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, an integrated anomaly detection approach for seeded bearing faults is presented, in which the Empirical Mode Decomposition and the Hilbert Huang transform are employed for the extraction of a compact feature set.
128 citations
Cites background or methods from "The empirical mode decomposition an..."
...[6] is another time–frequency tool, which has found growing applications in various fields....
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...Nowadays, EMD is a state-of-the-art signal processing method [6] that has been successfully employed in a number of fault detection studies in electrical [14] and mechanical systems [7–13]....
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...Cauchy type criterion [6,16], S-number criterion [17], fixed sifting time criterion [18], mean value criterion [19], orthogonality criterion [20], bandwidth criterion [21], the energy difference tracking method [22], etc)....
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...[6] in 1998 bridge this gap between theory and real life....
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TL;DR: In this paper, a torsional vibration signal analysis of planetary gearboxes is proposed to diagnose a single gear fault of a planetary gearbox, which can also be generalized to detect and locate multiple gear faults.
128 citations
TL;DR: A novel hybrid deep learning model is presented, which combines the VMD (variational mode decomposition) method and the LSTM (long short-term memory) network to construct a forecasting model, which has superior performance for non-ferrous metals price forecasting.
Abstract: Non-ferrous metals are indispensable industrial materials and strategic supports of national economic development. The price forecasting of non-ferrous metals is critical for investors, policymakers, and researchers. Nevertheless, an accurate and robust non-ferrous metals price forecasting is a difficult yet challenging problem due to severe fluctuations and irregular cycles in the metal price evolution. Motivated by the ”Divide-and-Conquer” principle, we present a novel hybrid deep learning model, which combines the VMD (variational mode decomposition) method and the LSTM (long short-term memory) network to construct a forecasting model in this paper. Here, the VMD method is firstly employed to disassemble the original price series into several components. The LSTM network is used to forecast for each component. Lastly, the forecasting results of each component are aggregated to formulate an ultimate forecasting output for the original price series. To investigate the forecasting performance of the proposed model, extensive experiments have been executed using the LME (London Metal Exchange) daily future prices of Zinc, Copper and Aluminum, and other six state-of-the-art methods are included for comparison. The experiment results demonstrate that the proposed model has superior performance for non-ferrous metals price forecasting.
128 citations
TL;DR: Application results indicate that the proposed hybrid forecasting approach performs well in terms of prediction accuracy and is especially suitable for short-term HSR passenger flow forecasting.
Abstract: Short-term forecasting of high-speed rail (HSR) passenger flow provides daily ridership estimates that account for day-to-day demand variations in the near future (e.g., next week, next month). It is one of the most critical tasks in high-speed passenger rail planning, operational decision-making and dynamic operation adjustment. An accurate short-term HSR demand prediction provides a basis for effective rail revenue management. In this paper, a hybrid short-term demand forecasting approach is developed by combining the ensemble empirical mode decomposition (EEMD) and grey support vector machine (GSVM) models. There are three steps in this hybrid forecasting approach: (i) decompose short-term passenger flow data with noises into a number of intrinsic mode functions (IMFs) and a trend term; (ii) predict each IMF using GSVM calibrated by the particle swarm optimization (PSO); (iii) reconstruct the refined IMF components to produce the final predicted daily HSR passenger flow, where the PSO is also applied to achieve the optimal refactoring combination. This innovative hybrid approach is demonstrated with three typical origin–destination pairs along the Wuhan-Guangzhou HSR in China. Mean absolute percentage errors of the EEMD-GSVM predictions using testing sets are 6.7%, 5.1% and 6.5%, respectively, which are much lower than those of two existing forecasting approaches (support vector machine and autoregressive integrated moving average). Application results indicate that the proposed hybrid forecasting approach performs well in terms of prediction accuracy and is especially suitable for short-term HSR passenger flow forecasting.
128 citations
TL;DR: The study signifies the important role of the self-adaptive multi-resolution utility (CEEMDAN) hybridized with the ELM algorithm to potentially develop automated prediction systems for forecasting soil moisture, with potential applications in agriculture.
128 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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