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 computational method derived from basic physics assumptions to quantify time asymmetry over multiple scales is provided and applied to the human heartbeat time series in health and disease and finds that the multiscale time asymmetric index is highest for a time series from young subjects and decreases with aging or heart disease.
Abstract: Time irreversibility, a fundamental property of nonequilibrium systems, should be of importance in assessing the status of physiological processes that operate over a wide range of scales. However, measurement of this property in living systems has been limited. We provide a computational method derived from basic physics assumptions to quantify time asymmetry over multiple scales and apply it to the human heartbeat time series in health and disease. We find that the multiscale time asymmetry index is highest for a time series from young subjects and decreases with aging or heart disease. Loss of time irreversibility may provide a new way of assessing the functionality of living systems that operate far from equilibrium.
202 citations
TL;DR: In this paper, a six-area, 377-machine power system is analyzed to examine the onset of nonlinear, non-stationary behavior and the applicability of the developed procedures to track the evolving dynamics of critical system modes.
Abstract: Hilbert spectral analysis (HSA) is used to characterize the time evolution of non-stationary power system oscillations following large perturbations. Using an analytical procedure based on the Hilbert-Huang Technique (HHT), data from transient stability simulations are decomposed into a finite number of time-varying oscillating components that can be associated with different time scales. Hilbert analysis is then utilized to characterize the time evolution of critical components giving rise to the observed oscillations. The objectives of this study are to obtain information of a quantitative nature on nonlinear processes in power system oscillatory phenomena and assess the applicability of the developed procedures to track the evolving dynamics of critical system modes. A six-area, 377-machine power system is analyzed to examine the onset of nonlinear, non-stationary behavior. Examples of the developed procedures to detect and quantify the strength of nonlinear interaction in power system behavior and to estimate the distribution of the non-stationarity are provided
201 citations
Cites methods from "The empirical mode decomposition an..."
...The EMD method is a technique to decompose an arbitrary signal , into a number of Intrinsic Mode Function (IMF) components with time variable amplitudes and frequencies [6]....
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TL;DR: In this article, the concept of adaptive passive tuned mass dampers (APTMD) is introduced, in which a tuning parameter such as frequency is adjusted passively based on some local mechanical feedback (displacement, velocity, rotation, etc.), but without associated sensing and computer feedback needed in a STMD.
Abstract: SUMMARY Tuned mass dampers (TMD), active mass dampers (AMD) and hybrid mass dampers (HMD) have been widely applied for vibration control of tall buildings and bridges in the past decade. Recently, the author and his coworkers have developed semiactive or smart tuned mass dampers (STMD) using semiactive variable stiffness systems. STMD’s are superior than TMD’s in reducing the response of the primary structure. In case the fundamental frequency of the primary structure changes due to damage or deterioration, then the TMD will be off-tune; hence, it will lose its effectiveness significantly, whereas the STMD is robust against such changes as it is always tuned. The author and his coworkers have shown that STMD can provide performance similar to AMD/HMD, but with an order of magnitude less power consumption. In this paper, new adaptive length pendulum STMD’s are introduced. The concept of adaptive passive tuned mass dampers (APTMD) is introduced. APTMD is a TMD in which a tuning parameter such as frequency is adjusted passively based on some local mechanical feedback (displacement, velocity, rotation, etc.), but without associated sensing and computer feedback needed in a STMD. Also, the concept of STMD is further developed in this paper and practical STMD’s and APTMD’s implementation in USA, Japan, and China is presented. Systems with semiactive variable stiffness devices and STMD/APTMD are linear time varying systems (LTV); hence, algorithms are needed for their identification and control. Recently, the author and his coworkers have developed instantaneous frequency tracking control algorithms. In this paper new system identification algorithms based on time frequency methods, such as Empirical Mode Decomposition (EMD), Hilbert Transform (HT), and short time Fourier transform (STFT), are developed. New real time tuning algorithms that identify the instantaneous frequency of the LTV system and tune the STMD are developed based on EMD, HT, and STFT. Systems with STMD subjected to stationary (harmonic,
199 citations
Cites methods from "The empirical mode decomposition an..."
...A criteria for stopping are accomplished by limiting the standard deviation, SD [41], of hðtÞ, obtained from consecutive sifting results as...
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...These functions are called IMF (denoted by imf i) obtained iteratively (Huang et al. 1998 [41])....
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...The EMD technique, developed by Huang [41], adaptively decomposes a signal into ‘intrinsic mode functions’ (IMF), which can then be converted to analytical signal using HT....
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TL;DR: A novel subject specific multivariate empirical mode decomposition (MEMD) based filtering method, namely, SS-MEMDBF to classify the motor imagery (MI) based EEG signals into multiple classes to obtain enhanced EEG signals which better represent motor imagery related brainwave modulations over μ and β rhythms.
Abstract: A brain-computer interface (BCI) facilitates a medium to translate the human motion intentions using electrical brain activity signals such as electroencephalogram (EEG) into control signals. EEG signals are non-stationary and subject specific. A major challenge in BCI research is to classify human motion intentions from non-stationary EEG signals. We propose a novel subject specific multivariate empirical mode decomposition (MEMD) based filtering method, namely, SS-MEMDBF to classify the motor imagery (MI) based EEG signals into multiple classes. The MEMD method simultaneously decomposes the multichannel EEG signals into a group of multivariate intrinsic mode functions (MIMFs). This decomposition enables us to extract the cross-channel information and also localize the specific frequency information. The MIMFs are considered as narrow-band, amplitude and frequency modulated (AFM) signals. The statistical measure, mean frequency has been used to automatically filter the MIMFs to obtain enhanced EEG signals which better represent motor imagery related brainwave modulations over μ and β rhythms. The sample covariance matrix has been computed and used as a feature set. The feature set has been classified into multiple MI tasks using Riemannian geometry. The proposed method has helped achieve mean Kappa value of 0.60 across nine subjects of the BCI competition IV dataset 2A which is superior to all the reported methods.
199 citations
Cites methods from "The empirical mode decomposition an..."
...Huang et al. (1998) proposed EMD, a single-channel decomposition technique which decomposes the original signal into a group of multivariate IMFs (MIMFs), described as follows: Fig....
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TL;DR: In this article, a modified ensemble empirical mode decomposition (MEEMD) method is proposed to reduce the computational cost of the original EEMD method as well as improving its performance.
198 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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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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