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: In this article, a time scale decomposition based on the theory of wavelets is proposed to analyze the relationship between the oil price and macroeconomy, and it is shown that the cycles which contribute the most to oil price variations are 20 to 40-year cycles, which correspond to the size of Kuznets infrastructure cycles.
89 citations
TL;DR: In this paper, the authors used hybrid models consisting of an ensemble empirical mode decomposition and general regression neural network (EEMD-GRNN), Adaptive Neuro-Fuzzy Inference System (ANFIS), principal component regression (PCR), and linear model such as multiple liner regression (MLR) model were used.
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TL;DR: A survey of existing broken rotor bar fault detection techniques with new classification based on fault signature is presented and classified based on loading level, number of broken bars, validation and signal processing.
Abstract: The induction motor is the most popular motor in energy conversion and industrial drive systems. This popularity is due to its robustness, low cost, and easy maintenance. Electrical, mechanical, thermal, magnetic and environmental stresses cause faults in the induction motor during the operation process. One of the challenging topics for many researchers is the development of a reliable efficient induction motor fault diagnostic techniques. The broken rotor bar fault is one of the critical faults that need to be early detected due to its sudden severe damages. The objective of this study is to present a survey of existing broken rotor bar fault detection techniques with new classification based on fault signature. Various monitoring conditions and signal processing techniques are considered for the detection process. A comprehensive list of references is reported for each fault signature and classified based on (i) loading level, (ii) the number of broken bars, (iii) validation and (vi) signal processing.
89 citations
TL;DR: In this article, an economic operation-based load dispatching strategy that can interactively adapt to the real measured wind and solar power production values is proposed, which is provided by the update mechanism employed in the meteorological condition forecasting algorithms provided by a combination of empirical mode decomposition, Cascade-Forward Neural Network and Linear Model through a fusion strategy.
89 citations
TL;DR: A new NBI suppression algorithm using the complex empirical mode decomposition (CEMD) method, which is robust to time-varying NBI and well-focused SAR imagery can be obtained from the separated target echoes using traditional SAR imaging algorithms.
Abstract: Narrow-band interference (NBI) is a common interference source in synthetic aperture radar (SAR) imaging. Its existence will degrade the imaging quality greatly. Based on detailed analysis on the characteristics of NBI, this letter proposes a new NBI suppression algorithm using the complex empirical mode decomposition (CEMD) method. In this algorithm, echoes that include NBI are recognized in the time domain first. Then, these echoes are decomposed into a number of intrinsic mode functions (IMFs) via the CEMD. After that, IMFs that correspond to NBI are subtracted from the echoes by thresholding. Finally, well-focused SAR imagery can be obtained from the separated target echoes using traditional SAR imaging algorithms. The effective data loss in this algorithm is smaller than other NBI suppression approaches. In addition, this algorithm is robust to time-varying NBI. Imaging results of measured data have proved the validity of this algorithm.
89 citations
Cites background or methods from "The empirical mode decomposition an..."
...The newly developed EMD algorithm [9] is a tool for the time–frequency analysis of nonlinear and nonstationary signals....
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...Due to the limitations of the available nonparametric NBI suppression algorithms, this letter proposes a new NBI suppression algorithm using the complex empirical mode decomposition (CEMD) [9], [10]....
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...Detailed information for the CEMD algorithm is given in [9] and [10]....
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...The band-limited signal can be regarded as the summation of fast changing signals onto the slowly changing ones [9]....
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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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