一种基于小波变换与奇异值分解对振动系统模态频率进行识别的新方法

针对从受噪声污染的脉冲响应信号和快速正弦扫频响应信号中识别振动系统的单模态和密集多模态的频率问题，将小波变换与奇异值分解（SVD）滤波相结合，利用基于小波变换的能量分布函数，为了提高对密集模态和含有噪声信号的识别效果，对该能量分布函数求n次方，再进行奇异值分解后，根据奇异值，求出主要分量，然后通过主要分量对应的n次方尺度图或频率计算公式，识别出模态的频率。仿真结果证明了该方法的有效性和可行性。

A New Method for Identifying Modal Frequencies of Vibration Systems with Wavelet Transform and SVD

In order to identify single mode and closing modal frequencies of vibration systems by impulse response and quick sinusoidal sweep response polluted by serious noise,wavelet transform is combined with singular value decomposition(SVD) filtering.Firstly,in order to improve identification precision of closing modes and signal with noise,the nth power of a energy distribution function based-on wavelet transform is used in SVD,then primary components are extracted on the basis of weights,finally modal frequencies are identified according to the nth power of the scalograms of the primary components or the frequency formula.Simulation results show that the method is feasible and effective.