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: The experimental results show that the proposed CEEMDAN-XGBOOST outperforms some state-of-the-art models in terms of several evaluation metrics.
Abstract: Crude oil is one of the most important types of energy for the global economy, and hence it is very attractive to understand the movement of crude oil prices. However, the sequences of crude oil prices usually show some characteristics of nonstationarity and nonlinearity, making it very challenging for accurate forecasting crude oil prices. To cope with this issue, in this paper, we propose a novel approach that integrates complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and extreme gradient boosting (XGBOOST), so-called CEEMDAN-XGBOOST, for forecasting crude oil prices. Firstly, we use CEEMDAN to decompose the nonstationary and nonlinear sequences of crude oil prices into several intrinsic mode functions (IMFs) and one residue. Secondly, XGBOOST is used to predict each IMF and the residue individually. Finally, the corresponding prediction results of each IMF and the residue are aggregated as the final forecasting results. To demonstrate the performance of the proposed approach, we conduct extensive experiments on the West Texas Intermediate (WTI) crude oil prices. The experimental results show that the proposed CEEMDAN-XGBOOST outperforms some state-of-the-art models in terms of several evaluation metrics.
93 citations
TL;DR: A computational method, Phaser, for estimating the phase of phase-locked oscillators from limited amounts of multivariate data in the presence of noise and measurement errors is presented.
Abstract: The state of a collection of phase-locked oscillators is determined by a single phase variable or cyclic coordinate. This paper presents a computational method, Phaser, for estimating the phase of phase-locked oscillators from limited amounts of multivariate data in the presence of noise and measurement errors. Measurements are assumed to be a collection of multidimensional time series. Each series consists of several cycles of the same or similar systems. The oscillators within each system are not assumed to be identical. Using measurements of the noise covariance for the multivariate input, data from the individual oscillators in the system are combined to reduce the variance of phase estimates for the whole system. The efficacy of the algorithm is demonstrated on experimental and model data from biomechanics of cockroach running and on simulated oscillators with varying levels of noise.
93 citations
TL;DR: The energy-based damage index demonstrates a more effective approach in detecting the damage compared to those based on IA and unwrapped phase parameters.
Abstract: Vibrations of complex structures such as bridges mostly present nonlinear and non-stationary behaviors. Recently, one of the most common techniques to analyze the nonlinear and non-stationary structural response is Hilbert-Huang Transform (HHT). This paper aims to evaluate the performance of HHT based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) technique using an Artificial Neural Network (ANN) as a proposed damage detection methodology. The performance of the proposed method is investigated for damage detection of a scaled steel-truss bridge model which was experimentally established as the case study subjected to white noise excitations. To this end, four key features of the intrinsic mode function (IMF), including energy, instantaneous amplitude (IA), unwrapped phase, and instantaneous frequency (IF), are extracted to assess the presence, severity, and location of the damage. By analyzing the experimental results through different damage indices defined based on the extracted features, the capabilities of the CEEMDAN-HT-ANN model in detecting, addressing the location and classifying the severity of damage are efficiently concluded. In addition, the energy-based damage index demonstrates a more effective approach in detecting the damage compared to those based on IA and unwrapped phase parameters.
93 citations
TL;DR: The experimental results show that the proposed model performs better than all other considered models without double decomposition, and the variational mode decomposition for error series can improve the effect of error correction strategy.
93 citations
TL;DR: In this paper, a model named EMD-GARCH that integrated empirical mode decomposition (EMD) with generalized autoregressive conditional heteroskedastic (GARCH) together is presented to forecast the carbon price of the five pilots (Shenzhen, Shanghai, Beijing, Guangdong, and Tianjin) in 2016 so as to provide exogenous data for later analysis.
93 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)....
[...]