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: A novel method based on an integration of multiscale logic regression and Gaussian process regression to tackle SOH estimation and prediction problem of Lithium-ion battery and results illustrate the potential applications of the proposed method as an effective tool for battery health prognostics.
161 citations
TL;DR: In this article, the authors developed a method based on combination of empirical-mode decomposition (EMD) and Hilbert transform for assessment of power quality events, which can be conceived as superimposition of various oscillating modes and EMD is used to separate out these intrinsic modes known as intrinsic mode functions.
Abstract: The aim of this paper is to develop a method based on combination of empirical-mode decomposition (EMD) and Hilbert transform for assessment of power quality events. A distorted waveform can be conceived as superimposition of various oscillating modes and EMD is used to separate out these intrinsic modes known as intrinsic mode functions (IMF). Hilbert transform is applied to first three IMF to obtain instantaneous amplitude and phase which are then used for constructing feature vector. The work evaluates the detection capability of the methodolpogy and a comparison with S-transform is made to show the superiority of the technique in detecting the PQ disturbance like voltage spike and notch. A probabilistic neural network is used as a mapping function for identifying the various disturbance classes. Results show a better classification accuracy of the methodology.
161 citations
Cites methods from "The empirical mode decomposition an..."
...Empirical mode decomposition [ 15 ] is basically a sifting process in which different modes of oscillation are sieved out of original signal....
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...(EMD) is a time frequency analysis method developed by Huang et al., [ 15 ] which is based on the local characteristic time scale of signal and decomposes the complicated signals into number of IMFs....
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TL;DR: EMD outperformed the three other algorithms for the denoising of data highly contaminated by muscular activity and suggests that the performance of muscle artifact correction methods strongly depend on the level of data contamination, and of the source configuration underlying EEG signals.
Abstract: Electroencephalographic (EEG) recordings are often contaminated with muscle artifacts. This disturbing myogenic activity not only strongly affects the visual analysis of EEG, but also most surely impairs the results of EEG signal processing tools such as source localization. This article focuses on the particular context of the contamination epileptic signals (interictal spikes) by muscle artifact, as EEG is a key diagnosis tool for this pathology. In this context, our aim was to compare the ability of two stochastic approaches of blind source separation, namely independent component analysis (ICA) and canonical correlation analysis (CCA), and of two deterministic approaches namely empirical mode decomposition (EMD) and wavelet transform (WT) to remove muscle artifacts from EEG signals. To quantitatively compare the performance of these four algorithms, epileptic spike-like EEG signals were simulated from two different source configurations and artificially contaminated with different levels of real EEG-recorded myogenic activity. The efficiency of CCA, ICA, EMD, and WT to correct the muscular artifact was evaluated both by calculating the normalized mean-squared error between denoised and original signals and by comparing the results of source localization obtained from artifact-free as well as noisy signals, before and after artifact correction. Tests on real data recorded in an epileptic patient are also presented. The results obtained in the context of simulations and real data show that EMD outperformed the three other algorithms for the denoising of data highly contaminated by muscular activity. For less noisy data, and when spikes arose from a single cortical source, the myogenic artifact was best corrected with CCA and ICA. Otherwise when spikes originated from two distinct sources, either EMD or ICA offered the most reliable denoising result for highly noisy data, while WT offered the better denoising result for less noisy data. These results suggest that the performance of muscle artifact correction methods strongly depend on the level of data contamination, and of the source configuration underlying EEG signals. Eventually, some insights into the numerical complexity of these four algorithms are given.
160 citations
TL;DR: A novel data-driven fault diagnosis method based on sparse representation and shift-invariant dictionary learning is proposed, which proves the effectiveness and robustness of the proposed method and the comparison with the state-of-the-art method is illustrated.
Abstract: It is always a primary challenge in fault diagnosis of a wind turbine generator to extract fault character information under strong noise and nonstationary condition. As a novel signal processing method, sparse representation shows excellent performance in time–frequency analysis and feature extraction. However, its result is directly influenced by dictionary, whose atoms should be as similar with signal's inner structure as possible. Due to the variability of operation environment and physical structure in industrial systems, the patterns of impulse signals are changing over time, which makes creating a proper dictionary even harder. To solve the problem, a novel data-driven fault diagnosis method based on sparse representation and shift-invariant dictionary learning is proposed. The impulse signals at different locations with the same characteristic can be represented by only one atom through shift operation. Then, the shift-invariant dictionary is generated by taking all the possible shifts of a few short atoms and, consequently, is more applicable to represent long signals that in the same pattern appear periodically. Based on the learnt shift-invariant dictionary, the coefficients obtained can be sparser, with the extracted impulse signal being closer to the real signal. Finally, the time–frequency representation of the impulse component is obtained with consideration of both the Wigner–Ville distribution of every atom and the corresponding sparse coefficient. The excellent performance of different fault diagnoses in a fault simulator and a wind turbine proves the effectiveness and robustness of the proposed method. Meanwhile, the comparison with the state-of-the-art method is illustrated, which highlights the superiority of the proposed method.
159 citations
Cites methods from "The empirical mode decomposition an..."
...For the purpose of reducing maintenance costs and extracting representative features from the complex nonstationary noisy signal, numerous signal processing approaches have been developed for fault diagnosis of electric generators used in wind turbines, such as statistical analysis, Fourier transform [15], wavelet transform [16], [17], Hilbert–Huang transform [18], and empirical mode decomposition [19], [20]....
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TL;DR: Empirical results demonstrate that the novel hybrid ensemble learning paradigm can outperform some other popular forecasting models in both level prediction and directional forecasting, indicating that it is a promising tool to predict complex time series with high volatility and irregularity.
159 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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