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。
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.
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
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参考文献
[1] J. Antoni. Cyclostationarity by examples[J]. Mechanical Systems & Signal Processing, 2009, 23(4):987-1036.
[2] J. Antoni, F. Bonnardot, et. al. Cyclostationary modelling of rotating machine vibration signals[J]. Mechanical Systems and Signal Processing,2004,18(6).
[3] 明阳,陈进,董广明.基于循环维纳滤波器和包络谱的轴承故障诊断[J].振动工程学报,2010,23(05):537-540.
Y. Ming , J. Chen , G. Dong. Bearing fault diagnosis based on cyclic Wiener filter and envelope spectrum[J].Chinese Journal of Vibration Engineering,2010,23(05):537-540.
[4] D. Abboud, J. Antoni, et al. Angle/time cyclo-stationarity for the analysis of rolling element bearing vibrations[J]. Measurement,2015,75.
[5] Z. Chen , A. Mauricio , W. Li , et al. A Deep Learning method for bearing fault diagnosis based on Cyclic Spectral Coherence and Convolutional Neural Networks [J]. Mechanical Systems and Signal Processing, 2020, 140.
[6] R. Sun, F. Du , et al. Cyclostationary Analysis of Irregular Statistical Cyclicity and Extraction of Rotating Speed for Bearing Diagnostics with Speed Fluctuations[J]. IEEE Transactions on Instrumentation and Measurement, 2021,(70):1-11.
[7] F. Umut, A. Tayfun. Compressive Sensing for Detecting Ships with Second-Order Cyclostationary Signatures[J]. IEEE Journal of Oceanic Engineering,2018, 43(4).
[8] J. Antoni , D. Hanson . Detection of Surface Ships From Interception of Cyclostationary Signature With the Cyclic Modulation Coherence[J]. IEEE Journal of Oceanic Engineering, 2012, 37(3):478-493.
[9] S. Li , C. Ning , Y. Peng , et al. Cyclostationary approach to detect flow-induced effects on vibration signals from centrifugal pumps[J]. Mechanical Systems and Signal Processing, 2019, 114(1):275-289.
[10] CANDèS E J , LI X , MA Y , et al. Robust principal component analysis [J]. Journal of the ACM (JACM), 2011, 58(3):1–37.
[11] L. Yu , J. Antoni, Q. Leclere . Spectral matrix completion by Cyclic Projection and application to sound source reconstruction from non-synchronous measurements[J]. Journal of Sound & Vibration, 2016:31-49.
[12] Yl A , Li L B , Yu Z B , et al. Nonconvex nonsmooth low-rank minimization for generalized image compressed sensing via group sparse representation[J]. Journal of the Franklin Institute, 2020, 357(10):6370-6405.
[13] Huang S , Yu L , Jiang W. Water entry sound detection in strong noise by using the spectrogram matrix decomposition method[J]. Applied Acoustics, 2020, 161:107171.
[14] YU L , HUANG S , JIANG W. Sparse Time–Frequency Representation for the Transient Signal Based on Low-Rank and Sparse Decomposition [J]. Journal of Acoustics, 2019, 1:1
[15] Du J , Huang H , Jiang W, et al. Cyclostationary feature based spectrum sensing via low-rank and sparse decomposition in cognitive radio networks [C] 16th International Symposium on Communications and Information Technologies (ISCIT). IEEE, 2016,1:615-619.
[16] Antoni J , Randall R B . The spectral kurtosis: application to the vibratory surveillance and diagnostics of rotating machines[J]. Mechanical Systems & Signal Processing, 2006, 20(2):308-331.
[17] 丁康, 黄志东, 林慧斌. 一种谱峭度和Morlet小波的滚动轴承微弱故障诊断方法[J]. 振动工程学报, 2014, 27(001):128-135.
K. Ding, Z. Huang, H. Lin. A method for diagnosing weak faults of roller bearings based on spectral kurtosis and Morlet wavelet. Chinese Journal of Vibration Engineering, 2014, 27 (001): 128-135.
[18] 张坤,胥永刚,马朝永等.经验快速谱峭度及其在滚动轴承故障诊断中的应用[J].振动工程学报,2020, 33(03):636-642.
K. Zhang, Y. Xu, C. Ma, et al Empirical rapid spectral kurtosis and its application. Chinese Journal of Vibration Engineering, 2020, 33 (03): 636-642.
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