The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

doi:10.1098/RSPA.1998.0193

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The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

Journal Article•DOI•

The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

Norden E. Huang¹, Zheng Shen², Steven R. Long³, Man-Li C. Wu¹, Hsing H. Shih⁴, Quanan Zheng⁵, Nai-Chyuan Yen⁶, C. C. Tung⁷, Henry H. Liu⁸ - Show less +5 more•Institutions (8)

Goddard Space Flight Center¹, Johns Hopkins University², Wallops Flight Facility³, National Ocean Service⁴, University of Delaware⁵, United States Naval Research Laboratory⁶, North Carolina State University⁷, Naval Surface Warfare Center⁸

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.

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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...

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Posted Content•

A survey of dimensionality reduction techniques.

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Carlos Oscar S. Sorzano, Javier Vargas, Alberto Pascual-Montano

12 Mar 2014-arXiv: Machine Learning

TL;DR: In this review, the plethora of dimension reduction techniques available are categorized and the mathematical insight behind them are given.

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Abstract: Experimental life sciences like biology or chemistry have seen in the recent decades an explosion of the data available from experiments. Laboratory instruments become more and more complex and report hundreds or thousands measurements for a single experiment and therefore the statistical methods face challenging tasks when dealing with such high dimensional data. However, much of the data is highly redundant and can be efficiently brought down to a much smaller number of variables without a significant loss of information. The mathematical procedures making possible this reduction are called dimensionality reduction techniques; they have widely been developed by fields like Statistics or Machine Learning, and are currently a hot research topic. In this review we categorize the plethora of dimension reduction techniques available and give the mathematical insight behind them.

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297 citations

Journal Article•DOI•

A Multivariate Approach for Patient-Specific EEG Seizure Detection Using Empirical Wavelet Transform

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Abhijit Bhattacharyya¹, Ram Bilas Pachori•Institutions (1)

Indian Institute of Technology Indore¹

09 Jan 2017-IEEE Transactions on Biomedical Engineering

TL;DR: Efficient detection of epileptic seizure is achieved when seizure events appear for long duration in hours long EEG recordings and the proposed method develops time–frequency plane for multivariate signals and builds patient-specific models for EEG seizure detection.

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Abstract: Objective : This paper investigates the multivariate oscillatory nature of electroencephalogram (EEG) signals in adaptive frequency scales for epileptic seizure detection. Methods : The empirical wavelet transform (EWT) has been explored for the multivariate signals in order to determine the joint instantaneous amplitudes and frequencies in signal adaptive frequency scales. The proposed multivariate extension of EWT has been studied on multivariate multicomponent synthetic signal, as well as on multivariate EEG signals of Children's Hospital Boston-Massachusetts Institute of Technology (CHB-MIT) scalp EEG database. In a moving-window-based analysis, 2-s-duration multivariate EEG signal epochs containing five automatically selected channels have been decomposed and three features have been extracted from each 1-s part of the 2-s-duration joint instantaneous amplitudes of multivariate EEG signals. The extracted features from each oscillatory level have been processed using a proposed feature processing step and joint features have been computed in order to achieve better discrimination of seizure and seizure-free EEG signal epochs. Results : The proposed detection method has been evaluated over 177 h of EEG records using six classifiers. We have achieved average sensitivity, specificity, and accuracy values as 97.91%, 99.57%, and 99.41%, respectively, using tenfold cross-validation method, which are higher than the compared state of art methods studied on this database. Conclusion : Efficient detection of epileptic seizure is achieved when seizure events appear for long duration in hours long EEG recordings. Significance : The proposed method develops time–frequency plane for multivariate signals and builds patient-specific models for EEG seizure detection.

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291 citations

Cites methods from "The empirical mode decomposition an..."

...In HHT-based time–frequency method, first the IMFs are extracted from the analyzed signal using empirical mode decomposition (EMD) method and then Hilbert transform is applied on each extracted IMF to obtain instantaneous amplitude and frequency [30]....
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...There exist several popular methods for obtaining time–frequency representation of nonstationary signals like wavelet skeleton method [29], Hilbert–Huang transform (HHT) method [30], [31], etc....
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...The analytic signal representation of each MODE ym, MODEn (t) is defined using Hilbert transform operator (H) as [30]...
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Journal Article•DOI•

Generator bearing fault diagnosis for wind turbine via empirical wavelet transform using measured vibration signals

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Jinglong Chen¹, Jun Pan¹, Zipeng Li¹, Yanyang Zi¹, Xuefeng Chen¹ - Show less +1 more•Institutions (1)

Xi'an Jiaotong University¹

01 Apr 2016-Renewable Energy

TL;DR: In this paper, an empirical wavelet transform (EWT) is used to extract inherent modulation information by decomposing signal into mono-components under an orthogonal basis, which is seen as a powerful tool for mechanical fault diagnosis.

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290 citations

Journal Article•DOI•

On the HHT, its problems, and some solutions

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Raul T. Rato, Manuel Duarte Ortigueira, Arnaldo Batista

01 Aug 2008

TL;DR: In this paper, the empirical mode decomposition (EMD) is reviewed and some questions related to its effective performance are discussed, and solutions for its drawbacks are proposed, and numerical simulations are carried out to empirically evaluate the proposed modified EMD.

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Abstract: The empirical mode decomposition (EMD) is reviewed and some questions related to its effective performance are discussed. Its interpretation in terms of AM/FM modulation is done. Solutions for its drawbacks are proposed. Numerical simulations are carried out to empirically evaluate the proposed modified EMD.

...read moreread less

290 citations

Cites background or methods from "The empirical mode decomposition an..."

...papers [1,2] a Hilbert spectral estimation is used to estimate the instantaneous frequency....
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...In Section 2 we describe the EMD algorithm as proposed in [1] and look inside it to understand the main difficulties and ways of avoiding them....
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...The EMD is the base of the so-called ‘‘Hilbert–Huang transform (HHT)’’ [1] that comprises the EMD and the Hilbert spectral analysis that performs a spectral analysis using the Hilbert transform (HT) followed by an instantaneous frequency computation....
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...This is the original definition of IMF presented in [1]....
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...[1] is a signal decomposition algorithm based on a successive removal of elemental signals: the IMFs....
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Journal Article•DOI•

Comparing the applications of EMD and EEMD on time-frequency analysis of seismic signal

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Tong Wang¹, Mingcai Zhang, Qihao Yu, Huyuan Zhang¹•Institutions (1)

Lanzhou University¹

01 Aug 2012-Journal of Applied Geophysics

TL;DR: In this paper, ensemble empirical mode decomposition (EEMD) is adopted instead of EMD to solve the mode mixing problem, and the results show that EEMD more realistically reflects the real geology than by EMD.

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289 citations

Cites background from "The empirical mode decomposition an..."

...Modemixing often was a consequence of signal intermittence (Huang et al., 1998) which frequently happened in seismic exploration....
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References

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Deterministic nonperiodic flow

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Edward N. Lorenz¹•Institutions (1)

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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.

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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.

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...(ii) Lorenz equation The famous Lorenz equation (Lorenz 1963) was proposed initially to study deterministic non-periodic flow....
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Linear and Nonlinear Waves

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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.

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Julius S. Bendat, Allan G. Piersol

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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.

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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.

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"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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Theory of communication

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Dennis Gabor

01 Jan 1946

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"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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Journal Article•DOI•

Mathematical analysis of random noise

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S. O. Rice

01 Jul 1944-Bell System Technical Journal

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.

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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

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"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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