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 proposed approach to intelligent fault diagnosis based on statistics analysis, an improved distance evaluation technique and adaptive neuro-fuzzy inference system (ANFIS) can reliably recognise different fault categories and severities.
Abstract: This paper presents a new approach to intelligent fault diagnosis based on statistics analysis, an improved distance evaluation technique and adaptive neuro-fuzzy inference system (ANFIS). The approach consists of three stages. First, different features, including time-domain statistical characteristics, frequency-domain statistical characteristics and empirical mode decomposition (EMD) energy entropies, are extracted to acquire more fault characteristic information. Second, an improved distance evaluation technique is proposed, and with it, the most superior features are selected from the original feature set. Finally, the most superior features are fed into ANFIS to identify different abnormal cases. The proposed approach is applied to fault diagnosis of rolling element bearings, and testing results show that the proposed approach can reliably recognise different fault categories and severities. Moreover, the effectiveness of the proposed feature selection method is also demonstrated by the testing results.
350 citations
Cites methods from "The empirical mode decomposition an..."
...To extract more information, each of these vibration signals is decomposed via the EMD method (Huang et al., 1998)....
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TL;DR: New features based on the 2D and 3D PSRs of IMFs have been proposed for classification of epileptic seizure and seizure-free EEG signals.
Abstract: We propose new features for classification of epileptic seizure EEG signals.Features were extracted from PSR of IMFs of EEG signals.We define ellipse area of 2D PSR and IQR of Euclidian distance of 3D PSR as features.LS-SVM classifier has been used for classification with the proposed features.Results were compared with other existing methods studied on the same EEG dataset. Epileptic seizure is the most common disorder of human brain, which is generally detected from electroencephalogram (EEG) signals. In this paper, we have proposed the new features based on the phase space representation (PSR) for classification of epileptic seizure and seizure-free EEG signals. The EEG signals are firstly decomposed using empirical mode decomposition (EMD) and phase space has been reconstructed for obtained intrinsic mode functions (IMFs). For the purpose of classification of epileptic seizure and seizure-free EEG signals, two-dimensional (2D) and three-dimensional (3D) PSRs have been used. New features based on the 2D and 3D PSRs of IMFs have been proposed for classification of epileptic seizure and seizure-free EEG signals. Two measures have been defined namely, 95% confidence ellipse area for 2D PSR and interquartile range (IQR) of the Euclidian distances for 3D PSR of IMFs of EEG signals. These measured parameters show significant difference between epileptic seizure and seizure-free EEG signals. The combination of these measured parameters for different IMFs has been utilized to form the feature set for classification of epileptic seizure EEG signals. Least squares support vector machine (LS-SVM) has been employed for classification of epileptic seizure and seizure-free EEG signals, and its classification performance has been evaluated using different kernels namely, radial basis function (RBF), Mexican hat wavelet and Morlet wavelet kernels. Simulation results with various performance parameters of classifier, have been included to show the effectiveness of the proposed method for classification of epileptic seizure and seizure-free EEG signals.
349 citations
TL;DR: The biggest challenge in realization of health monitoring of large real-life structures is automated detection of damage out of the huge amount of very noisy data collected from dozens of sensors on a daily, weekly, and monthly basis.
Abstract: Signal processing is the key component of any vibration-based structural health monitoring (SHM). The goal of signal processing is to extract subtle changes in the vibration signals in order to detect, locate and quantify the damage and its severity in the structure. This paper presents a state-of-the-art review of recent articles on signal processing techniques for vibration-based SHM. The focus is on civil structures including buildings and bridges. The paper also presents new signal processing techniques proposed in the past few years as potential candidates for future SHM research. The biggest challenge in realization of health monitoring of large real-life structures is automated detection of damage out of the huge amount of very noisy data collected from dozens of sensors on a daily, weekly, and monthly basis. The new methodologies for on-line SHM should handle noisy data effectively, and be accurate, scalable, portable, and efficient computationally.
349 citations
TL;DR: Two hybrid forecasting models are proposed in this paper which combine the two kinds of empirical mode decomposition (EMD) with the long short-term memory (LSTM) with a better performance in one-step-ahead forecasting of financial time series.
Abstract: In order to improve the accuracy of the stock market prices forecasting, two hybrid forecasting models are proposed in this paper which combine the two kinds of empirical mode decomposition (EMD) with the long short-term memory (LSTM). The financial time series is a kind of non-linear and non-stationary random signal, which can be decomposed into several intrinsic mode functions of different time scales by the original EMD and the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). To ensure the effect of historical data onto the prediction result, the LSTM prediction models are established for all each characteristic series from EMD and CEEMDAN deposition. The final prediction results are obtained by reconstructing each prediction series. The forecasting performance of the proposed models is verified by linear regression analysis of the major global stock market indices. Compared with single LSTM model, support vector machine (SVM), multi-layer perceptron (MLP) and other hybrid models, the experimental results show that the proposed models display a better performance in one-step-ahead forecasting of financial time series.
346 citations
TL;DR: Two new post-transformations for the short-time Fourier transform that achieve a compact time-frequency representation while allowing for the separation and the reconstruction of the modes are introduced.
Abstract: This paper considers the analysis of multicomponent signals, defined as superpositions of real or complex modulated waves. It introduces two new post-transformations for the short-time Fourier transform that achieve a compact time-frequency representation while allowing for the separation and the reconstruction of the modes. These two new transformations thus benefit from both the synchrosqueezing transform (which allows for reconstruction) and the reassignment method (which achieves a compact time-frequency representation). Numerical experiments on real and synthetic signals demonstrate the efficiency of these new transformations, and illustrate their differences.
345 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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