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•

Condition assessment for the performance degradation of bearing based on a combinatorial feature extraction method

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Sheng Hong¹, Zheng Zhou, Enrico Zio², Kan Hong¹•Institutions (2)

Beihang University¹, Supélec²

01 Apr 2014-Digital Signal Processing

TL;DR: The analysis results from the bearing's signals with multiple faults show that the proposed assessment model can effectively indicate the degradation state and help to estimate remaining useful life (RUL) of the bearings.

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194 citations

Journal Article•DOI•

Output only modal identification and structural damage detection using time frequency & wavelet techniques

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Satish Nagarajaiah¹, Biswajit Basu²•Institutions (2)

Rice University¹, Trinity College, Dublin²

01 Dec 2009-Earthquake Engineering and Engineering Vibration

TL;DR: In this paper, the authors developed output only modal identification and structural damage detection based on Time-frequency (TF) techniques such as short-time Fourier transform (STFT), empirical mode decomposition (EMD), and wavelets.

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Abstract: The primary objective of this paper is to develop output only modal identification and structural damage detection. Identification of multi-degree of freedom (MDOF) linear time invariant (LTI) and linear time variant (LTV—due to damage) systems based on Time-frequency (TF) techniques—such as short-time Fourier transform (STFT), empirical mode decomposition (EMD), and wavelets—is proposed. STFT, EMD, and wavelet methods developed to date are reviewed in detail. In addition a Hilbert transform (HT) approach to determine frequency and damping is also presented. In this paper, STFT, EMD, HT and wavelet techniques are developed for decomposition of free vibration response of MDOF systems into their modal components. Once the modal components are obtained, each one is processed using Hilbert transform to obtain the modal frequency and damping ratios. In addition, the ratio of modal components at different degrees of freedom facilitate determination of mode shape. In cases with output only modal identification using ambient/random response, the random decrement technique is used to obtain free vibration response. The advantage of TF techniques is that they are signal based; hence, can be used for output only modal identification. A three degree of freedom 1:10 scale model test structure is used to validate the proposed output only modal identification techniques based on STFT, EMD, HT, wavelets. Both measured free vibration and forced vibration (white noise) response are considered. The secondary objective of this paper is to show the relative ease with which the TF techniques can be used for modal identification and their potential for real world applications where output only identification is essential. Recorded ambient vibration data processed using techniques such as the random decrement technique can be used to obtain the free vibration response, so that further processing using TF based modal identification can be performed.

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193 citations

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

...A criteria for stopping is accomplished by limiting the standard deviation, SD (Huang et al., 1998), of h(t), obtained from consecutive sifting results as...
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...These functions are called intrinsic mode functions (IMF denoted by imfi) and are obtained iteratively (Huang et al., 1998)....
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...A criteria for stopping is accomplished by limiting the standard deviation, SD (Huang et al., 1998), of h(t), obtained from consecutive sifting results as SD = ( ) − ( )( ) ( ) ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ − −= ∑ h k t h k t h k t j j jk l 1 2 1 2 0 Δ Δ Δ (26) where l T t= / Δ and T = total time....
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...Time-frequency methods (Cohen, 1995; Huang et al., 1998), such as short-time Fourier transform (STFT) and wavelets, are used extensively for signal processing....
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...New techniques such as Empirical Mode Decomposition (EMD) (Huang et al., 1998) have been developed for signal processing of non-stationary signals....
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Journal Article•DOI•

Iterative filtering as an alternative algorithm for empirical mode decomposition

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Luan Lin¹, Yang Wang², Haomin Zhou¹•Institutions (2)

Georgia Institute of Technology¹, Michigan State University²

01 Oct 2009-Advances in Adaptive Data Analysis

TL;DR: This paper proposes an alternative algorithm for EMD based on iterating certain filters, such as Toeplitz filters, which yields similar results as the more traditional sifting algorithm, and can be rigorously proved.

