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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TL;DR: It is shown that, in the case of machines with one or several broken bars, the IF of the LSHst exhibits a very characteristic and easy to identify pattern, which is physically justified, and a universal fault indicator can be defined.
Abstract: In this paper, a new method for detecting the presence of broken rotor bars is presented. The proposed approach is valid for induction machines started at constant frequency and consists of extracting the instantaneous frequency (IF) of the left sideband harmonic (LSH) from the start-up current (LSHst), via the Hilbert transform. It is shown that, in the case of machines with one or several broken bars, the IF of the LSHst exhibits a very characteristic and easy to identify pattern, which is physically justified. This paper also shows that, if the IF of the LSHst is represented against the slip, a universal fault indicator (nondependent neither on the machine characteristics nor on the starting conditions) can be defined. This fault indicator consists of the correlation between the experimental IF of the LSHst and its theoretical evolution. This approach is theoretically introduced and experimentally validated by testing a commercial motor in faulty and healthy conditions, under different operating conditions.
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TL;DR: Based on the local approximation of linear frequency modulation mode, this paper analyzed the well-separated condition of non-stationary multicomponent signals using the adaptive short-time Fourier transform (STFT) with the Gaussian window function.
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08 Nov 2006
TL;DR: A novel approach to passive detection of image splicing by using support vector machine (SVM) as the classifier and initial experimental results demonstrate that the proposed scheme outperforms the prior arts.
Abstract: Image splicing is a commonly used technique in image tampering. This paper presents a novel approach to passive detection of image splicing. In the proposed scheme, the image splicing detection problem is tackled as a twoclass classification problem under the pattern recognition framework. Considering the high non-linearity and non-stationarity nature of image splicing operation, a recently developed Hilbert-Huang transform (HHT) is utilized to generate features for classification. Furthermore, a well established statistical natural image model based on moments of characteristic functions with wavelet decomposition is employed to distinguish the spliced images from the authentic images. We use support vector machine (SVM) as the classifier. The initial experimental results demonstrate that the proposed scheme outperforms the prior arts.
105 citations
Cites background or methods from "The empirical mode decomposition an..."
...An intrinsic mode function (IMF) is a function that satisfies the following two conditions [6]: (1) In the whole data set, the number of extrema and the number of zero crossings must either equal or differ at most by one....
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...The IMFs of a signal can be obtained by sifting algorithm [6]....
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...1 Hilbert-Huang Transform The HHT technology is a highly efficient tool capable of analyzing time-varying processes [6]....
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...Our proposed scheme utilizes the newly developed Hilbert-Huang Transform (HHT) [6] to generate more effective features for classification....
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01 Jan 2015
TL;DR: In this article, the classification of power quality disturbances based on VMD (Variational Mode Decomposition) and EWT (Empirical Wavelet Transform) using SVM (Support Vector Machine) is done for producing feature vectors that can extract salient and unique nature of these disturbances.
Abstract: This work considers the classification of power quality disturbances based on VMD (Variational Mode Decomposition) and EWT (Empirical Wavelet Transform) using SVM (Support Vector Machine). Performance comparison of VMD over EWT is done for producing feature vectors that can extract salient and unique nature of these disturbances. In this paper, these two adaptive signal processing methods are used to produce three Intrinsic Mode Function (IMF) components of power quality signals. Feature vectors produced by finding sines and cosines of statistical parameter vector of three different IMF candidates are used for training SVM. Validation for six different classes of power qualities including normal sinusoidal signal, sag, swell, harmonics, sag with harmonics, swell with harmonics is performed using synthetic data in MATLAB. Classification results using SVM shows that VMD outperforms over EWT for feature extraction process and the classification accuracy is tabled.
105 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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