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•

Noncontact Accurate Measurement of Cardiopulmonary Activity Using a Compact Quadrature Doppler Radar Sensor

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Wei Hu¹, Zhangyan Zhao, Yunfeng Wang, Haiying Zhang, Fujiang Lin¹ - Show less +1 more•Institutions (1)

University of Science and Technology of China¹

01 Mar 2014-IEEE Transactions on Biomedical Engineering

TL;DR: The designed sensor enables accurate reconstruction of chest-wall movement caused by cardiopulmonary activities, and the algorithm enables estimation of respiration, heartbeat rate, and some indicators of heart rate variability (HRV).

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Abstract: The designed sensor enables accurate reconstruction of chest-wall movement caused by cardiopulmonary activities, and the algorithm enables estimation of respiration, heartbeat rate, and some indicators of heart rate variability (HRV). In particular, quadrature receiver and arctangent demodulation with calibration are introduced for high linearity representation of chest displacement; 24-bit ADCs with oversampling are adopted for radar baseband acquisition to achieve a high signal resolution; continuous-wavelet filter and ensemble empirical mode decomposition (EEMD) based algorithm are applied for cardio/pulmonary signal recovery and separation so that accurate beat-to-beat interval can be acquired in time domain for HRV analysis. In addition, the wireless sensor is realized and integrated on a printed circuit board compactly. The developed sensor system is successfully tested on both simulated target and human subjects. In simulated target experiments, the baseband signal-to-noise ratio (SNR) is 73.27 dB, high enough for heartbeat detection. The demodulated signal has 0.35% mean squared error, indicating high demodulation linearity. In human subject experiments, the relative error of extracted beat-to-beat intervals ranges from 2.53% to 4.83% compared with electrocardiography (ECG) R-R peak intervals. The sensor provides an accurate analysis for heart rate with the accuracy of 100% for p = 2% and higher than 97% for p = 1%.

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192 citations

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

...However, wavelets alone cannot always find every heartbeat with clearly seen peaks, so peak detecting method cannot provide a fairly accurate analysis for HR. Recently, the empirical mode decomposition (EMD) [18] has been used to process nonstationary signals and is applied in many related fields....
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...The EEMD algorithm is proposed as a noise-assisted data analysis method for solving the EMD-mode mixing and other problems [19]....
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...The EEMD algorithm provides an exact reconstruction of the original signal and a better spectral separation of the modes....
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...If x[n] is the targeted data, we can describe the EEMD method by the following algorithm: 1) Add a white noise series to x[n]....
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...Recently, the empirical mode decomposition (EMD) [18] has been used to process nonstationary signals and is applied in many related fields....
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Journal Article•DOI•

Wheel-bearing fault diagnosis of trains using empirical wavelet transform

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Hongrui Cao¹, Fei Fan¹, Kai Zhou¹, Zhengjia He¹•Institutions (1)

Xi'an Jiaotong University¹

01 Mar 2016-Measurement

TL;DR: In this paper, a novel method called empirical wavelet transform (EWT) is used for the vibration signal analysis and fault diagnosis of wheel-bearing, which combines the classic wavelet with the empirical mode decomposition.

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192 citations

Journal Article•DOI•

Emotion recognition from EEG signals by using multivariate empirical mode decomposition

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Ahmet Can Mert¹, Aydin Akan²•Institutions (2)

Bursa Technical University¹, Istanbul University²

01 Feb 2018-Pattern Analysis and Applications

TL;DR: A MEMD-based feature extraction method is proposed to process multichannel EEG signals for emotion recognition and the results are compared with similar previous studies for benchmarking.

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Abstract: This is the artifact for the paper titled "POKER: Permutation-based SIMD Execution of Intensive Tree Search by Path Encoding" accepted at CGO 2018. This artifact helps reproduce the results presented in Figures 7 - 9 and Tables 2 - 3 in Section 4. For more information on how to use it, please refer to our paper and the README.txt file in this package. Please note that POKER is a work in progress. This artifact is a snapshot of this work and thus is only applicable under the experimental settings described in this paper. Please feel free to contact the authors if you have any questions.

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192 citations

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

...namely upper and lower envelope should be zero [7]....
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...Empirical mode decomposition (EMD) is proposed as an alternative method to process nonlinear and nonstationary signals [7]....
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Journal Article•DOI•

Application of Bandwidth EMD and Adaptive Multiscale Morphology Analysis for Incipient Fault Diagnosis of Rolling Bearings

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Yongbo Li¹, Minqiang Xu¹, Xihui Liang², Wenhu Huang¹•Institutions (2)

Harbin Institute of Technology¹, University of Alberta²

10 Jan 2017-IEEE Transactions on Industrial Electronics

TL;DR: Results show that the proposed method outperforms EMD-AMma, ensemble empirical mode decomposition-AMMA, and generalized empirical mode decompposition-empirical envelope demodulation in detecting early inner race fault.

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Abstract: This paper presents a novel signal processing scheme, bandwidth empirical mode decomposition, and adaptive multiscale morphological analysis (BEMD-AMMA) for early fault diagnosis of rolling bearings. In this scheme, we propose a bandwidth based method to select the best envelope interpolation method. First, multiple envelope algorithms are defined and separately subtracted from the original data to obtain the preintrinsic mode functions (PIMFs). Second, an IMF with the smallest frequency bandwidth is selected to be the optimal IMF (OIMF). Third, this OIMF is subtracted from the original signal, and then repeat the sifting process until the residual is a constant or monotonic. Since the OIMF has the smallest frequency bandwidth, the mode mixing phenomenon can be significantly weakened. After that the OIMFs with clear fault information are used to construct the main component of the original signal. Then, the AMMA is introduced to demodulate the constructed main component. Simulation and experimental vibration signals are employed to evaluate the effectiveness of the proposed method. Results show that the proposed method outperforms EMD-AMMA, ensemble empirical mode decomposition-AMMA, and generalized empirical mode decomposition-empirical envelope demodulation in detecting early inner race fault.

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192 citations

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

...The monocomponent of EMD called IMF is obtained by subtracting the local mean from the original signal, where the local mean is obtained using the envelope interpolation [7]....
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...is able to decompose vibration signals into a set of intrinsic mode functions (IMFs) and a residual [7]....
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...This can be taken as the calculation error caused by the computer [7]....
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...[7], it can also be constructed using OIMFs as follows:...
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...Compared with traditional demodulation techniques: Hilbert transform (HT) [7] and Teager–Kaiser energy operator (TKEO) [23], AMMA has a...
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Journal Article•DOI•

Estimating the impact of extreme events on crude oil price: An EMD-based event analysis method

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Xun Zhang, Lean Yu, Shouyang Wang, Kin Keung Lai

01 Sep 2009-Energy Economics

TL;DR: In this article, the impact of extreme events on crude oil markets was analyzed using an EMD-based approach. And the empirical results reveal that the EMDbased event analysis method provides a feasible solution to estimating the impact on crudeoil prices variation, while the secondary modes provide valuable information on subsequent factors.

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192 citations

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References

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Deterministic nonperiodic flow

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Edward N. Lorenz¹•Institutions (1)

Massachusetts Institute of Technology¹

01 Mar 1963-Journal of the Atmospheric Sciences

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.

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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.

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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

01 Jan 1946

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"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 Article•DOI•

Mathematical analysis of random noise

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S. O. Rice

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)....
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