The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
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DOI：
10.1098/rspa.1998.0193
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发表时间：
1998-03-08
影响因子：
3.5
通讯作者：
Liu, HH
中科院分区：
文献类型：
--
作者：
Huang, NE;Shen, Z;Liu, HH
本文提出了一种分析非线性、非平稳数据的新方法。该方法的关键部分是“经验模式分解”方法，任何复杂的数据集可以被分解成一个有限的，往往是少数的“固有模式函数”，承认良好的希尔伯特变换。这种分解方法是自适应的，因此是高效的。由于分解是基于数据的局部特征时间尺度，因此它适用于非线性和非平稳过程。通过希尔伯特变换，“隐式模态函数”产生瞬时频率作为时间的函数，从而给出嵌入结构的清晰识别。结果的最终表示是能量-频率-时间分布，称为希尔伯特谱。在这种方法中，主要的概念创新是引入基于信号的局部特性的“固有模式函数”，这使得瞬时频率有意义;以及引入复杂数据集的瞬时频率，这消除了对杂散谐波的需要，以表示非线性和非平稳信号。经典非线性方程组的数值结果和代表自然现象的数据的例子来证明这种新方法的权力。经典的非线性系统的数据是特别有趣的，因为它们用来说明所发挥的作用的非线性和非平稳效应的能量-频率-时间分布。
A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the 'empirical mode decomposition' method with which any complicated data set can be decomposed into a finite and often small number of 'intrinsic mode functions' that admit well-behaved Hilbert transforms. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and non-stationary processes. With the Hilbert transform, the 'instrinic mode functions' yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert spectrum. In this method, the main conceptual innovations are the introduction of 'intrinsic mode functions' based on local properties of the signal, which makes the instantaneous frequency meaningful; and the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need for spurious harmonics to represent nonlinear and non-stationary signals. Examples from the numerical results of the classical nonlinear equation systems and data representing natural phenomena are given to demonstrate the power of this new method. Classical nonlinear system data are especially interesting, for they serve to illustrate the roles played by the nonlinear and non-stationary effects in the energy-frequency-time distribution.