混沌干扰中基于同步挤压小波变换的谐波信号提取方法

Harmonic signal extraction from chaotic interference based on synchrosqueezed wavelet transform

针对混沌干扰背景下多个谐波信号的提取问题,提出了一种基于同步挤压小波变换(SST)的谐波信号抽取方法.首先利用SST将混沌信号和谐波信号组成的混合信号分解为不同的内蕴模态类函数,然后利用Hilbert变换对分离出的内蕴模态类函数进行频率识别,从中分离出各谐波信号.以Duffing混沌背景为例,对混沌干扰下多谐波信号的提取进行了实验分析.实验结果表明:对于不同频率间隔的多个谐波分量,本文方法的提取结果都具有较高的精度,而且所提方法对高斯白噪声的干扰具有较好的鲁棒性,综合提取效果优于经典的经验模态分解方法.

Extracting the harmonic signal from the chaotic interference background is very important for theory and practical application. The wavelet transform and empirical mode decomposition （EMD） have been widely applied to harmonic extraction from chaotic interference, but because the wavelet and EMD both present the mode mixing and are sensitive to noise, the harmonic signal often cannot be precisely separated out. The synchrosqueezing wavelet transform （SST） is based on the continuous wavelet transform, through compressing the time-frequency map of wavelet transform in the frequency domain, the highly accurate time-frequency curve is obtained. The time-frequency curve of SST which does not exist between cross terms, can better improve the mode mixing. The SST has also good robustness against noise. When the signal is a mixed strong noise, the SST can still obtain the clear time-frequency curve and approximate invariant decomposition results. In this paper, the SST is applied to the multiple harmonic signal extraction from chaotic interference background, and a new harmonic extracting method is proposed based on the SST. First, the signal obtained by mixing chaotic and harmonic signals is decomposed into intrinsic mode type function （IMTF） by the SST. Then using the Hilbert transform the frequency of each IMTF is analyzed, and the harmonic signals are separated from the mixed signal. Selecting the Duffing signal as the chaotic interference signal, the extracting ability of the proposed method for multiple harmonic signals is analyzed. The different harmonic extraction experiments are conducted by using the proposed SST method for different frequency intervals and different noise intensity multiple harmonic signals. And the experimental results are compared with those from the classical EMD method. When the chaotic interference signal is not contained by noise, the harmonic signal extraction effect is seriously affected by the frequency interval between harmonic signals. If the harmonic frequency interval between harmonic signals is relatively narrow, each harmonic signal cannot be accurately extracted by the EMD method. However, the harmonic extraction precision of SST method is not seriously influenced by the change of harmonic frequency interval, and when the frequency interval between harmonic signals is small the SST method can still accurately extract each harmonic signal from chaotic interference. When the noise contains a chaotic interference signal, the harmonic extraction effect of EMD method significantly decreases with noise intensity increasing. When the noise level reaches 80%, the extracted harmonic signal from the EMD method is seriously distorted, the correlation coefficient of the extracted harmonic signal with original harmonic signal is only about 0.6. With the increase Of noise intensity, the harmonic extraction effect of SST method has also a declining trend. But as the noise intensity is within 120%, the harmonic extraction effect of SST method does not greatly change and the extracted harmonic signal precision is still higher, which shows that the harmonic extraction method based on the SST has good robustness against noise. The comprehensive experimental results show that the proposed SST method has high extracting precision for multiple harmonic signals of different frequency intervals, and the SST method has better robustness against Gauss white noise. The extracted results of harmonic signal are better than those from the classical empirical mode decomposition method.