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...
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212 citations
TL;DR: An original tool for EEG signal processing giving physicians the possibility to diagnose brain functionality abnormalities is presented in this paper and results indicate the usefulness of the tool and its use as an efficient diagnostic tool.
Abstract: Classification method capable of recognizing abnormal activities of the brain functionality are either brain imaging or brain signal analysis. The abnormal activity of interest in this study is characterized by a disturbance caused by changes in neuronal electrochemical activity that results in abnormal synchronous discharges. The method aims at helping physicians discriminate between healthy and seizure electroencephalographic (EEG) signals. Discrimination in this work is achieved by analyzing EEG signals obtained from freely accessible databases. MATLAB has been used to implement and test the proposed classification algorithm. The analysis in question presents a classification of normal and ictal activities using a feature relied on Hilbert-Huang Transform. Through this method, information related to the intrinsic functions contained in the EEG signal has been extracted to track the local amplitude and the frequency of the signal. Based on this local information, weighted frequencies are calculated and a comparison between ictal and seizure-free determinant intrinsic functions is then performed. Methods of comparison used are the t-test and the Euclidean clustering. The t-test results in a P-value < 0.02 and the clustering leads to accurate (94%) and specific (96%) results. The proposed method is also contrasted against the Multivariate Empirical Mode Decomposition that reaches 80% accuracy. Comparison results strengthen the contribution of this paper not only from the accuracy point of view but also with respect to its fast response and ease to use. An original tool for EEG signal processing giving physicians the possibility to diagnose brain functionality abnormalities is presented in this paper. The proposed system bears the potential of providing several credible benefits such as fast diagnosis, high accuracy, good sensitivity and specificity, time saving and user friendly. Furthermore, the classification of mode mixing can be achieved using the extracted instantaneous information of every IMF, but it would be most likely a hard task if only the average value is used. Extra benefits of this proposed system include low cost, and ease of interface. All of that indicate the usefulness of the tool and its use as an efficient diagnostic tool.
212 citations
Cites background or methods from "The empirical mode decomposition an..."
...This drawback makes Hilbert Transform to be not a very good choice to track frequency [17]....
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...One of the methods that might be coupled to Hilbert Transform in order to get narrow-band signal is the nonlinear local technique known as Huang transform [17]....
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TL;DR: Nonlinear methods which can capture the small variations in the ECG signal and provide improved accuracy in the presence of noise are discussed in greater detail in this review.
211 citations
Cites methods from "The empirical mode decomposition an..."
...This technique expands a given ECG signal into a few number of intrinsic mode functions (IMFs) to yield the instantaneous frequency [102]....
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...Ying-Hsiang [95] used higher order statistics and Hermite basis function decomposition for ECG beat classification [102]....
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TL;DR: In this paper, a Hilbert-Huang transform was used to diagnose demagnetization in a permanent-magnet synchronous motor (PMSM) under nonstationary conditions of velocity.
Abstract: This paper presents a novel method to diagnose demagnetization in permanent-magnet synchronous motor (PMSM). Simulations have been performed by 2-D finite-element analysis in order to determine the current spectrum and the magnetic flux distribution due to this failure. The diagnostic just based on motor current signature analysis can be confused by eccentricity failure because the harmonic content is the same. Moreover, it can only be applied under stationary conditions. In order to overcome these drawbacks, a novel method is used based upon the Hilbert-Huang transform. It represents time-dependent series in a 2-D time-frequency domain by extracting instantaneous frequency components through an empirical-mode decomposition process. This tool is applied by running the motor under nonstationary conditions of velocity. The experimental results show the reliability and feasibility of the methodology in order to diagnose the demagnetization of a PMSM.
211 citations
Cites background or methods from "The empirical mode decomposition an..."
...Each of the traditional time–frequency analysis techniques have their own limitations [22], [ 23 ]....
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...The local energy and the instantaneous frequency derived from the IMFs through the Hilbert transform can give us a full energy–frequency–time distribution of the data [ 23 ]; it would be the ideal tool for nonlinear and nonstationary data analysis....
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TL;DR: In this article, the authors conducted a geological and geomorphological investigation with the aim of reconstructing the events leading up to the Shiaolin landslide and to clarify factors that contributed to its development.
211 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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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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