一种基于样条插值的经验模态分解改进算法

Improving Empirical Mode Decomposition with Cubic Smoothing Spline Fitting

经验模态分解过程中经常由于信号采样率不足而产生伪固有模式函数(IMF),希尔伯特变换中也常出现无物理意义的负瞬时频率,就这两个问题进行研究后认为,HHT谱中产生负频率的主要原因是由于经验模态分解结果中的伪IMF所造成的,而伪IMF产生的原因主要是信号采样率不足引起的,并提出以HHT谱是否稳定来判断IMF的真伪。还针对信号采样率不足这一问题,提出了一种应用三次平滑样条拟合插值来加密信号采样点,进行信号重构的方法,算例表明:该重构方法可以有效消除分解过程中由于信号采样率不足而引起的包络线失真,从而可有效消除分解结果中的伪固有模式函数和HHT谱中的负频率。

Aim. Pseudo intrinsic mode often appears in the process of empirical mode decomposition （EMD） and negative instantaneous frequencies are also induced into the succeeding Hilbert-Huang Transform （HHT）. We aim to find what causes the appearance of these phenomena and then to propose a method for improving EMD, which can suppress these phenomena. In the full paper, we explain what we do in some detail. In this abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is： the effect of sampling rate on EMD results. Its two subtopics are： the effect of signal sampling rate on EMD and HHT transform （subtopicl. 1） and the analysis of reasons for the negative instantaneous frequencies in HHT spectra （subtopic1.2）. In subtopic 1.2, we explain that the negative instantaneous frequencies are caused by pseudo intrinsic modes because the signal sampling rate is too low. Thus a criterion to judge the pseudo intrinsic mode of EMD is proposed that, if the HHT spectrum is not stable or negative frequency appears, the corresponding mode is a pseudo intrinsic mode. The second topic is： the improvement of EMD through fitting with cubic smoothing spline. In this topic, we use the cubic smoothing spline fitting to interpolate and reconstruct the original signals to increase the nominal signal sampling rate. Also in this topic, numerical simulation results, given in Figs. 6 and 7 in the full paper, show preliminarily that the improved EMD can effectively avoid the distortion of the envelope curve induced by low sampling rate, thus eliminating pseudo intrinsic modes in EMD and negative instantaneous frequencies in HHT.