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
Shibin Wang1, Guoying Li1, Xuefeng Chen1, Yi Xia, Zhonghua Liu 
06 May 2013
TL;DR: The analysis results show that the matching demodulation transform is powerful in the analysis of FM signals and is an effective tool for the feature extraction of rub-impact faults.
Abstract: Conventional time-frequency representation (TFR) methods have played an important role in characterizing the time-frequency (TF) pattern of the nonstationary signal. In this paper, a new TFR algorithm, called matching demodulation transform (MDT), is introduced to extract the feature of highly oscillating frequency modulation for rotor rub-impact fault. When the early rub-impact fault occurs in the rotor system, the vibration signals will present frequency modulation feature because of the periodic rub-impact between the stator and the rotor. Through an iterative demodulation procedure, the highly oscillating frequency modulation feature is represented with satisfactory energy concentration in TF plane. The validity of the technique is then demonstrated on a real rotor system of a gas turbine with rub-impact fault. The analysis result of this application shows that the MDT method is powerful in the analysis of frequency modulation signals and is an effective tool for the feature extraction of rub-impact faults.

88 citations


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

  • ...The analysis results behave better than HHT and SWT, as shown in Fig....

    [...]

  • ...For the purpose of comparison, the TFR of HHT is shown in Fig....

    [...]

  • ...In this case, the HHT spectrum can reveal some oscillation feature....

    [...]

  • ...Some effective methods have been widely studied and used, such as empirical mode decomposition and Hilbert–Huang transform (HHT) [3]–[6], wavelet transform [7]–[11], synchrosqueezed wavelet transform (SWT) [12], [13], and time–frequency analysisbased methods [14], [15]....

    [...]

  • ...The HHT spectrum is also incapable of characterizing the entire oscillation behavior of the vibration signal in this case....

    [...]

Proceedings ArticleDOI
01 Aug 2006
TL;DR: Results indicate that the baseline wander and power line interference of ECG are removed effectively by this new method based on empirical mode decomposition and notch filter.
Abstract: Removal of baseline wander and power line interference in ECG signal is a classical problem. A new method is proposed to remove baseline wander and power line interference in ECG signal based on Empirical Mode Decomposition and notch filter. Principles and characteristics of Empirical Mode Decomposition are presented; ECG signal is decomposed into a series of Intrinsic Mode Functions (IMFs). Then 50Hz notch filter is designed, by which the IMF of ECG signal containing 50Hz power line inference is filtered. The "clean" ECG signal is reconstructed by properly selecting IMFs. To evaluate the performance of the filter, Clinic ECG signals are used. Results indicate that the baseline wander and power line interference of ECG are removed effectively by this new method.

88 citations

Journal ArticleDOI
TL;DR: The objective of the present paper is to introduce another mathematical theory, along with rigorous methods and computational schemes, to achieve a more ambitious goal than the SST approach, first to extract the polynomial-like trend from the source signal, then to compute the exact number of signal components according to a less restrictive AHM model, and finally to separate the signal components from the (blind) source signal.

88 citations


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

  • ...Furthermore, our computational scheme can be realized in near real-time, and our mathematical theory has direct extension to the multivariate setting....

    [...]

Journal ArticleDOI
TL;DR: A new remaining useful life prediction approach based on deep feature representation and long short-term memory neural network is proposed, and a new criterion, named support vector data normalized correlation coefficient, is proposed to automatically divide the whole bearing life as normal state and fast degradation state.
Abstract: For bearing remaining useful life prediction problem, the traditional machine-learning-based methods are generally short of feature representation ability and incapable of adaptive feature extracti...

88 citations

Journal ArticleDOI
TL;DR: In this article, the authors examined the statistical relationship of the Antarctic Oscillation (AAO) with the major tropical climate signals at the intraseasonal and interannual time scales and their consequences on its potential influence on rainfall variability at regional scales.
Abstract: The Antarctic Oscillation (AAO) is the leading mode of atmospheric variability in the Southern Hemisphere mid- and high latitudes (south of 20°S). In this paper, the authors examine its statistical relationships with the major tropical climate signals at the intraseasonal and interannual time scales and their consequences on its potential influence on rainfall variability at regional scales. At the intraseasonal time scale, although the AAO shows its most energetic fluctuations in the 30–60-day range, it is not unambiguously related to the global-scale Madden–Julian oscillation (MJO) activity, with in particular no coherent phase relationship with the MJO index. Moreover, in the high southern latitudes, the MJO-associated anomaly fields do not appear to project coherently on the well-known AAO patterns and are never of an annular nature. At the interannual time scale, a strong teleconnection with ENSO is found during the peak of the austral summer season, corroborating previous studies. El Nino (...

88 citations


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

  • ...The EMD has been introduced by Huang et al. (1998) for the analysis of 1D signals, in the context of time series analysis, as part of the Hilbert– Huang transform....

    [...]

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)....

    [...]