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

doi:10.1098/RSPA.1998.0193

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

Journal Article•DOI•

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

Norden E. Huang¹, Zheng Shen², Steven R. Long³, Man-Li C. Wu¹, Hsing H. Shih⁴, Quanan Zheng⁵, Nai-Chyuan Yen⁶, C. C. Tung⁷, Henry H. Liu⁸ - Show less +5 more•Institutions (8)

Goddard Space Flight Center¹, Johns Hopkins University², Wallops Flight Facility³, National Ocean Service⁴, University of Delaware⁵, United States Naval Research Laboratory⁶, North Carolina State University⁷, Naval Surface Warfare Center⁸

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.

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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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Journal Article•DOI•

Hilbert–Huang transform based signal analysis for the characterization of gas–liquid two-phase flow

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Hao Ding¹, Zhiyao Huang¹, Zhihuan Song¹, Yong Yan²•Institutions (2)

Zhejiang University¹, University of Kent²

01 Mar 2007-Flow Measurement and Instrumentation

TL;DR: In this paper, a differential pressure fluctuation signal of gas-liquid two-phase flow is adaptively decomposed into Intrinsic Mode Functions (IMFs) through the use of empirical mode decomposition (EMD) methods.

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98 citations

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

...Once the elementary function is determined, it will be used to analyze all the data [2,4]....
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...The conventional FT uses linear superposition of trigonometric functions to approach the original signal [4]....
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...a series of scales that cannot reveal precisely the relationship between time and instantaneous frequency [4]....
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...When the FT is used to analyze the differential pressure fluctuation signal, many frequency components are introduced to simulate the inherent features of the signal, but their existence disperses the energy to a much wider frequency range [4]....
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...In practice, it is difficult for WT to obtain a quantitative definition of the energy–frequency–time distribution by the limited size of the elementary wavelet function [4,8]....
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Journal Article•DOI•

Application of the Variational-Mode Decomposition for Seismic Time–frequency Analysis

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Ya-juan Xue¹, Junxing Cao¹, Da-xing Wang², Hao-kun Du, Yao Yao³ - Show less +1 more•Institutions (3)

Chengdu University of Technology¹, PetroChina², Chengdu University of Information Technology³

02 Mar 2016-IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing

TL;DR: Application of the VMD on field data demonstrates that instantaneous spectrum after VMD targets the thickness variation in the coal seam more sensitively than the conventional tools and highlights the fine details that might escape unnoticed.

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Abstract: Seismic time–frequency analysis methods play an important role in seismic interpretation for its superiority in significantly revealing the frequency content of a seismic signal changes with time variation. Variational-mode decomposition (VMD) is a newly developed methodology for decomposition on adaptive and quasi-orthogonal signal and can decompose a seismic signal into a number of band-limited quasi-orthogonal intrinsic mode functions (IMFs). Each mode is an AM–FM signal with the narrow-band property and nonnegative smoothly varying instantaneous frequencies. Analysis on synthetic and real data shows that this method is more robust to noise and has stronger local decomposition ability than the empirical mode decomposition (EMD)-based methods. Comparing with the short-time Fourier transform (STFT) or wavelet transform (WT), instantaneous spectrum after VMD promises higher spectral and spatial resolution. Application of the VMD on field data demonstrates that instantaneous spectrum after VMD targets the thickness variation in the coal seam more sensitively than the conventional tools and highlights the fine details that might escape unnoticed. The technique is more promising for seismic signal processing and interpretation.

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98 citations

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

...For the theory about EMD, EEMD, and CEEMD, one can found it in [16]–[18]....
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...Despite EMD which can recursively decompose a multicomponent seismic trace into a number of intrinsic mode functions (IMFs) has progressed from EMD [16] to mode mixing elimination methods such as ensemble EMD (EEMD) [17] and complete EEMD (CEEMD) [18], there are still some apparent limitations such as its sensitivity to noise and sampling and lack of mathematical theory and so on....
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...IMF is explicitly defined having the characteristics that the number of extrema and zerocrossings must either equal or differ at most by one in the whole signal segment and the mean value of the envelope defined by the local maxima and the envelope defined by the local minima is zero at any point [16]....
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Journal Article•DOI•

Audio Watermarking Via EMD

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Kais Khaldi, Abdel-Ouahab Boudraa¹•Institutions (1)

École Navale¹

01 Mar 2013-IEEE Transactions on Audio, Speech, and Language Processing

TL;DR: A new adaptive audio watermarking algorithm based on Empirical Mode Decomposition (EMD) is introduced and the robustness of the hidden watermark for additive noise, MP3 compression, re-quantization, filtering, cropping and resampling is shown.

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Abstract: In this paper a new adaptive audio watermarking algorithm based on Empirical Mode Decomposition (EMD) is introduced. The audio signal is divided into frames and each one is decomposed adaptively, by EMD, into intrinsic oscillatory components called Intrinsic Mode Functions (IMFs). The watermark and the synchronization codes are embedded into the extrema of the last IMF, a low frequency mode stable under different attacks and preserving audio perceptual quality of the host signal. The data embedding rate of the proposed algorithm is 46.9-50.3 b/s. Relying on exhaustive simulations, we show the robustness of the hidden watermark for additive noise, MP3 compression, re-quantization, filtering, cropping and resampling. The comparison analysis shows that our method has better performance than watermarking schemes reported recently.

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97 citations

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

...To overcome this limitation, recently, a new signal decomposition method referred to as Empirical Mode Decomposition (EMD) has been introduced for analyzing non-stationary signals derived or not from linear systems in totally adaptive way [6]....
[...]

Journal Article•DOI•

Gear fault identification based on Hilbert-Huang transform and SOM neural network

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Gang Cheng¹, Yu-long Cheng¹, Li-hua Shen, Jin-bo Qiu, Shuai Zhang¹ - Show less +1 more•Institutions (1)

China University of Mining and Technology¹

01 Apr 2013-Measurement

TL;DR: In this article, the authors proposed a new gear fault identification method based on HHT and SOM neural network, which can compensate for the disadvantage of HHT for adaptive analysis of non-linear and non-stationary signals.

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97 citations

Journal Article•DOI•

A hybrid fault diagnosis method using morphological filter–translation invariant wavelet and improved ensemble empirical mode decomposition

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Lingjie Meng¹, Lingjie Meng², Jiawei Xiang¹, Yanxue Wang², Yongying Jiang¹, Haifeng Gao¹ - Show less +2 more•Institutions (2)

Wenzhou University¹, Guilin University of Electronic Technology²

01 Jan 2015-Mechanical Systems and Signal Processing

TL;DR: In this article, the morphological filter combining with translation invariant wavelet is taken as the pre-filter process unit to reduce the narrowband impulses and random noises in the original signal, then the purified signal will be decomposed by improved ensemble empirical mode decomposition (EEMD).

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97 citations

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Edward N. Lorenz¹•Institutions (1)

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...(ii) Lorenz equation The famous Lorenz equation (Lorenz 1963) was proposed initially to study deterministic non-periodic flow....
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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.

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Julius S. Bendat, Allan G. Piersol

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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.

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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.

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...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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Theory of communication

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Dennis Gabor

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...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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01 Jul 1944-Bell System Technical Journal

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.

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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

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...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)....
[...]