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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01 May 2015
TL;DR: To find a subset of handwriting features suitable for identifying subjects with PD and to build a predictive model to efficiently diagnose PD, handwriting samples were collected from medicated PD patients and age- and sex-matched controls.
Abstract: Parkinson’s disease (PD) is a neurodegenerative disorder which impairs motor skills, speech, and other functions such as behavior, mood, and cognitive processes. One of the most typical clinical hallmarks of PD is handwriting deterioration, usually the first manifestation of PD. The aim of this study is twofold: (a) to find a subset of handwriting features suitable for identifying subjects with PD and (b) to build a predictive model to efficiently diagnose PD. We collected handwriting samples from 37 medicated PD patients and 38 age- and sex-matched controls. The handwriting samples were collected during seven tasks such as writing a syllable, word, or sentence. Every sample was used to extract the handwriting measures. In addition to conventional kinematic and spatio-temporal handwriting measures, we also computed novel handwriting measures based on entropy, signal energy, and empirical mode decomposition of the handwriting signals. The selected features were fed to the support vector machine classifier with radial Gaussian kernel for automated diagnosis. The accuracy of the classification of PD was as high as 88.13%, with the highest values of sensitivity and specificity equal to 89.47% and 91.89%, respectively. Handwriting may be a valuable marker as a diagnostic and screening tool.
122 citations
Cites background from "The empirical mode decomposition an..."
...Each IMF satisfies two basic assumptions [26]: (1) The number of maxima, which are strictly positive, and the number of minima, which are strictly negative, for each IMF, are either equal or differ by no more than one....
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...The motivation for using only the first two IMFs is, that in practice, the first few IMFs contain only time-varying high spectral components representing the noise [9], [26], [27]....
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TL;DR: A novel multimodal signal decomposition and feature extraction strategy is presented to obtain effective features for sub-band signals and a rule-free refinement process based on hidden Markov model (HMM) is proposed to optimize the classification results automatically.
Abstract: Sleep stage classification is a most important process in sleep scoring which is used to evaluate sleep quality and diagnose sleep-related diseases. Compared to complex sleep analysis devices, automatic sleep stage classification methods using single-channel electroencephalography (EEG) records benefit from the convenience of wearing and less interference in the sleep, thus are appropriate for home-based sleep analysis. In these methods, the design of representative features for classification plays the most important role in determining the performance. Previous works have not achieved satisfactory outcomes for ignoring several kinds of effective features. In this work, a novel multimodal signal decomposition and feature extraction strategy is presented to obtain effective features for sub-band signals. Meanwhile, a rule-free refinement process based on hidden Markov model (HMM) is proposed to optimize the classification results automatically. Experimental results show the superior classification performance of the proposed method compared to state-of-the-art works, wherein the rule-free refinement also outperforms previous rule-based correction algorithms. This sleep stage classification method is expected to contribute to the design of home-based sleep monitoring and analyzing system.
121 citations
TL;DR: This paper presents a systematic and up-to-date review on adaptive mode decomposition in two major topics, i.e., mono-component decomposition algorithms and instantaneous frequency estimation approaches reported in more than 80 representative articles published since 1998.
Abstract: Effective signal processing methods are essential for machinery fault diagnosis. Most conventional signal processing methods lack adaptability, thus being unable to well extract the embedded meaningful information. Adaptive mode decomposition methods have excellent adaptability and high flexibility in describing arbitrary complicated signals, and are free from the limitations imposed by conventional basis expansion, thus being able to adapt to the signal characteristics, extract rich characteristic information, and therefore reveal the underlying physical nature. This paper presents a systematic and up-to-date review on adaptive mode decomposition in two major topics, i.e., mono-component decomposition algorithms (such as empirical mode composition, local mean decomposition, intrinsic time-scale decomposition, local characteristic scale decomposition, Hilbert vibration decomposition, empirical wavelet transform, variational mode decomposition, nonlinear mode decomposition, and adaptive local iterative filtering) and instantaneous frequency estimation approaches (including Hilbert-transform-based analytic signal, direct quadrature, and normalized Hilbert transform based on empirical AM-FM decomposition, as well as generalized zero-crossing and energy separation) reported in more than 80 representative articles published since 1998. Their fundamental principles, advantages and disadvantages, and applications to signal analysis in machinery fault diagnosis, are examined. Examples are provided to illustrate their performance.
121 citations
Cites background or methods from "The empirical mode decomposition an..."
...[6], [7] can adaptively decompose a complicated multi-component signal into constituent mono-components....
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...Based on the instantaneous frequency and instantaneous amplitude, a quality time–frequency representation can be constructed as a linear superposition of constituent components’ time–frequency representations, which has high time– frequency resolution and is free from both inner and outer interferences, thus being effective in resolving the frequency contents and their time–frequency structure of arbitrary nonstationary complicated signals [6]–[26]....
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...The decomposition by EMD is complete, adaptive, and almost orthogonal in applications [6]....
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...3, stop the inner sifting loop steps 1-5 [6]....
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...Usually, the aforementioned adaptive mode decomposition algorithms in Section 3 can separate a signal into such mono-components [6]–[26]....
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TL;DR: The results indicate that the proposed emotion recognition method based on empirical mode decomposition (EMD) and sample entropy is more suitable for emotion recognition than several methods of comparison.
121 citations
Cites methods from "The empirical mode decomposition an..."
...Empirical mode decomposition EMD is a data-driven signal processing analysis technique [8]....
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...In recent years, empirical mode decomposition (EMD) method based on Hilbert-Huang transformation is widely used in the field of signal processing [8,9]....
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19 Jan 2012
TL;DR: A new method of lower-limb exoskeleton control aimed at improving the agility of leg-swing motion is presented, which emulates inertia compensation by adding a feedback loop consisting of low-pass filtered angular acceleration multiplied by a negative gain.
Abstract: A new method of lower-limb exoskeleton control aimed at improving the agility of leg-swing motion is presented. In the absence of control, an exoskeleton's mechanism usually hinders agility by adding mechanical impedance to the legs. The uncompensated inertia of the exoskeleton will reduce the natural frequency of leg swing, probably leading to lower step frequency during walking as well as increased metabolic energy consumption. The proposed controller emulates inertia compensation by adding a feedback loop consisting of low-pass filtered angular acceleration multiplied by a negative gain. This gain simulates negative inertia in the low-frequency range. The resulting controller combines two assistive effects: increasing the natural frequency of the lower limbs and performing net work per swing cycle. The controller was tested on a statically mounted exoskeleton that assists knee flexion and extension. Subjects performed movement sequences, first unassisted and then using the exoskeleton, in the context of a computer-based task resembling a race. In the exoskeleton's baseline state, the frequency of leg swing and the mean angular velocity were consistently reduced. The addition of inertia compensation enabled subjects to recover their normal frequency and increase their selected angular velocity. The work performed by the exoskeleton was evidenced by catch trials in the protocol.
121 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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