频率添加奇异值分解算法及其在故障特征提取中的应用

Frequency Adding Singular Value Decomposition Algorithm and Its Application in Fault Feature Extraction

针对奇异值分解(Singular value decomposition, SVD)的频率分离问题,研究了SVD对单个频率的分离条件,发现SVD分离单个频率的效果取决于各频率的幅值差异。若不同频率的幅值很接近,则SVD就不能分离这些频率,由此提出一种频率添加SVD算法。为了提取原信号中的特征频率,先对原信号添加该频率的理想正弦信号,使原信号中该频率成分和其他频率的幅值产生差异,从而实现对该频率成分的提取,从理论上证明此算法的可行性。仿真信号处理实例表明,即使对于频率值非常接近的两个频率,频率添加SVD算法亦可将它们准确分离,分离结果波形误差小,克服了原来SVD频率分离算法的缺陷。将此算法应用某转子系统的振动特征提取,准确地提取到振动的高阶倍频,发现高阶倍频振幅的周期性波动特征,并分析这种振幅周期性波动的原因。

For the frequency separation of singular value decomposition(SVD), the separation condition of SVD for single frequency is studied. It is found that the effect of SVD to separate a single frequency depends on the amplitude difference of the frequencies. If the amplitudes of different frequencies are very close, then SVD cannot separate these frequencies. Based on this characteristic, a frequency adding SVD algorithm is proposed. In order to extract the feature frequency of the original signal, the ideal sinusoidal signal of this frequency is added to the original signal, which makes the amplitude of this feature frequency different from the ones of other frequencies, so that this frequency can be separated by SVD. The feasibility of frequency adding SVD is proved theoretically. The simulation signal example shows that for the frequencies with very close frequency values, the frequency adding SVD algorithm can also separate them accurately, and the defects of the traditional SVD frequency separation algorithm is overcome. Finally, this algorithm is applied to extract the vibration features of a rotor system and the high-order harmonics of the vibration signal are extracted separately, which reveal the periodic fluctuation characteristic of the amplitudes of high-order harmonics, and the cause of periodic fluctuation of the amplitudes is analyzed.