基于RPCA低秩稀疏分解的循环频率检测方法

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摘要在强噪声干扰时循环频率的准确检测对于循环平稳信号处理有重要意义。本文提出了一种低信噪比（Signal-to-Noise Ratio, SNR）下将基于鲁棒主成分分析（Robust Principal Component Analysis, RPCA）的低秩稀疏分解技术应用于循环谱密度（Cyclic Spectral Density, CSD）矩阵，从而进行循环频率检测的新方法。首先，采用RPCA将循环谱密度矩阵分解为表示噪声干扰的低秩矩阵和表示循环平稳特征的稀疏矩阵。随后，利用稀疏矩阵构造检测函数实现循环频率的自动检测。仿真结果证明了该方法在强噪声干扰下检测概率方面的优越性，并可根据检测各阶循环频率谐波的受试者工作特征（Receiver Operating Characteristic, ROC）曲线为不同信噪比条件下选择检测阶数提供参考。为了进一步验证该方法在应用中的有效性，将该方法应用于滚动轴承的早期故障诊断中。滚动轴承加速疲劳寿命试验数据上的分析结果证明该方法能够在轴承早期故障阶段从低SNR的振动信号中准确检测出轴承的故障特征频率，实现轴承的早期故障诊断。

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	王冉1
	余龙靖1
	余亮2
	蒋伟康2

关键词 ：循环频率检测, 鲁棒主成分分析（Robust Principal Component Analysis, RPCA）, 低秩稀疏分解, 循环谱密度（Cyclic Spectral Density, CSD）, 滚动轴承故障诊断

Abstract：The accurate detection of cyclic frequency under strong noise interference is of great significance for cyclostationary signal processing. This paper proposes a new method of low-rank sparse decomposition technology based on Robust Principal Component Analysis (RPCA) applied to cyclic spectral density (CSD) matrix under low signal-to-noise ratio (SNR) to detect cyclic frequency. Firstly, RPCA is used to decompose the cyclic spectral density matrix into a low noise matrix representing noise interference and a sparse matrix representing cyclostationary characteristics. Subsequently, the sparse matrix is used to construct the detection function to realize the automatic detection of the cyclic frequency. The simulation results prove the superiority of the method in terms of detection probability under strong noise interference, and can provide the detection order for different signal-to-noise ratio conditions according to the receiver operating characteristic (ROC) curve of the detection of each order of cycle frequency harmonics. reference. In order to further verify the effectiveness of this method in application, this method is applied to the early fault diagnosis of rolling bearings. The analysis results on the accelerated fatigue life test data of rolling bearings prove that the method can accurately detect the characteristic frequency of the bearing fault from the low SNR vibration signal in the early stage of bearing failure, and realize the early fault diagnosis of the bearing.

收稿日期: 2021-10-27 出版日期: 2023-02-28

引用本文:

王冉1，余龙靖1，余亮2，蒋伟康2. 基于RPCA低秩稀疏分解的循环频率检测方法[J]. 振动与冲击, 2023, 42(4): 88-94.
WANG Ran1，YU Longjing1，YU Liang2，JIANG Weikang2. A cyclic frequency detection method based on RPCA low-rank sparse decomposition. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(4): 88-94.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2023/V42/I4/88

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