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...
Citations
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TL;DR: In this article, the theoretical ability of wavelet analysis and empirical mode decomposition to effectively remove only the DC drift component is evaluated based on their mutual performance for the first time, and the correlation coefficient between individual signals after both trend removal techniques proved to be superior compared to the correlation coefficients between these and the signals after moving average, polynomial and linear trend removal.
86 citations
TL;DR: A comprehensive review of islanding issues, standard test systems, criteria and shifting of research trends in islanding detection methods (IDMs) is given.
Abstract: The augmentation in electricity demand, power system privatization as well as efficacy of renewable resources has paved the way for power system companies and researchers to exploit the field of grid connected distributed generation (DG) and its issues, islanding being a dominant one. Several research works have been conducted to mitigate the issues of islanding detection (ID). In context of this, the paper gives a comprehensive review of islanding issues, standard test systems, criteria and shifting of research trends in islanding detection methods (IDMs). The significant contributions pertain to categorization of IDMs, evaluation of non-detection zone (NDZ) for each test system, disquisition on evolution and advancement of IDMs and its comparisons based on criteria such as NDZ, run on time, nuisance tripping percentage, applicability in multi DG system and implementation cost to draw out the strength and shortcomings of individual methods that will come to aid to the companies or researchers for establishing the applicability and appropriateness of such method for their concerned domain.
86 citations
Cites methods from "The empirical mode decomposition an..."
...In first stage, by applying empirical mode decomposition (EMD), the concerned signal is decomposed into intrinsic mode functions (IMFs) to obtain meaningful instantaneous amplitudes and frequencies [82]....
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TL;DR: Experimental results indicate that the proposed denoising method outperforms other denoised methodologies in terms of signal-to-noise ratio, mean square error, and percent root mean square difference.
86 citations
TL;DR: In this paper, the authors investigated the characteristics of aging bridges by comparison with their structural properties, and discussed the possible influence of the frequency function on the structural properties of these bridges.
Abstract: Many bridges in Taiwan have been in use from the period that Taiwan was governed by the Japanese, over 50 years ago, which is the average ultimate usable lifetime of such structures. Three-quarters of the bridges on major highways have been in use for more than 20 years and numerous bridges on country roads have also been in use for more than 20 years. In other words, most of the bridges in Taiwan are aging and may require repair or replacement. Ambient vibration tests are utilized to measure the response of old bridges, which are difficult to equip with accelerometers. The Fourier transform method is traditionally used to gain important information about ambient vibration records. However, the development of information technology over the last 20 years has meant that there are more kinds of signal management technologies, including the wavelet and Hilbert—Huang transform (HHT) methods. In this study we investigate the characteristics of aging bridges by comparison with their structural properties. We analyze their ambient vibration, and discuss the possible influence of the frequency function. Long-term environmental impacts create many structural problems, but with traditional methods examination of bridge health is difficult. Therefore, in our HHT management system, we examine destroyed bridges. The characteristics and behavior of bridges subjected to random loading can be understood by analysis with the random decrement technique and the frequency response function method.
86 citations
Cites background from "The empirical mode decomposition an..."
...In 1996, Norden Huang published Empirical Mode Deposition (Huang, 1998)....
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TL;DR: Empirical results reveal that the prediction using M–EEMD–ELM model is consistently better than basic artificial neural networks (ANNs) and unmodified EEMD-based extreme learning machine (ELM) ensemble learning paradigm in terms of the same measurements.
Abstract: In this paper, an M–EEMD–ELM model (modified ensemble empirical mode decomposition (EEMD)-based extreme learning machine (ELM) ensemble learning paradigm) is proposed for landslide displacement prediction. The nonlinear original surface displacement deformation monitoring time series of landslide is first decomposed into a limited number of intrinsic mode functions (IMFs) and one residual series using EEMD technique for a deep insight into the data structure. Then, these sub-series except the high frequency are forecasted, respectively, by establishing appropriate ELM models. At last, the prediction results of the modeled IMFs and residual series are summed to formulate an ensemble forecast for the original landslide displacement series. A case study of Baishuihe landslide in the Three Gorges reservoir area of China is presented to illustrate the capability and merit of our model. Empirical results reveal that the prediction using M–EEMD–ELM model is consistently better than basic artificial neural networks (ANNs) and unmodified EEMD–ELM in terms of the same measurements.
85 citations
Cites background or methods from "The empirical mode decomposition an..."
...A suggested stoppage criterion (Huang et al. 1998), which is determined by using a Cauchy type of convergence test, is defined as follows: SDk 1⁄4 X‘ t1⁄41 jh1ðk 1ÞðtÞ h1kðtÞj(2) h(2) 1ðk 1ÞðtÞ ð4Þ...
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...According to Huang et al. (1998), IMFs must satisfy the following conditions: 1....
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...The empirical mode decomposition (EMD) is an adaptive and efficient time series decomposition technique applied to decompose nonlinear and non-stationary signals using the Hilbert–Huang transform (HHT) (Huang et al. 1998)....
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...A suggested stoppage criterion (Huang et al. 1998), which is determined by using a Cauchy type of convergence test, is defined as follows: SDk ¼ X‘ t¼1 jh1ðk 1ÞðtÞ h1kðtÞj2 h2 1ðk 1ÞðtÞ ð4Þ Here, SDk is less than a predetermined value....
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...2.1 EMD and EEMD The empirical mode decomposition (EMD) is an adaptive and efficient time series decomposition technique applied to decompose nonlinear and non-stationary signals using the Hilbert–Huang transform (HHT) (Huang et al. 1998)....
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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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