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...
Citations
More filters
TL;DR: This article aims to unpack the theoretical background for an analytical method allowing rigorous test of interactivity in a variety of empirical settings and describes a direct estimation method for computing the multifractal spectrum.
Abstract: Interactivity is a central theme of ecological psychology. According to Gibsonian views, behavior is the emergent property of interactions between organism and environment. Hence, an important challenge for ecological psychology has been to identify physical principles that provide an empirical window into interactivity. We suspect that multifractality, a concept from statistical physics, may be helpful in this regard, and we offer this article as a tutorial on multifractality with 2 main goals. First, we aim to describe multifractality with a series of simple, concrete, but progressively more elaborate examples that will incrementally elucidate the relationship between multifractality and interactivity. Second, we aim to describe a direct estimation method for computing the multifractal spectrum (e.g., Chhabra & Jensen, 1989), presenting it as an alternative that avoids the pitfalls of more popular methods and that may address more appropriately the measurements traditionally taken by ecological psycholo...
118 citations
TL;DR: EMD is utilized in this paper to improve hyperspectral-image-classification accuracy by effectively exploiting the feature that EMD performs a decomposition that is spatially adaptive with respect to intrinsic features.
Abstract: This paper presents the utilization of empirical mode decomposition (EMD) of hyperspectral images to increase the classification accuracy using support vector machine (SVM)-based classification. EMD has been shown in the literature to be particularly suitable for nonlinear and nonstationary signals and is used in this paper to decompose hyperspectral image bands into several intrinsic mode functions (IMFs) and a final residue. EMD is utilized in this paper to improve hyperspectral-image-classification accuracy by effectively exploiting the feature that EMD performs a decomposition that is spatially adaptive with respect to intrinsic features. This paper presents two different approaches for improved hyperspectral image classification making use of EMD. In the first approach, IMFs corresponding to each hyperspectral image band are obtained and the sums of lower order IMFs are used as new features for classification with SVM. In the second approach, the pieces of information contained in the first and second IMFs of each hyperspectral image band are combined using composite kernels for SVM classification with higher accuracy.
118 citations
Cites background or methods from "The empirical mode decomposition an..."
...In this paper, it is proposed to use EMD to obtain the IMFs of hyperspectral image bands and to use these IMFs in the classification step to provide increased classification accuracy....
[...]
...Table II shows the NoS used for the DC Mall data for all classes used in the experiments....
[...]
...It is seen that the lower order IMFs such as the first and second IMFs are much more structured and reflect the spatial structural content of the image and that higher order IMFs have a rather low-pass characteristic and lack local spatial structure....
[...]
TL;DR: The proposed method has provided detection of focal temporal lobe epilepsy with increased accuracy and has been compared to the existing methods for detecting focalporal lobe epilepsy from intracranial EEG signals.
Abstract: Epileptic seizure is generated by abnormal synchronization of neurons of the cerebral cortex of the patients, which is commonly detected by electroencephalograph (EEG) signals. In this paper, the intracranial EEG signals have been used to detect focal temporal lobe epilepsy. This paper presents a new method based on empirical mode decomposition (EMD) of EEG signals for detection of epileptic seizures. The proposed method uses the Hilbert transformation of intrinsic mode functions (IMFs), obtained by EMD process that provides analytic signal representation of IMFs. The instantaneous area measured from the trace of the windowed analytic IMFs of EEG signals provides rules-based detection of focal temporal lobe epilepsy. The experiment results on intracranial EEG signals are included to show the effectiveness of the proposed method for detection of focal temporal lobe epilepsy. The performance evaluation of the proposed method for epileptic seizure detection has performed by computing the sensitivity (SEN), specificity (SPE), positive predictive value (PPV), negative predictive value (NPV) and error rate detection (ERD). The proposed method has been compared to the existing methods for detecting focal temporal lobe epilepsy from intracranial EEG signals. The proposed method has provided detection of focal temporal lobe epilepsy with increased accuracy.
117 citations
TL;DR: In this paper, a large-scale shaking table test was performed to study the dynamic response of slopes parallel to geological bedding (bedding slopes) and slopes that cross-cut geological beds (counter-bedding slope), and the test results showed that the acceleration amplification coefficients increase with increasing elevation and, when the input earthquake amplitude is greater than 0.3 ǫ, both bedding and counter-Bedding slopes begin to show nonlinear dynamic response characteristics.
Abstract: A large-scale shaking table test was performed to study the dynamic response of slopes parallel to geological bedding (bedding slopes) and slopes that cross-cut geological bedding (counter-bedding slopes). The test results show that the acceleration amplification coefficients increase with increasing elevation and, when the input earthquake amplitude is greater than 0.3 g, both bedding and counter-bedding slopes begin to show nonlinear dynamic response characteristics. With increasing elevation, the displacement of the bedding slope surface increases greatly. Conversely, the displacement of the counter-bedding slope surface increases first and then decreases; the slope develops a bulge at the relative elevation of 0.85. The displacement of the bedding slope surface is greater than that of the counter-bedding slope. The counter-bedding slope is more seismically stable compared with the bedding slope. Based on the Hilbert–Huang transform and marginal spectrum theories, the processes that develop dynamic damage of the bedding and counter-bedding slopes are identified. It is shown that the dynamic failure mode of the bedding slope is mainly represented by vertical tensile cracks at the rear of the slope, bedding slide of the strata along the weak intercalation, and rock collapse from the slope crest. However, the dynamic failure mode of the counter-bedding slope is mainly represented by staggered horizontal and vertical fissures, extrusion of the weak intercalation, and breakage at the slope crest.
117 citations
Cites methods from "The empirical mode decomposition an..."
...Huang et al. (1998) proposed a new signal processing method that differs from Fourier transform....
[...]
TL;DR: The results show that the Artificial bee colony takes the least time, while the genetic algorithm takes the longest time, the accuracy of the artificial bee colony algorithm is better than the others.
117 citations
References
More filters
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....
[...]
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)....
[...]
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…...
[...]
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....
[...]
...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)....
[...]