电子学报 ›› 2017, Vol. 45 ›› Issue (8): 2008-2018.DOI: 10.3969/j.issn.0372-2112.2017.08.029

• 学术论文 • 上一篇    下一篇

非零奇异值和频率的关系及其在信号分解中的应用

赵学智, 叶邦彦   

  1. 华南理工大学机械与汽车工程学院, 广东广州 510640
  • 收稿日期:2016-01-12 修回日期:2017-01-08 出版日期:2017-08-25 发布日期:2017-08-25
  • 作者简介:赵学智,男,1970年出生于湖南邵东,博士,华南理工大学机械与汽车工程学院教授、博士生导师,主要从事信号处理、奇异值分解理论与算法、模式识别和故障诊断等方面的研究.E-mail:mezhaoxz@scut.edu.cn;叶邦彦,男,1949年出生于广东广州,博士,华南理工大学机械与汽车工程学院教授、博士生导师,中国图像图形学会高级会员、中国机械工程学会高级会员、全国高等学校制造自动化研究会常务理事兼中南分会理事长.主要从事制造过程状态监测、图像处理、机器视觉、计算机检测与控制等方面的研究工作.
  • 基金资助:
    国家自然科学基金(No.51375178);广东省自然科学基金(No.S2012010008789)

The Relationship Between Non-Zero Singular Values and Frequencies and Its Application to Signal Decomposition

ZHAO Xue-zhi, YE Bang-yan   

  1. School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, Guangdong 510640, China
  • Received:2016-01-12 Revised:2017-01-08 Online:2017-08-25 Published:2017-08-25

摘要: 研究了Hankel矩阵方式下确定性信号的非零奇异值和信号所含频率数量之间的关系,发现只要矩阵维数大于信号中频率数量的二倍,此后不管维数再怎样增大,非零奇异值的数目始终维持为信号中频率数量的两倍不变.研究了非零奇异值和单个频率之间存在的对应关系,提出利用奇异值分解来分离单个的频率成分,发现了奇异值分解分离单个频率成分的条件,在这种条件下奇异值分解可以准确地分离出任何的单个频率成分.利用奇异值分解的这一特性对轴承振动信号进行特征提取,分离出了轴承各个振动频率清晰的时域波形,由此准确地揭示了轴承的实际振动状态.

关键词: 奇异值分解, 非零奇异值, 信号分解, 矩阵维数

Abstract: The relationship between the number of non-zero singular values of the deterministic signal under the Hankel matrix and the number of frequencies in this signal is studied.It is found that if the dimension of matrix is larger than two times the number of frequencies,then no matter how much the dimension of matrix is increased,the number of non-zero singular values is always twice as much as the number of frequencies.The corresponding relationship between the non-zero singular values and single frequency component is studied,and singular value decomposition (SVD) is proposed to separate the single frequency component.The condition under which SVD separates the single frequency component is found,and SVD can accurately separate any single frequency component under this condition.This property of SVD is applied to the feature extraction of the bearing vibration signal,the time domain waveform of each vibration frequency is accurately extracted and the bearing vibration status is accurately revealed.

Key words: singular value decomposition, non-zero singular value, signal decomposition, matrix dimension

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