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 time-windowing feature extraction approach based on time-frequency (TF) analysis is adopted here to investigate the time-course of the discrimination between musical appraisal electroencephalogram (EEG) responses, under the parameter of familiarity.
Abstract: A time-windowing feature extraction approach based on time-frequency (TF) analysis is adopted here to investigate the time-course of the discrimination between musical appraisal electroencephalogram (EEG) responses, under the parameter of familiarity. An EEG data set, formed by the responses of nine subjects during music listening, along with self-reported ratings of liking and familiarity, is used. Features are extracted from the beta (13-30 Hz) and gamma (30-49 Hz) EEG bands in time windows of various lengths, by employing three TF distributions (spectrogram, Hilbert-Huang spectrum, and Zhao-Atlas-Marks transform). Subsequently, two classifiers (k-NN and SVM) are used to classify feature vectors in two categories, i.e., "likea and "dislike,a under three cases of familiarity, i.e., regardless of familiarity (LD), familiar music (LDF), and unfamiliar music (LDUF). Key findings show that best classification accuracy (CA) is higher and it is achieved earlier in the LDF case {91.02 ± 1.45% (7.5-10.5 s)} as compared to the LDUF case {87.10 ± 1.84% (10-15 s)}. Additionally, best CAs in LDF and LDUF cases are higher as compared to the general LD case {85.28 ± 0.77%}. The latter results, along with neurophysiological correlates, are further discussed in the context of the existing literature on the time-course of music-induced affective responses and the role of familiarity.
91 citations
Additional excerpts
...Index Terms—Appraisal classification, EEG, familiarity, music, pattern recognition, signal processing Ç...
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TL;DR: In this paper, a review of the recent advances in non-linear non-stationary signal processing algorithms particularly suited for variable speed wind turbines is presented. And the authors make an attempt to review the recent research advances in Non-linear Non-Stable Signal Processing (NLSP) algorithms for vibration analysis.
91 citations
TL;DR: In this article, an empirical mode decomposition (EMD) method was used to decompose the vibration signal into a number of intrinsic mode functions (IMFs) by which the initial feature vector matrices could be formed automatically.
Abstract: Targeting the characteristics that periodic impulses usually occur whilst the rotating machinery exhibits local faults and the limitations of singular value decomposition (SVD) techniques, the SVD technique based on empirical mode decomposition (EMD) is applied to the fault feature extraction of the rotating machinery vibration signals. The EMD method is used to decompose the vibration signal into a number of intrinsic mode functions (IMFs) by which the initial feature vector matrices could be formed automatically. By applying the SVD technique to the initial feature vector matrices, the singular values of matrices could be obtained, which could be used as the fault feature vectors of support vector machines (SVMs) classifier. The analysis results from the gear and roller bearing vibration signals show that the fault diagnosis method based on EMD, SVD and SVM can extract fault features effectively and classify working conditions and fault patterns of gears and roller bearings accurately even when the number of samples is small.
91 citations
91 citations
TL;DR: In this paper, a double layer confining the hot plasma inside a spoke was proposed to explain the presence of very energetic ions in high power impulse magnetron sputtering (HiPIMS) plasmas.
Abstract: High power impulse magnetron sputtering (HiPIMS) plasmas generate energetic metal ions at the substrate as a major difference to conventional direct current magnetron sputtering (dcMS). The origin of these very energetic ions in HiPIMS is still an open issue, which is unravelled using two fast diagnostics: time-resolved mass spectrometry with a temporal resolution of 2 µs and phase resolved optical emission spectroscopy with a temporal resolution of 1 µs. A power scan from dcMS-like to HiPIMS plasmas was performed, with a 2 inch magnetron and a titanium target as sputter source and argon as working gas. Clear differences in the transport as well as the energetic properties of Ar + ,A r 2+ ,T i + and Ti 2+ were observed. For discharges with highest peak power densities a high energetic group of Ti + and Ti 2+ could be identified with energies of approximately 25 eV and of 50 eV, respectively. A cold group of ions was always present. It is found that hot ions are observed only when the plasma enters the spokes regime, which can be monitored by oscillations in the IV characteristics in the MHz range that are picked up by the used VI probes. These oscillations are correlated with the spokes phenomenon and are explained as an amplification of the Hall current inside the spokes as hot ionization zones. To explain the presence of energetic ions, we propose a double layer (DL) confining the hot plasma inside a spoke: if an atom becomes ionized inside the spokes region it is accelerated because of the DL to higher energies whereas its energy remains unchanged if it is ionized outside. In applying this DL model to our measurements the observed phenomena as well as several measurements from other groups can be explained. Only if spokes and a DL are present can the confined particles gain enough energy to leave the magnetic trap. We conclude from our findings that the spoke phenomenon represents the essence of HiPIMS plasmas, explaining their good performance for material synthesis applications.
91 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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