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
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TL;DR: In this paper, the complementary EEMD (CEEMD) is used for bearing fault detection, which not only overcomes the mode mixing, but also eliminates the residual of added white noise persisting into the IMFs and enhances the calculation efficiency.
108 citations
TL;DR: A hybrid prediction model that integrates an improved whale swarm algorithm (IWOA) and relevance vector machine (RVM) and empirical mode decomposition (EMD), approximate entropy (ApEn), and C-C method are introduced to aid the calculation.
Abstract: Accurate short-term prediction of the natural gas load is of great significance to the operation and allocation of the pipeline network. Because the short-term natural gas load has obvious nonlinearity and randomness, the traditional regression model is difficult to predict accurately. Therefore, this paper proposes a hybrid prediction model that integrates an improved whale swarm algorithm (IWOA) and relevance vector machine (RVM). In addition, empirical mode decomposition (EMD), approximate entropy (ApEn), and C-C method are introduced to aid the calculation. In this paper, the IWOA is used to test the four functions and compared with the other five algorithms. The results show that the convergence accuracy and convergence speed of the new algorithm are higher than other algorithms, indicating that it has better global optimization ability. Second, the IWOA-RVM model is used to predict the supply data of two natural gas stations in Anhui Province, China. The prediction results are compared with the five algorithms including RBFNN, GRNN, ELMANNN, LSSVM, and SMOSVM. The results show that: 1) through the test of four functions, IWOA has better ability to jump out of local optimum, has higher optimization performance, and the calculation speed is at a medium level and 2) compared with other models, the IOWA-RVM model has higher prediction accuracy when the amount of data is larger or smaller, but the calculation time is relatively long, but the calculation time is acceptable in engineering.
108 citations
Cites methods from "The empirical mode decomposition an..."
...Its related theory and implementation methods are shown in the literature [31]....
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TL;DR: In this article, the authors proposed a new method for bridge damage detection using the response measured in a passing vehicle, which includes three main components; vehicle frequency, bridge natural frequency and a vehicle speed pseudo-frequency component.
Abstract: A new method is proposed in this paper for bridge damage detection using the response measured in a passing vehicle. It is shown theoretically that such a response includes three main components; vehicle frequency, bridge natural frequency and a vehicle speed pseudo-frequency component. The Empirical Mode Decomposition (EMD) method is used to decompose the signal into its main components. A damage detection method is proposed using the Intrinsic Mode Functions (IMFs) corresponding to the vehicle speed component of the response measured on the passing vehicle. Numerical case studies using Finite Element modelling of Vehicle Bridge Interaction are used to show the performance of the proposed method. It is demonstrated that it can successfully localise the damage location in the absence of road profile. A difference in the acceleration signals of healthy and corresponding damaged structures is used to identify the damage location in the presence of a road profile. The performance of the method for changes in the transverse position of the vehicle on the bridge is also studied.
108 citations
Cites methods from "The empirical mode decomposition an..."
...Empirical Mode Decomposition (EMD) The EMD method (Huang et al., 1999; Huang et al., 1998) is a new signal processing tool which decomposes any signal, non-stationary or even nonlinear, into several so-called Intrinsic Mode Functions (IMFs)....
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TL;DR: In this paper, empirical mode decomposition (EMD) was used to identify the natural frequencies and modal damping ratios of the Tsing Ma suspension bridge during Typhoon Victor using the newly emerged EMD method in conjunction with the Hilbert transform technique.
108 citations
TL;DR: A comparative study of the modal parameter identification of structures based on the continuous wavelet transform (WT) using the modified complex Morlet wavelet function and the improved Hilbert–Huang transform to demonstrate that both methods are applicable for the system with well-separated modes when the time-frequency resolutions are sufficiently taken into account.
Abstract: Modal parameter identification is an important topic in vibration-based structural health monitoring. This paper presents a comparative study of the modal parameter identification of structures based on the continuous wavelet transform (WT) using the modified complex Morlet wavelet function and the improved Hilbert–Huang transform (HHT). Special attention is given to some implementation issues, such as the modal separation and end effect in the WT, the optimal parameter selection of the wavelet function, the new stopping criterion for the empirical mode decomposition and the end effect in the HHT. The capabilities of these two techniques are compared and assessed by using three examples: a numerical simulation for a damped system with two very close modes; an impact test on an experimental model with three well-separated modes; and an ambient vibration test on the Z24-bridge benchmark problem. The results demonstrate that both methods are applicable for the system with well-separated modes when the time-frequency resolutions are sufficiently taken into account. For the system with very close modes, the WT method seems to be more effective than HHT. One reason is that the frequency separation of HHT is partially dependent on the decomposition performance of the preprocess tool. Therefore, if the adjacent frequency components are very close, it is difficult to design appropriate parameters for the filters to separate them clearly.
108 citations
Cites background or methods from "The empirical mode decomposition an..."
...Hence, in some sense, our proposed method, although requiring time-consuming work, seems to be more theoretical than the methods of Huang et al. (1998) and Rilling et al. (2003)....
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...The EMD method, as the key ingredient in the HHT, is first summarized after Huang et al. (1998)....
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...The HHT method proposed by Huang et al. (1998) performs a time adaptive decomposition operation termed empirical mode decomposition to decouple the signal into a finite number of intrinsic mode functions (IMF), and then the Hilbert transform is applied to each IMF to obtain the time–frequency…...
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...As proposed by Huang et al. (1998), in the implementation of a sifting process on a signal x(t), one of the steps is to interpolate the local extrema and minima by cubic spline to form upper envelope emax(t), lower envelope emin(t), and their mean m(t) = (emax(t) + emin(t))/2....
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...The SD proposed by Huang et al. (1998) was commonly used although the numerical simulations indicated that it was too stringent, requiring many siftings and excessive computing time....
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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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