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 resonance-based signal decomposition algorithm presented in this paper utilizes sparse signal representations, morphological component analysis, and constant-Q (wavelet) transforms with adjustable Q-factor.
204 citations
Cites background from "The empirical mode decomposition an..."
...Empirical mode decomposition: Empirical mode decomposition (EMD) is another nonlinear signal decomposition [46, 55]....
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TL;DR: In this article, a novel feature extraction method for a user-independent emotion recognition system, namely, HAF-HOC, from electroencephalograms (EEGs), was provided by applying Genetic Algorithms to the empirical mode decomposition based representation of EEG signals.
Abstract: This paper aims at providing a new feature extraction method for a user-independent emotion recognition system, namely, HAF-HOC, from electroencephalograms (EEGs). A novel filtering procedure, namely, Hybrid Adaptive Filtering (HAF), for an efficient extraction of the emotion-related EEG-characteristics was developed by applying Genetic Algorithms to the Empirical Mode Decomposition-based representation of EEG signals. In addition, Higher Order Crossings (HOCs) analysis was employed for feature extraction realization from the HAF-filtered signals. The introduced HAF-HOC scheme incorporated four different classification methods to accomplish a robust emotion recognition performance. Through a series of facial-expression image projection, as a Mirror Neuron System-based emotion elicitation process, EEG data related to six basic emotions (happiness, surprise, anger, fear, disgust, and sadness) have been acquired from 16 healthy subjects using three EEG channels. Experimental results from the application of the HAF-HOC to the collected EEG data and comparison with previous approaches have shown that the HAF-HOC scheme clearly surpasses the latter in the field of emotion recognition from brain signals for the discrimination of up to six distinct emotions, providing higher classification rates up to 85.17 percent. The promising performance of the HAF-HOC surfaces the value of EEG signals within the endeavor of realizing more pragmatic, affective human-machine interfaces.
204 citations
TL;DR: In this article, a variational nonlinear chirp mode decomposition (VNCMD) is proposed to analyze wide-band NCSs, which can be viewed as a time-frequency filter bank, which concurrently extracts all the signal modes.
Abstract: Variational mode decomposition (VMD), a recently introduced method for adaptive data analysis, has aroused much attention in various fields. However, the VMD is formulated based on the assumption of narrow-band property of the signal model. To analyze wide-band nonlinear chirp signals (NCSs), we present an alternative method called variational nonlinear chirp mode decomposition (VNCMD). The VNCMD is developed from the fact that a wideband NCS can be transformed to a narrow-band signal by using demodulation techniques. Our decomposition problem is, thus, formulated as an optimal demodulation problem, which is efficiently solved by the alternating direction method of multipliers. Our method can be viewed as a time–frequency filter bank, which concurrently extracts all the signal modes. Some simulated and real data examples are provided showing the effectiveness of the VNCMD in analyzing NCSs containing close or even crossed modes.
204 citations
Cites methods from "The empirical mode decomposition an..."
...Most decomposition methods directly extract each signal mode in the time domain, among which the empirical mode decomposition (EMD) is the most well-known one [6]....
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TL;DR: In this paper, a technique based on a recent enhancement on wavelets known as complex wavelets is proposed for identifying multiple faults in vector controlled induction motor drives (VCIMDs).
Abstract: Embedded variable frequency induction motor drives are now an integral part of any industry due to their improved speed regulation and fast dynamic response. Hence, their diagnosis becomes vital to avoid downtimes and economic losses. In this paper, a technique based on a recent enhancement on wavelets, known as complex wavelets, is proposed for identifying multiple faults in vector controlled induction motor drives (VCIMDs). Radial, axial, and tangential vibrations are analyzed for diagnostic purpose. Initially, a relatively simple thresholding based method is investigated for feasibility of diagnosis under variable frequency and load conditions. In the second part, the feature extraction and classifier modeling are discussed, in which the nearly shift-invariant complex wavelet based model is compared with the discrete wavelet transform (DWT) for its applicability in detecting multiple faults. The fault conditions considered here are the most prominent ones such as interturn fault, interturn fault under progression, and bearing damage. Comparable performances of support vector machine (SVM) based models and simple technique based on k-nearest neighbor (k-NN) show the importance of efficient representation of input space by analytical wavelet based feature extraction. The performance indexes show the applicability of the scheme for industrial drives under variable frequencies and load conditions.
202 citations
Cites result from "The empirical mode decomposition an..."
...The proposed technique is nearly shift-insensitive, in comparison to the standard discrete wavelet transform (DWT) [3], [23]–[26] or other time-frequency based analysis methods [27], [28]....
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01 Jan 2014
TL;DR: This study characterize each of the 156 sustained vowel /a/ phonations with 309 dysphonia measures, select a parsimonious subset using a robust feature selection algorithm, and automatically distinguish the two cohorts (acceptable versus unacceptable) with about 90% overall accuracy.
Abstract: Vocal performance degradation is a common symptom for the vast majority of Parkinson's disease (PD) subjects, who typically follow personalized one-to-one periodic rehabilitation meetings with speech experts over a long-term period. Recently, a novel computer program called Lee Silverman voice treatment (LSVT) Companion was developed to allow PD subjects to independently progress through a rehabilitative treatment session. This study is part of the assessment of the LSVT Companion, aiming to investigate the potential of using sustained vowel phonations towards objectively and automatically replicating the speech experts' assessments of PD subjects' voices as “acceptable” (a clinician would allow persisting during in-person rehabilitation treatment) or “unacceptable” (a clinician would not allow persisting during in-person rehabilitation treatment). We characterize each of the 156 sustained vowel /a/ phonations with 309 dysphonia measures, select a parsimonious subset using a robust feature selection algorithm, and automatically distinguish the two cohorts (acceptable versus unacceptable) with about 90% overall accuracy. Moreover, we illustrate the potential of the proposed methodology as a probabilistic decision support tool to speech experts to assess a phonation as “acceptable” or “unacceptable.” We envisage the findings of this study being a first step towards improving the effectiveness of an automated rehabilitative speech assessment tool.
202 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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