scispace - formally typeset
Search or ask a question
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...

Content maybe subject to copyright    Report

Citations
More filters
Journal ArticleDOI
TL;DR: A new necessary condition on the envelope is presented that questions the current assumption that the envelope passes through the extreme points of an intrinsic mode function (IMF) and presents a solution to the mode-mixing problem that occurs when multicomponent AM-FM signals are separated.
Abstract: Empirical mode decomposition (EMD) is an adaptive and data-driven approach for analyzing multicomponent nonlinear and nonstationary signals. The stop criterion, envelope technique, and mode-mixing problem are the most important topics that need to be addressed in order to improve the EMD algorithm. In this paper, we study the envelope technique and the mode-mixing problem caused by separating multicomponent AM-FM signals with the EMD algorithm. We present a new necessary condition on the envelope that questions the current assumption that the envelope passes through the extreme points of an intrinsic mode function (IMF). Then, we present a solution to the mode-mixing problem that occurs when multicomponent AM-FM signals are separated. We experiment on several signals, including simulated signals and real-life signals, to demonstrate the efficacy of the proposed method in resolving the mode-mixing problem.

142 citations

Journal ArticleDOI
02 May 2014-Energies
TL;DR: In this article, the best Weibull distribution methods for the assessment of wind energy potential at different altitudes in desired locations are statistically diagnosed in a study, and the results show that MOM and MLM are the most efficient methods for determining the value of wind turbine.
Abstract: The best Weibull distribution methods for the assessment of wind energy potential at different altitudes in desired locations are statistically diagnosed in this study. Seven different methods, namely graphical method (GM), method of moments (MOM), standard deviation method (STDM), maximum likelihood method (MLM), power density method (PDM), modified maximum likelihood method (MMLM) and equivalent energy method (EEM) were used to estimate the Weibull parameters and six statistical tools, namely relative percentage of error, root mean square error (RMSE), mean percentage of error, mean absolute percentage of error, chi-square error and analysis of variance were used to precisely rank the methods. The statistical fittings of the measured and calculated wind speed data are assessed for justifying the performance of the methods. The capacity factor and total energy generated by a small model wind turbine is calculated by numerical integration using Trapezoidal sums and Simpson’s rules. The results show that MOM and MLM are the most efficient methods for determining the value of

142 citations

Journal ArticleDOI
TL;DR: A novel time-frequency decomposition approach for analyzing seismic data inspired by the newly developed variational mode decomposition (VMD), which can nonrecursively decompose a multicomponent signal into several quasi-orthogonal intrinsic mode functions.
Abstract: We have introduced a novel time-frequency decomposition approach for analyzing seismic data. This method is inspired by the newly developed variational mode decomposition (VMD). The principle of VMD is to look for an ensemble of modes with their respective center frequencies, such that the modes collectively reproduce the input signal and each mode is smooth after demodulation into baseband. The advantage of VMD is that there is no residual noise in the modes and it can further decrease redundant modes compared with the complete ensemble empirical mode decomposition (CEEMD) and improved CEEMD (ICEEMD). Moreover, VMD is an adaptive signal decomposition technique, which can nonrecursively decompose a multicomponent signal into several quasi-orthogonal intrinsic mode functions. This new tool, in contrast to empirical mode decomposition (EMD) and its variations, such as EEMD, CEEMD, and ICEEMD, is based on a solid mathematical foundation and can obtain a time-frequency representation that is less sens...

142 citations

Journal ArticleDOI
TL;DR: In this article, the authors used the empirical mode decomposition to produce a unique feature vector from the human micro-Doppler signals following which a support vector machine was used to classify human motions.
Abstract: The ability to identify human movements can serve as an important tool in many different applications such as surveillance, military combat situations, search and rescue operations and patient monitoring in hospitals. This information can provide soldiers, security personnel and search and rescue workers with critical knowledge that can be used to potentially save lives and/or avoid dangerous situations. Most research involving human activity recognition employs the short-time Fourier transform (STFT) as a method of analysing human micro-Doppler signatures. However, the STFT has time-frequency resolution limitations and Fourier transform-based methods are not well-suited for use with non-stationary and non-linear signals. The authors approach uses the empirical mode decomposition to produce a unique feature vector from the human micro-Doppler signals following which a support vector machine is used to classify human motions. This study presents simulations of simple human motions, which are subsequently validated using experimental data obtained from both an S-band radar and a W-band millimetre wave (mm-wave) radar. Very good classification accuracies are obtained at distances of up to 90 m between the human and the radar.

142 citations

Journal ArticleDOI
TL;DR: An empirical mode decomposition (EMD)-based deep learning approach which combines the EMD method with the long short-term memory network model to estimate electricity demand for the given season, day, and time interval of a day is proposed.
Abstract: Electricity is of great significance for national economic, social, and technological activities, such as material production, healthcare, and education The nationwide electricity demand has grown rapidly over the past few decades Therefore, efficient electricity demand estimation and management are required for better strategies planning, energy utilization, waste management, improving revenue, and maintenance of power systems In this paper, we propose an empirical mode decomposition (EMD)-based deep learning approach which combines the EMD method with the long short-term memory network model to estimate electricity demand for the given season, day, and time interval of a day For this purpose, the EMD algorithm decomposes a load time series signal into several intrinsic mode functions (IMFs) and residual Then, a LSTM model is trained separately for each of the extracted IMFs and residual Finally, the prediction results of all IMFs are combined by summation to determine an aggregated output for electricity demand To demonstrate the applicability of the proposed approach, it is applied to electricity consumption data of city Chandigarh Furthermore, the performance of the proposed approach is evaluated by comparing the prediction results with recurrent neural network (RNN), LSTM, and EMD-based RNN (EMD+RNN) models

141 citations


Additional excerpts

  • ...EMD [30], [31] is a nonlinear analysis approach for nonstationary time series data....

    [...]

References
More filters
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....

    [...]

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…...

    [...]

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....

    [...]

  • ...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)....

    [...]