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: In this article, the authors use Hilbert spectral analysis to visualize and characterize nonlinear oscillations from synchronized wide-area measurements, which has the potential to be applied for real-time, wide area monitoring and analysis.
Abstract: Characterization of the dynamic phenomena that arise when the system is subjected to a perturbation is important in real-time power system monitoring and analysis. This paper discusses the use of Hilbert spectral analysis to visualize and characterize nonlinear oscillations from synchronized wide-area measurements. The method has the potential to be applied for real-time, wide-area monitoring and analysis. As an illustrative example, synchronized phasor measurements of a real event in northern Mexico are used to examine the potential usefulness of nonlinear time series analysis techniques to characterize the time evolution of nonlinear, nonstationary oscillations and to determine the nature and propagation of the system disturbance. The proposed approach is also compared with Prony analysis
110 citations
Cites background or methods from "The empirical mode decomposition an..."
...For a background on the numerical aspects of the method, see [6] and [8]....
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...Note that the first IMF captures the highest frequency content; the frequency content then decreases with the increase in IMF [6], [8]....
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...The approach in [6]–[8] was used to investigate the temporal characteristics of measured data....
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...2) Computation of Analytic Signals: The above procedure allows the definition of uniquely defined time-varying quantities using the notion of an analytic signal [6]....
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TL;DR: By using independent component analysis (ICA) and multivariate empirical mode decomposition (MEMD), the ICA-based MEMD method was proposed to remove EOG artifacts (EOAs) from multichannel EEG signals and preserve useful EEG information with little loss.
Abstract: The recorded electroencephalography (EEG) signals are usually contaminated by electrooculography (EOG) artifacts. In this paper, by using independent component analysis (ICA) and multivariate empirical mode decomposition (MEMD), the ICA-based MEMD method was proposed to remove EOG artifacts (EOAs) from multichannel EEG signals. First, the EEG signals were decomposed by the MEMD into multiple multivariate intrinsic mode functions (MIMFs). The EOG-related components were then extracted by reconstructing the MIMFs corresponding to EOAs. After performing the ICA of EOG-related signals, the EOG-linked independent components were distinguished and rejected. Finally, the clean EEG signals were reconstructed by implementing the inverse transform of ICA and MEMD. The results of simulated and real data suggested that the proposed method could successfully eliminate EOAs from EEG signals and preserve useful EEG information with little loss. By comparing with other existing techniques, the proposed method achieved much improvement in terms of the increase of signal-to-noise and the decrease of mean square error after removing EOAs.
110 citations
Cites methods from "The empirical mode decomposition an..."
...In order to remove this limitation, the EMD method was extended to the MEMD method which can simultaneously decompose multichannel of signals into multiple paired IMFs within the same frequency bands [20]....
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...Subsequently, some investigators introduce the techniques based on the combination of wavelet transform and ICA for suppression of EOAs in EEG recordings [11]–[13]....
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Proceedings Article•
15 Oct 2012TL;DR: In this article, the multifractal detrended fluctuation analysis (MF-DFA) is applied to uncover the multifractality buried in nonstationary time series for exploring rolling bearing fault data.
Abstract: Vibrations of a defective rolling bearing often exhibit nonstationary and nonlinear characteristics which are submerged in strong noise and interference components. Thus, diagnostic feature extraction is always a challenge and has aroused wide concerns for a long time. In this paper, the multifractal detrended fluctuation analysis (MF-DFA) is applied to uncover the multifractality buried in nonstationary time series for exploring rolling bearing fault data. Subsequently, a new approach for fault diagnosis is proposed based on MF-DFA and Mahalanobis distance criterion. The multifractality of bearing data is estimated with the generalized the Hurst exponent and the multifractal spectrum. Five characteristic parameters which are sensitive to changes of bearing fault conditions are extracted from the spectrum for diagnosis of fault sizes. For benchmarking this new method, the empirical mode decomposition (EMD) method is also employed to analyze the same dataset. The results show that MF-DFA outperforms EMD in revealing the nature of rolling bearing fault data.
110 citations
Additional excerpts
...Nonetheless, when used to analyze complex bearing vibration data, all the previous methods often produce unsatisfactory results because of their own drawbacks [8-10]....
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TL;DR: A robust preprocessing method comprising noise elimination, heartbeat normalization and quality measurement is proposed to eliminate the effects of noise and heart rate variability in a human electrocardiogram identification system based on ensemble empirical mode decomposition (EEMD).
Abstract: In this paper, a human electrocardiogram (ECG) identification system based on ensemble empirical mode decomposition (EEMD) is designed. A robust preprocessing method comprising noise elimination, heartbeat normalization and quality measurement is proposed to eliminate the effects of noise and heart rate variability. The system is independent of the heart rate. The ECG signal is decomposed into a number of intrinsic mode functions (IMFs) and Welch spectral analysis is used to extract the significant heartbeat signal features. Principal component analysis is used reduce the dimensionality of the feature space, and the K-nearest neighbors (K-NN) method is applied as the classifier tool. The proposed human ECG identification system was tested on standard MIT-BIH ECG databases: the ST change database, the long-term ST database, and the PTB database. The system achieved an identification accuracy of 95% for 90 subjects, demonstrating the effectiveness of the proposed method in terms of accuracy and robustness.
110 citations
TL;DR: In this paper, the authors present a review of micro-Doppler based on subject type, sensor capabilities, as well as environmental effects, and then propose future research areas for micro doppler.
Abstract: Micro-Doppler signals refer to Doppler scattering returns produced by the motions of the target other than gross translation. The small micro-motions of a subject, and even just parts of a subject, can be observed through the micro-Doppler signature it creates in response to an active emitter such as a radar, laser, and even acoustic emitters. These micro-Doppler signatures are produced by the kinematic properties of the subject's motion and can be used to extract the salient features of the subject's motion, and often, identify the subject. The rapidly declining cost of micro-Doppler-capable active sensors like radar with their dramatically improving capabilities, provide significant motivation in developing micro-Doppler techniques that can improve the exploitation of these sensors. Micro-Doppler techniques aim at extracting the micro-motion of the subject that may be unique to a particular subject class or activity in order to distinguish probable false alarms from real detections, as well as to increase the value of the information extracted from the sensor. The source of micro-motion depends on the subject and can be a rotating propeller on a fixed-wing aircraft, the multiple spinning rotor blades of a helicopter, or an unmanned aerial vehicle (UAV); the vibrations of an engine shaking a vehicle; an antenna rotating on a ship; the flapping wings of birds; the swinging arms and legs of a walking person; and many other sources. Confuser detections, such as birds for UAVs or animals for humans, can be interpreted as false alarms for a sensor system, so using the available micro-Doppler returns for classification can significantly reduce the sensor false alarm rate, thereby improving the utility of the sensor system. This study reviews the current research in micro-Doppler based on subject type, sensor capabilities, as well as environmental effects, and then proposes future research areas for micro-Doppler.
110 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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