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Journal ArticleDOI

The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

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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Citations
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Journal ArticleDOI
TL;DR: A nonparametric technique called empirical mode decomposition trend filtering is developed, based on an empirical analysis of the EMD, and an automatic procedure for selecting the requisite intrinsic mode functions is proposed.

97 citations


Cites background or methods from "The empirical mode decomposition an..."

  • ...It is philosophically similar to the “low-frequency approach” described in the preceding paragraph....

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  • ...Other approaches exist which do not impose such a strict model on the trend....

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  • ...(5) If h is not an IMF, in the sense that it does not satisfy the two requirements described in the beginning of this section, then increment i and go to step (1) with ρi−1 = h. (Huang et al. (1998) call this the sifting process ; it is this process which depends on the stopping criterion.)...

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  • ...Recall (Huang et al., 1998) that the EMD is an algorithm which decomposes a time series into a finite additive superposition of “intrinsic mode functions,” or IMFs....

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  • ...An obvious initial barrier to solving the trend filtering problem is that the terms “decomposition,” “trend,” and “fluctuation” are context-dependent....

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Journal ArticleDOI
TL;DR: An extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, is presented to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space and it seems that Hilbert and DFA methods provide better singularity spectra than SF and WL.
Abstract: In this paper we present an extended version of Hilbert-Huang transform, namely arbitrary-order Hilbert spectral analysis, to characterize the scale-invariant properties of a time series directly in an amplitude-frequency space. We first show numerically that due to a nonlinear distortion, traditional methods require high-order harmonic components to represent nonlinear processes, except for the Hilbert-based method. This will lead to an artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus the power law, if it exists, is contaminated. We then compare the Hilbert method with structure functions (SF), detrended fluctuation analysis (DFA), and wavelet leader (WL) by analyzing fractional Brownian motion and synthesized multifractal time series. For the former simulation, we find that all methods provide comparable results. For the latter simulation, we perform simulations with an intermittent parameter $\ensuremath{\mu}=0.15$. We find that the SF underestimates scaling exponent when $qg3$. The Hilbert method provides a slight underestimation when $qg5$. However, both DFA and WL overestimate the scaling exponents when $qg5$. It seems that Hilbert and DFA methods provide better singularity spectra than SF and WL. We finally apply all methods to a passive scalar (temperature) data obtained from a jet experiment with a Taylor's microscale Reynolds number Re${}_{\ensuremath{\lambda}}\ensuremath{\simeq}250$. Due to the presence of strong ramp-cliff structures, the SF fails to detect the power law behavior. For the traditional method, the ramp-cliff structure causes a serious artificial energy flux from the low-frequency (large scale) to the high-frequency (small scale) part. Thus DFA and WL underestimate the scaling exponents. However, the Hilbert method provides scaling exponents ${\ensuremath{\xi}}_{\ensuremath{\theta}}(q)$ quite close to the one for longitudinal velocity, indicating a less intermittent passive scalar field than what was believed before.

97 citations

Journal ArticleDOI
TL;DR: In this paper, an artificial neural network (ANN) and empirical mode decomposition (EMD) based condition monitoring approach of a wind turbine using Simulink, FAST (fatigue, aerodynamics, structures and turbulence) and TurbSim is presented.
Abstract: In this study, an artificial neural network (ANN) and empirical mode decomposition (EMD) based condition monitoring approach of a wind turbine using Simulink, FAST (fatigue, aerodynamics, structures and turbulence) and TurbSim is presented. The complete dynamics of a permanent magnet synchronous generator (PMSG) based wind turbine [i.e. wind turbine generator (WTG)] model is simulated in an amalgamated domain of Simulink, FAST and TurbSim under six distinct conditions, i.e. aerodynamic asymmetry, rotor-furl imbalance, tail-furl imbalance, blade imbalance, nacelle-yaw imbalance and normal operating scenarios. The simulation results in time domain of the PMSG output stator current are decomposed into the intrinsic mode functions using EMD method then RapidMiner-based principal component analysis method is used to select most relevant input variables. An ANN model is then proposed to differentiate the normal operating scenarios from five fault conditions. The analysed results proclaim the effectiveness of the proposed approach to identify the different imbalance faults in WTG. The presented work renders initial results that are helpful for online condition monitoring and health assessment of WTG.

97 citations

Journal ArticleDOI
TL;DR: In this paper, a joint amplitude and frequency demodulation method is proposed for fault diagnosis of planetary gearboxes by matching the dominant peaks in the envelope spectrum and the spectrum of instantaneous frequency with the theoretical characteristic frequencies of faulty gears.

97 citations

Journal ArticleDOI
TL;DR: Li et al. as mentioned in this paper proposed a novel hybrid model to address the issues of predictive stability and poor initial parameters, which significantly affected the air pollution prediction performance, and a new multi-objective Harris hawks optimization algorithm was developed to tune the parameters of the extreme learning machine (ELM) model with high forecasting accuracy and stability for prediction air pollution.

97 citations

References
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Journal ArticleDOI
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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Journal ArticleDOI
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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