基于主成分分析的特征频率提取算法及应用  

Feature Frequency Extraction Algorithm Based on Principal Component Analysis and Its Application

作　　者：李振 李伟光[1] 赵学智[1] 郑相立 

机构地区：[1]华南理工大学机械与汽车工程学院,广州510640

出　　处：《振动．测试与诊断》2018年第4期834-842,共9页Journal of Vibration,Measurement & Diagnosis

基　　金：国家高技术研究发展计划("八六三"计划)资助项目(2015AA043005);国家自然科学基金资助项目(51375178)

摘　　要：通过研究主成分分析(principal component analysis,简称PCA)中有效特征值与信号频率和幅值之间的关系,发现有效特征值的数量是由原始信号中频率成分的个数决定,与幅值、频率和相位的大小无关。信号中每个频率产生两个有效的特征值,且幅值决定协方差矩阵C的特征值在其分布图中的排列顺序。提出了一种基于PCA的特征频率提取算法,该算法可实现对单个或多个特征频率的准确提取。将此方法应用于大型转子系统轴心轨迹的提纯上,效果优于谐波小波和小波包算法。The relationship among the effective eigenvalue,the frequency and its amplitude in principal component analysis(PCA)is studied.It is found that the number of valid eigenvalues,which are irrelevant size of the amplitude,phase and frequency of the signal,are determined by the number of signal frequency components.The sequence of the eigenvalues in the covariance matrix Ccharacteristic distribution chart depend on the amplitude of the signal frequency.Each characteristic frequency in the signal produces two valid eigenvalues.A new characteristic frequency separation method is proposed,based on the above-mentioned discoveries of PCA theory.This method can be well applied to filter the single frequency and extract the characteristic frequency,which is used in the application to purify the axis orbit of the large rotor vibration test bed.The simulation and experimental results manifest that the proposed algorithm has advantages in feature frequency extraction.

关 键 词：故障诊断 信号分析 主成分分析 特征提取 轴心轨迹 

分 类 号：TH113.1[机械工程—机械设计及理论] TH165.3