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: The results indicate that the four long-term LAI products were neither intraconsistent over time nor interconsistent with each other, and these inconsistencies may be due to NOAA satellite orbit changes and MODIS sensor degradation.
Abstract: Understanding the long-term performance of global satellite leaf area index (LAI) products is important for global change research. However, few effort has been devoted to evaluating the long-term time-series consistencies of LAI products. This study compared four long-term LAI products (GLASS, GLOBMAP, LAI3g, and TCDR) in terms of trends, interannual variabilities, and uncertainty variations from 1982 through 2011. This study also used four ancillary LAI products (GEOV1, MERIS, MODIS C5, and MODIS C6) from 2003 through 2011 to help clarify the performances of the four long-term LAI products. In general, there were marked discrepancies between the four long-term LAI products. During the pre-MODIS period (1982-1999), both linear trends and interannual variabilities of global mean LAI followed the order GLASS>LAI3g>TCDR>GLOBMAP. The GLASS linear trend and interannual variability were almost 4.5 times those of GLOBMAP. During the overlap period (2003-2011), GLASS and GLOBMAP exhibited a decreasing trend, TCDR no trend, and LAI3g an increasing trend. GEOV1, MERIS, and MODIS C6 also exhibited an increasing trend, but to a much smaller extent than that from LAI3g. During both periods, the R2 of detrended anomalies between the four long-term LAI products was smaller than 0.4 for most regions. Interannual variabilities of the four long-term LAI products were considerably different over the two periods, and the differences followed the order GLASS>LAI3g>TCDR>GLOBMAP. Uncertainty variations quantified by a collocation error model followed the same order. Our results indicate that the four long-term LAI products were neither intraconsistent over time nor interconsistent with each other. These inconsistencies may be due to NOAA satellite orbit changes and MODIS sensor degradation. Caution should be used in the interpretation of global changes derived from the four long-term LAI products.
153 citations
Cites methods from "The empirical mode decomposition an..."
...The EEMD method decomposes time series into a group of oscillatory components at different frequency levels without any predetermined basis functions (Huang et al., 1998), and EEMD is its enhanced version overcoming the scale mixing problem (Wang, 2009)....
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TL;DR: This analytical study proposes a hybrid short-term prediction approach that can successfully preprocess the original wind speed data to enhance the forecasting accuracy and delivers high accuracy, less uncertainty and low computational burden in the forecasts attained.
153 citations
TL;DR: The empirical results indicate that the proposed model statistically outperforms all considered benchmark models and similar decomposition–ensemble models with other existing reconstruction methods, since it has higher prediction accuracy and less computational time.
153 citations
Cites methods from "The empirical mode decomposition an..."
...[37] uses the Hilbert–Huang transform (HHT) to decompose the original series data into some independent and nearly periodic IMFs based on local characteristic scales, which meet the following two conditions....
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TL;DR: It can be anticipated that owing to its use of only one channel of EEG signal, the proposed method will be suitable for device implementation, eliminate the onus of clinicians for analyzing a large bulk of data manually, and expedite epilepsy diagnosis.
153 citations
TL;DR: In this article, the authors examined the rationale of Hilbert-Huang transform (HHT) for analyzing dynamic and earthquake motion recordings in studies of seismology and engineering, and proposed a method to analyze the Hilbert Huang transform for seismic data.
Abstract: This study examines the rationale of Hilbert-Huang transform (HHT) for analyzing dynamic and earthquake motion recordings in studies of seismology and engineering. In particular, this paper first p...
152 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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