基于支持矢量回归机的Hilbert-Huang变换端点效应问题的处理方法

Hilbert-Huang变换的端点效应表现在两个方面,对信号进行经验模态分解(Empirical mode decomposition, EMD)和对各个内禀模态函数(Intrinsic mode function,IMF)进行Hilbert变换时都会产生端点效应。为了克服 Hilbert-Huang变换中的端点效应,采用支持矢量回归机对信号延拓后再进行经验模态分解,该方法可以有效地克服EMD方法的端点效应问题,得到具有物理意义的内禀模态函数;然后再次采用支持矢量回归机对IMF分量进行延拓后进行Hilbert变换,可有效地抑制Hilbert变换中的端点效应,获得准确的瞬时频率和瞬时幅值,从而得到具有物理意义的Hilbert谱。对仿真和实际信号的分析结果表明,基于支持矢量回归机的数据序列延拓方法能有效地解决Hilbert-Huang变换中存在的端点效应问题,而且其效果优于基于神经网络的数据序列延拓方法。

PROCESS METHOD FOR END EFFECTS OF HILBERT-HUANG TRANSFORM BASED ON SUPPORT VECTOR REGRESSION MACHINES

The end effects of Hilbert-Huang transform are shown in two aspects. On one hand, the end effects are produced when the signal is decomposed by empirical mode de- composition (EMD) method; on the other hand, the end effects are produced too when the Hilbert transforms are applied to the intrinsic mode functions (IMFs). To overcome the end effects of Hilbert-Huang transform, the support vector regression machines are used to predict the signal before the signal is decomposed by EMD (Empirical Mode Decomposition), thus the end effects could be overcome effectively and the IMFs (Intrinsic Mode Functions) with physical sense could be obtained. After that, to restrain the end effects of Hilbert transform, the support vector regression machines are used again to predict the IMFs before the Hilbert transform of the IMFs, therefore, the accurate instantaneous frequencies and instantaneous amplitudes could be obtained and the Hilbert spectrum with physical sense could be acquired. The analysis results from the simulated and practical signals demonstrate that the end effects of Hilbert-Huang transform could be resolved effectively by the time series forecasting method based on support vector regression machines which is superior to the time series forecasting method based on neural networks.