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Journal ArticleDOI

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

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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Citations
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Journal ArticleDOI
TL;DR: This work presents research highlights ranging from determination of the molecular interaction network within a cell to studies of architectural and functional properties of brain networks and biological transportation networks, and focuses on synergies between network science and data analysis, which enable us to determine functional connectivity patterns in multicellular systems.

306 citations


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

  • ...First, the recorded time series are processed by a band-pass filter or by other advanced methods, such as Huang–Hilbert empirical model decomposition [105,106]....

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  • ...[106] Huang N, Shen Z, Long S, Wu M, Shih H, Zheng Q, et al....

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Journal ArticleDOI
27 Sep 2017
TL;DR: In this paper, an empirical study of feature extraction methods for the application of low-speed bearing condition monitoring is presented, where the selected features such as impulse factor, margin factor, approximate entropy and largest Lyapunov exponent (LLE) show obvious changes in bearing condition from normal condition to final failure.
Abstract: This paper presents an empirical study of feature extraction methods for the application of low-speed slew bearing condition monitoring. The aim of the study is to find the proper features that represent the degradation condition of slew bearing rotating at very low speed (≈ 1 r/min) with naturally defect. The literature study of existing research, related to feature extraction methods or algorithms in a wide range of applications such as vibration analysis, time series analysis and bio-medical signal processing, is discussed. Some features are applied in vibration slew bearing data acquired from laboratory tests. The selected features such as impulse factor, margin factor, approximate entropy and largest Lyapunov exponent (LLE) show obvious changes in bearing condition from normal condition to final failure.

301 citations


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

  • ...Empirical Mode Decomposition-Based Hilbert Huang Transform Empirical mode decomposition (EMD) [42] has been used in some applications that involve non-stationary signals (see, e....

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  • ...Empirical Mode Decomposition-Based Hilbert Huang Transform Empirical mode decomposition (EMD) [42] has been used in some applications that involve nonstationary signals (see, e....

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Proceedings Article
01 Sep 2004
TL;DR: Numerical simulations are reported on illustrating the potentialities and limitations of EMD in two signal processing tasks, namely detrending and denoising.
Abstract: Empirical Mode Decomposition (EMD) has recently been introduced as a local and fully data-driven technique aimed at decomposing nonstationary multicomponent signals in “intrinsic” AM-FM contributions. Although the EMD principle is appealing and its implementation easy, performance analysis is difficult since no analytical description of the method is available. We will here report on numerical simulations illustrating the potentialities and limitations of EMD in two signal processing tasks, namely detrending and denoising. In both cases, the idea is to make use of partial reconstructions, the relevant modes being selected on the basis of the statistical properties of modes that have been empirically established.

300 citations


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

  • ...In a nutshell, the starting point of EMD is to consider oscillatory signals at the level of their local oscillations and to formalize the idea that: “signal = fast oscillations superimposed to slow oscillations,” and to iterate on the slow oscillations component considered as a new signal....

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  • ...Empirical Mode Decomposition (EMD) has been recently pioneered by Huang et al. [2] for adaptively decomposing signals in a sum of “well-behaved” AM-FM components....

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  • ...This property of perfect reconstruction, together with the spectral interpretation outlined above, suggests to achieve partial reconstructions only, so as to selectively remove slow or fast oscillations (detrending or denoising, respectively)....

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Journal ArticleDOI
TL;DR: A detailed review of existing methods for phenology detection and emerging new techniques based on the analysis of time-series, multispectral remote sensing imagery is presented in this paper.

300 citations

Journal ArticleDOI
TL;DR: In this article, a method of fault feature extraction based on intrinsic mode function (IMF) envelope spectrum is proposed to overcome the limitations of conventional envelope analysis method by utilizing the proposed feature extraction method, the disadvantages of conventional analysis method such as the chosen of central frequency of filter with experience in advance, looking for spectral line of fault characteristic frequencies in envelope spectrum and so on could be overcome.

299 citations

References
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Journal ArticleDOI
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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Journal ArticleDOI
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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