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 paper, the authors compared eight methods to improve the continuity by filling gaps and consistency by smoothing the time course of the MODIS leaf area index product for the period 2000-2008.
Abstract: . Moderate resolution satellite sensors including MODIS (Moderate Resolution Imaging Spectroradiometer) already provide more than 10 yr of observations well suited to describe and understand the dynamics of earth's surface. However, these time series are associated with significant uncertainties and incomplete because of cloud cover. This study compares eight methods designed to improve the continuity by filling gaps and consistency by smoothing the time course. It includes methods exploiting the time series as a whole (iterative caterpillar singular spectrum analysis (ICSSA), empirical mode decomposition (EMD), low pass filtering (LPF) and Whittaker smoother (Whit)) as well as methods working on limited temporal windows of a few weeks to few months (adaptive Savitzky–Golay filter (SGF), temporal smoothing and gap filling (TSGF), and asymmetric Gaussian function (AGF)), in addition to the simple climatological LAI yearly profile (Clim). Methods were applied to the MODIS leaf area index product for the period 2000–2008 and over 25 sites showed a large range of seasonal patterns. Performances were discussed with emphasis on the balance achieved by each method between accuracy and roughness depending on the fraction of missing observations and the length of the gaps. Results demonstrate that the EMD, LPF and AGF methods were failing because of a significant fraction of gaps (more than 20%), while ICSSA, Whit and SGF were always providing estimates for dates with missing data. TSGF (Clim) was able to fill more than 50% of the gaps for sites with more than 60% (80%) fraction of gaps. However, investigation of the accuracy of the reconstructed values shows that it degrades rapidly for sites with more than 20% missing data, particularly for ICSSA, Whit and SGF. In these conditions, TSGF provides the best performances that are significantly better than the simple Clim for gaps shorter than about 100 days. The roughness of the reconstructed temporal profiles shows large differences between the various methods, with a decrease of the roughness with the fraction of missing data, except for ICSSA. TSGF provides the smoothest temporal profiles for sites with a % gap > 30%. Conversely, ICSSA, LPF, Whit, AGF and Clim provide smoother profiles than TSGF for sites with a % gap
168 citations
Cites background or methods from "The empirical mode decomposition an..."
...The threshold for convergence is set to 0.3 according to Huang et al. (1998) and the maximum number of IMFs was restricted to 10 after trial and error....
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...This method proposed by Huang et al. (1998) consists in decomposing the time series into a small number of intrinsic mode frequencies (IMFs) derived directly from the time series itself using an adaptive iterative process where the data are represented by intrinsic mode functions, to which the…...
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TL;DR: In this paper, an ensemble super-wavelet transform (ESW) is proposed for investigating vibration features of motor bearing faults, which is based on the combination of tunable Q-factor wavelet transform and Hilbert transform.
167 citations
TL;DR: It is suggested that seizure prediction may work better in closed loop seizure control devices rather than as seizure advisory devices and the emergence of a large database of annotated long-term EEG recordings should help prospective assessment of prediction methods.
167 citations
TL;DR: In this paper, the frontal eye field (FEF) in prefrontal cortex (PFC) modulates processing in visual cortex with attention, although the evidence that it is necessary is equivocal.
Abstract: It is widely held that the frontal eye field (FEF) in prefrontal cortex (PFC) modulates processing in visual cortex with attention, although the evidence that it is necessary is equivocal. To help identify critical sources of attentional feedback to area V4, we surgically removed the entire lateral PFC, including the FEF, in one hemisphere and transected the corpus callosum and anterior commissure in two macaques. This deprived V4 of PFC input in one hemisphere while keeping the other hemisphere intact. In the absence of PFC, attentional effects on neuronal responses and synchrony in V4 were substantially reduced and the remaining effects of attention were delayed in time, indicating a critical role for PFC. Conversely, distracters captured attention and influenced V4 responses. However, because the effects of attention in V4 were not eliminated by PFC lesions, other sources of top-down attentional control signals to visual cortex must exist outside of PFC.
166 citations
TL;DR: Empirical results demonstrate that the proposed novel ensemble learning paradigm statistically outperforms all considered benchmark models in both prediction accuracy and effectiveness and is a promising tool to predict complicated time series with high volatility and irregularity.
166 citations
Cites methods from "The empirical mode decomposition an..."
...Since the seminal works of Wu and Huang, (2009) and Huang et al. (1998) were published, EMD and EEMD have widely been applied to various complex system analyses, and the results indicated the effectiveness of EMD and EEMD in decomposing complex time series data (Zhang et al., 2008; Xie et al.,…...
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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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