The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
08 Mar 1998-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (The Royal Society)-Vol. 454, Iss: 1971, pp 903-995
TL;DR: In this paper, a new method for analysing nonlinear and nonstationary data has been developed, which is the key part of the method is the empirical mode decomposition method with which any complicated data set can be decoded.
Abstract: 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 dec...
Citations
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01 Oct 2014
TL;DR: A novel EMD-ENN approach, a hybrid of empirical mode decomposition and Elman neural network, is proposed to forecast wind speed, which shows that the proposed approach is suitable for wind speed prediction.
Abstract: Because of the chaotic nature and intrinsic complexity of wind speed, it is difficult to describe the moving tendency of wind speed and accurately forecast it. In our study, a novel EMD-ENN approach, a hybrid of empirical mode decomposition (EMD) and Elman neural network (ENN), is proposed to forecast wind speed. First, the original wind speed datasets are decomposed into a collection of intrinsic mode functions (IMFs) and a residue by EMD, yielding relatively stationary sub-series that can be readily modeled by neural networks. Second, both IMF components and residue are applied to establish the corresponding ENN models. Then, each sub-series is predicted using the corresponding ENN. Finally, the prediction values of the original wind speed datasets are calculated by the sum of the forecasting values of every sub-series. Moreover, in the ENN modeling process, the neuron number of the input layer is determined by a partial autocorrelation function. Four prediction cases of wind speed are used to test the performance of the proposed hybrid approach. Compared with the persistent model, back-propagation neural network, and ENN, the simulation results show that the proposed EMD-ENN model consistently has the minimum statistical error of the mean absolute error, mean square error, and mean absolute percentage error. Thus, it is concluded that the proposed approach is suitable for wind speed prediction.
221 citations
TL;DR: A new method for analysis of electroencephalogram (EEG) signals using empirical mode decomposition (EMD) and Fourier-Bessel expansion and the MF feature of the IMFs has provided statistically significant difference between ictal and seizure-free EEG signals.
Abstract: A new method for analysis of electroencephalogram (EEG) signals using empirical mode decomposition (EMD) and Fourier-Bessel (FB) expansion has been presented in this paper. The EMD decomposes an EEG signal into a finite set of band-limited signals termed intrinsic mode functions (IMFs). The mean frequency (MF) for each IMF has been computed using FB expansion. The MF measure of the IMFs has been used as a feature in order to identify the difference between ictal and seizure-free intracranial EEG signals. It has been shown that the MF feature of the IMFs has provided statistically significant difference between ictal and seizure-free EEG signals. Simulation results are included to illustrate the effectiveness of the proposed method.
221 citations
Cites background or methods from "The empirical mode decomposition an..."
...non-linear and non-stationary time-series analysis [9] and the Fourier- Bessel (FB) expansion suitable for nonstationary signal representation [10]....
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...The principle of the EMD technique is to decompose a signal x(t) automatically into a set of the band-limited functions Dp(t) named intrinsic mode functions (IMFs) [9]....
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TL;DR: The rolling bearing fault diagnosis method based on LMD, MPE, LS and ISVM-BT is proposed and the experimental results indicate the proposed method is effective in identifying the different categories of rolling bearings.
221 citations
TL;DR: In this article, a method for monitoring the evolution of gear faults based on the newly developed empirical mode decomposition scheme is presented, which can be used for system failure prediction and is shown that the instantaneous frequency of the vibration signal is a sensitive indicator of the existence of damage in the gear pair.
220 citations
TL;DR: In this paper, the frontal eye fields (FEF) signals were recorded simultaneously from both areas in a covert attention task and in a saccade task to test the relative contributions of oculomotor and attention-related FEF signals to such feedback.
219 citations
References
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TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Abstract: Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
16,554 citations
"The empirical mode decomposition an..." refers background in this paper
...(ii) Lorenz equation The famous Lorenz equation (Lorenz 1963) was proposed initially to study deterministic non-periodic flow....
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Book•
01 Jan 1974
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Abstract: Introduction and General Outline. HYPERBOLIC WAVES. Waves and First Order Equations. Specific Problems. Burger's Equation. Hyperbolic Systems. Gas Dynamics. The Wave Equation. Shock Dynamics. The Propagation of Weak Shocks. Wave Hierarchies. DISPERSIVE WAVES. Linear Dispersive Waves. Wave Patterns. Water Waves. Nonlinear Dispersion and the Variational Method. Group Velocities, Instability, and Higher Order Dispersion. Applications of the Nonlinear Theory. Exact Solutions: Interacting Solitary Waves. References. Index.
8,808 citations
Book•
01 Jan 1971
TL;DR: A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems, is presented in this article.
Abstract: From the Publisher:
A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems. With more than 100,000 copies in print and six foreign translations, the first edition standardized the methodology in this field. This new edition covers all new procedures developed since 1971 and extends the application of random data analysis to aerospace and automotive research; digital data analysis; dynamic test programs; fluid turbulence analysis; industrial noise control; oceanographic data analysis; system identification problems; and many other fields. Includes new formulas for statistical error analysis of desired estimates, new examples and problem sets.
6,693 citations
"The empirical mode decomposition an..." refers background in this paper
...A brief tutorial on the Hilbert transform with the emphasis on its physical interpretation can be found in Bendat & Piersol (1986)....
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01 Jan 1946
5,910 citations
"The empirical mode decomposition an..." refers methods in this paper
...In order to obtain meaningful instantaneous frequency, restrictive conditions have to be imposed on the data as discussed by Gabor (1946), Bedrosian (1963) and, more recently, Boashash (1992): for any function to have a meaningful instantaneous frequency, the real part of its Fourier transform has…...
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TL;DR: In this paper, the authors used the representations of the noise currents given in Section 2.8 to derive some statistical properties of I(t) and its zeros and maxima.
Abstract: In this section we use the representations of the noise currents given in section 2.8 to derive some statistical properties of I(t). The first six sections are concerned with the probability distribution of I(t) and of its zeros and maxima. Sections 3.7 and 3.8 are concerned with the statistical properties of the envelope of I(t). Fluctuations of integrals involving I2(t) are discussed in section 3.9. The probability distribution of a sine wave plus a noise current is given in 3.10 and in 3.11 an alternative method of deriving the results of Part III is mentioned. Prof. Uhlenbeck has pointed out that much of the material in this Part is closely connected with the theory of Markoff processes. Also S. Chandrasekhar has written a review of a class of physical problems which is related, in a general way, to the present subject.22
5,806 citations
"The empirical mode decomposition an..." refers background in this paper
...In general, if more quantitative results are desired, the original skeleton presentation is better; if more qualitative results are desired, the smoothed presentation is better....
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...Therefore, the parameter, ν, defined as N21 −N20 = 1 π2 m4m0 −m22 m2m0 = 1 π2 ν2, (3.7) offers a standard bandwidth measure (see, for example, Rice 1944a, b, 1945a, b; Longuet-Higgins 1957)....
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