Abstract: 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.

Key words: singular value decomposition, frequency adding, amplitude difference, single frequency, feature extraction