非零奇异值数量的理论分析及其在滑动轴承-转子振动特征提取应用

实验分析了Hankel矩阵下非零奇异值数目与信号中的频率个数成两倍的数量关系,验证了奇异值成对出现规律,当构造的m×n的Hankel矩阵行数与列数充分接近时,信号中同一频率下的两个非零奇异值会紧密排列在一起。根据Hankel矩阵的构造方式,从理论上证明了非零奇异值与频率之间的数量关系规律:对于一个含有固定频率数目的确定性信号,利用其构造m×n的Hankel矩阵,当矩阵维数大于信号中频率个数的两倍之后,非零奇异值数目始终是与频率个数成2倍的数量关系,且非零奇异值数目是与幅值和相位无关的。将Hankel矩阵下非零奇异值的这一规律应用于旋转机械中的滑动轴承-转子振动信号的特征提取,实现了对转子不对中故障轴心轨迹的准确提纯。

Theoretical analysis for number of non-zero singular values and its application in vibration feature extraction of a sliding bearing-rotor system

Here, firstly the quantitative relation that the number of non-zero singular values of Hankel matrix is 2 times of the number of frequencies in a signal was analyzed with tests. It was shown that the law that singular values appear in pairs is verified;when the number of rows and that of columns in a m×n Hankel matrix are sufficiently close, two non-zero singular values corresponding to one frequency in a signal are closely spaced;according to the construction mode of Hankel matrix, the quantitative relation between its non-zero singular values and frequencies in a signal is theoretically proved, this relation is that using a deterministic signal with a fixed number of frequencies, a m×n Hankel matrix is constructed, after the matrix’s dimensions are more than twice the number of frequencies in the signal, the number of non-zero singular values is always 2 times of the number of frequencies, the former is unrelated to the signal’s amplitude and phase. This relation law was applied in vibration feature extraction for a sliding bearing-rotor system to realize correct extraction of a rotor axial center’s misalignment fault trajectory.