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Abstract: The empirical mode decomposition (EMD) was a method pioneered by (N. Huang et al., The empirical mode decomposition and the Hilbert spectrum for nonlinear nonstationary time series analysis, Proc. Roy. Soc. Lond. A454 (1998) 903–995) as an alternative technique to the traditional Fourier and wavelet techniques for studying signals. It decomposes a signal into several components called intrinsic mode functions (IMFs), which have shown to admit better behaved instantaneous frequencies via Hilbert transforms. In this paper, we propose an alternative algorithm for EMD based on iterating certain filters, such as Toeplitz filters. This approach yields similar results as the more traditional sifting algorithm for EMD. In many cases the convergence can be rigorously proved.

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193 citations

Journal Article•DOI•

Noise Reduction in ECG Signals Using Fully Convolutional Denoising Autoencoders

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Hsin-Tien Chiang¹, Yi-Yen Hsieh¹, Szu-Wei Fu², Kuo-Hsuan Hung², Yu Tsao², Shao-Yi Chien¹ - Show less +2 more•Institutions (2)

National Taiwan University¹, Center for Information Technology²

18 Apr 2019-IEEE Access

TL;DR: A DAE using the fully convolutional network (FCN) is proposed for ECG signal denoising and it is believed that the proposed FCN-based DAE has a good application prospect in clinical practice.

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Abstract: The electrocardiogram (ECG) is an efficient and noninvasive indicator for arrhythmia detection and prevention. In real-world scenarios, ECG signals are prone to be contaminated with various noises, which may lead to wrong interpretation. Therefore, significant attention has been paid on denoising of ECG for accurate diagnosis and analysis. A denoising autoencoder (DAE) can be applied to reconstruct the clean data from its noisy version. In this paper, a DAE using the fully convolutional network (FCN) is proposed for ECG signal denoising. Meanwhile, the proposed FCN-based DAE can perform compression with regard to the DAE architecture. The proposed approach is applied to ECG signals from the MIT-BIH Arrhythmia database and the added noise signals are obtained from the MIT-BIH Noise Stress Test database. The denoising performance is evaluated using the root-mean-square error (RMSE), percentage-root-mean-square difference (PRD), and improvement in signal-to-noise ratio (SNR imp ). The results of the experiments conducted on noisy ECG signals of different levels of input SNR show that the FCN acquires better performance as compared to the deep fully connected neural network- and convolutional neural network-based denoising models. Moreover, the proposed FCN-based DAE reduces the size of the input ECG signals, where the compressed data is 32 times smaller than the original. The results of the study demonstrate the superiority of FCN in denoising, with lower RMSE and PRD, as well as higher SNR imp . According to the results, we believe that the proposed FCN-based DAE has a good application prospect in clinical practice.

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193 citations

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

...In order to prevent noisy inference, several approaches have been reported to denoise ECG signals based on adaptive filtering [8]–[10], wavelet methods [11]–[13], and empirical mode decomposition (EMD) [14]–[16]....
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...[16] M. A. Kabir and C. Shahnaz, ‘‘Denoising of ECG signals based on noise reduction algorithms in EMD and wavelet domains,’’ Biomed....
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...Meanwhile, it is reported that the Hilbert transform used in EMD could not separate similar frequency signals perfectly....
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...In [16], the authors proposed a hybrid approach based on EMD and wavelet methods to obtain a further improvement on denoising....
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...As the high frequency noise is embedded in the first few IMFs, the EMD method may not perfectly distinguish between high frequency noise and the QRS complexes....
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Journal Article•DOI•

A hybrid forecasting model with parameter optimization for short-term load forecasting of micro-grids

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Nian Liu¹, Qingfeng Tang¹, Jianhua Zhang¹, Wei Fan¹, Jie Liu¹ - Show less +1 more•Institutions (1)

North China Electric Power University¹

15 Sep 2014-Applied Energy

TL;DR: A hybrid load forecasting model with parameter optimization is proposed for short-term load forecasting of micro-grids, being composed of Empirical Mode Decomposition (EMD), Extended Kalman Filter (EKF), Extreme Learning Machine with Kernel (KELM), and Particle Swarm Optimization (PSO).

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193 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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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.

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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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Dennis Gabor

01 Jan 1946

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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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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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