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 paper tends to review the current artifact removal of various contaminations in encephalogram recordings and discusses the characteristics of EEG data and the types of different artifacts.
Abstract: Electroencephalogram (EEG) plays an important role in identifying brain activity and behavior. However, the recorded electrical activity always be contaminated with artifacts and then affect the analysis of EEG signal. Hence, it is essential to develop methods to effectively detect and extract the clean EEG data during encephalogram recordings. Several methods have been proposed to remove artifacts, but the research on artifact removal continues to be an open problem. This paper tends to review the current artifact removal of various contaminations. We first discuss the characteristics of EEG data and the types of different artifacts. Then, a general overview of the state-of-the-art methods and their detail analysis are presented. Lastly, a comparative analysis is provided for choosing a suitable methods according to particular application.
398 citations
Cites methods from "The empirical mode decomposition an..."
...Empirical mode decomposition (EMD) was first discussed in 1998 [70] as a heuristic technique for non-stationary and non-linear signal processing....
[...]
TL;DR: In this paper, the authors used wavelet analysis and envelope detection (ED) to detect bearing failure in a motor-pump driven system, which can detect both periodic and non-periodic signals, allowing the machine operator to more easily detect the remaining types of bearing faults.
Abstract: The components which often fail in a rolling element bearing are the outer-race, the inner-race, the rollers, and the cage. Such failures generate a series of impact vibrations in short time intervals, which occur at Bearing Characteristic Frequencies (BCF). Since BCF contain very little energy, and are usually overwhelmed by noise and higher levels of macro-structural vibrations, they are difficult to find in their frequency spectra when using the common technique of Fast Fourier Transforms (FFT). Therefore, Envelope Detection (ED) is always used with FFT to identify faults occurring at the BCF. However, the computation of ED is complicated, and requires expensive equipment and experienced operators to process. This, coupled with the incapacity of FFT to detect nonstationary signals, makes wavelet analysis a popular alternative for machine fault diagnosis. Wavelet analysis provides multi-resolution in time-frequency distribution for easier detection of abnormal vibration signals. From the results of extensive experiments performed in a series of motor-pump driven systems, the methods of wavelet analysis and FFT with ED are proven to be efficient in detecting some types of bearing faults. Since wavelet analysis can detect both periodic and nonperiodic signals, it allows the machine operator to more easily detect the remaining types of bearing faults which are impossible by the method of FFT with ED. Hence, wavelet analysis is a better fault diagnostic tool for the practice in maintenance.
387 citations
TL;DR: The EEMD is shown to be a vital technique for crude oil price analysis and a substantial improvement of EMD which can better separate the scales naturally by adding white noise series to the original time series and then treating the ensemble averages as the true intrinsic modes.
384 citations
Book•
07 Aug 2013TL;DR: In this article, the authors used satellite passive-microwave observations for 20.2 years (1979-1998) to study the variability of Antarctic sea ice cover and found that small ice increases occur in all seasons with the largest increase during autumn.
Abstract: The principal characteristics of the variability of Antarctic sea ice cover as previously described from satellite passive-microwave observations are also evident in a systematically-calibrated and analyzed data set for 20.2 years (1979-1998). The total Antarctic sea ice extent (concentration > 15 %) increased by 13,440 +/- 4180 sq km/year (+1.18 +/- 0.37%/decade). The area of sea ice within the extent boundary increased by 16,960 +/- 3,840 sq km/year (+1.96 +/- 0.44%/decade). Regionally, the trends in extent are positive in the Weddell Sea (1.5 +/- 0.9%/decade), Pacific Ocean (2.4 +/- 1.4%/decade), and Ross (6.9 +/- 1.1 %/decade) sectors, slightly negative in the Indian Ocean (-1.5 +/- 1.8%/decade, and strongly negative in the Bellingshausen-Amundsen Seas sector (-9.5 +/- 1.5%/decade). For the entire ice pack, small ice increases occur in all seasons with the largest increase during autumn. On a regional basis, the trends differ season to season. During summer and fall, the trends are positive or near zero in all sectors except the Bellingshausen-Amundsen Seas sector. During winter and spring, the trends are negative or near zero in all sectors except the Ross Sea, which has positive trends in all seasons. Components of interannual variability with periods of about 3 to 5 years are regionally large, but tend to counterbalance each other in the total ice pack. The interannual variability of the annual mean sea-ice extent is only 1.6% overall, compared to 5% to 9% in each of five regional sectors. Analysis of the relation between regional sea ice extents and spatially-averaged surface temperatures over the ice pack gives an overall sensitivity between winter ice cover and temperature of -0.7% change in sea ice extent per K. For summer, some regional ice extents vary positively with temperature and others negatively. The observed increase in Antarctic sea ice cover is counter to the observed decreases in the Arctic. It is also qualitatively consistent with the counterintuitive prediction of a global atmospheric-ocean model of increasing sea ice around Antarctica with climate warming due to the stabilizing effects of increased snowfall on the Southern Ocean.
373 citations
TL;DR: A survey of wavelet analysis in economics can be found in this article, where the existing economics and finance literature that utilizes wavelets is surveyed and explored, most using Canadian, US and Finnish industrial production data.
Abstract: Wavelet analysis, although used extensively in disciplines such as signal processing, engineering, medical sciences, physics and astronomy, has not fully entered the economics discipline yet. In this survey article, wavelet analysis is introduced in an intuitive manner, and the existing economics and finance literature that utilizes wavelets is surveyed and explored. Extensive examples of exploratory wavelet analysis are given, most using Canadian, US and Finnish industrial production data. Finally, potential and possible future applications for wavelet analysis in economics are discussed.
373 citations
Cites methods from "The empirical mode decomposition an..."
...A good example might be the empirical mode decomposition (EMD) technique pioneered by Huang et al. (1998), which can applied to both nonlinear and nonstationary time series.23 EMD essentially decomposes a time series into its intrinsic cycles, using the data itself as a basis for mapping cycles of…...
[...]
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)....
[...]