关键词: 主成分分析, 特征频率提取算法, 奇异值分解, 协方差矩阵特征值, 矩阵奇异值

Abstract: A PCA feature frequency extraction algorithm based on SVD principle was proposed to solve the noise pollution problem in the measured displacement signal of rotor． Firstly，the intrinsic relationship between PCA and SVD was deduced theoretically． That is，the eigenvalue of the covariance matrix generated by PCA was equal to the square of the singular value of the matrix generated by SVD，and the eigenvector generated by PCA was equal to the left singular vector generated by SVD． Then，based on the above conclusions，a PCA feature frequency ex- traction algorithm based on SVD principle was proposed，and the effectiveness of the algorithm was verified by simu- lation signals． Finally，the algorithm was applied to purify axis orbits of the rotor of a large sliding bearing test bed． The axis orbits are clear and concentrated，the misalignment and friction faults were identified successfully．

Key words: principal component analysis ( PCA), feature frequency extraction algorithm, singular value decom- position ( SVD), eigenvalues of covariance matrix, singular values of Hankel matrix