基于SVD差分谱和IMF能量谱的改进HHT方法

针对随机噪声和虚假IMF会导致改进HHT中EEMD分解质量下降和Hilbert谱混乱,提出了一种基于SVD差分谱降噪预处理和IMF能量谱剔除虚假分量的改进HHT.该方法首先对原始信号进行SVD降噪,通过基本不等式原理来确定相空间重组的最佳Hankel矩阵结构,利用奇异值差分谱来确定有效奇异值的阶次;然后对消噪的信号进行EEMD分解,通过IMF能量谱来去除虚假分量;最后对主IMF进行Hilbert谱分析.仿真和实验结果表明,SVD能提高信噪比,抑制噪声对EEMD分解精度的干扰;能量谱能有效地消除虚假IMF对Hilbert谱分析的影响;Hilbert谱中各频率成分清晰,解决了随机噪声和虚假分量对传统改进HHT的不良影响.

Improved HHT Method based on SVD Difference Spectrumand IMF Energy Spectrum

For the phenomenon of random noise and false intrinsic mode function (IMF) decline the quality of ensemble empirical mode decomposition (EEMD) and disrupt the Hilbert spectrum. An improved HHT method is presented based on singular value decomposition (SVD) difference spectrum to de-noise and IMF energy spectrum to remove the false IMFs. Firstly, the original signals are de-noised by SVD which the best Hankel matrix structure is determined by the basic principle of inequality and difference spectrum is used to determine the valid order of singular values. Secondly, de-noised signals are decomposed through EEMD and IMF energy spectrum is used to remove the false component. Finally, the main IMFs are analyzed by the Hilbert spectrum. Simulation and experimental results show that SVD can improve signal to noise ratio and depress the noise impact of the accuracy of EEMD; Energy entropy spectrum can effectively remove the false IMF. The each frequency of Hilbert spectrum is clear and the problem that random noise and false component interfere improved HHT has been solved.