表征轴承外圈剥落的多个单一模式分量。通过对比验证了所提出方法的噪声抑制能力显著优于以谱峭度和群组稀疏优化为代表的对主流机械故障特征提取技术。

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	曹新城1
	陈彬强1
	姚斌1
	贺王鹏2

关键词 ：机械故障诊断, 拓扑集分形理论, 多分辨分析, 中心嵌套子空间簇, 滚动轴承

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.

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

收稿日期: 2018-05-28 出版日期: 2020-03-15

引用本文:

曹新城1，陈彬强1，姚斌1，贺王鹏2. 机械故障特征提取的拓扑集分形稀疏字典[J]. 振动与冲击, 2020, 39(6): 210-219.
CAO Xincheng1,CHEN Binqiang1,YAO Bin1,HE Wangpeng2. Sparsity promoted dictionary using topological fractal multi-resolution and its applications in mechanical fault detection. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(6): 210-219.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I6/210

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