The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
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.
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...
Citations
More filters
TL;DR: The empirical results confirm that the proposed approach outperforms benchmark models in terms of some statistical measures and robustness and can be utilized as an effective model for the forecasting of carbon price.
Abstract: In order to deal with non-stationary and nonlinear carbon price series, a hybrid forecasting approach is proposed in this study, which is incorporated variational mode decomposition (VMD), mode reconstruction (MR) and optimal combined forecasting model (CFM). The proposed approach introduces a new modes reconstruction method by using evolutionary clustering algorithm, and utilizes optimal combined model to forecast the reconstructed modes. The major steps of developed method can be summarized as: Firstly, carbon price is decomposed into several modes via VMD model, and the modes are obtained adaptively. Secondly, the comprehensive contribution index (CCI) of each mode is calculated and modes are further reconstructed by evolutionary clustering algorithm according to CCI. Then, a new sub-series called virtual modes (V-Modes) is defined and obtained. Thirdly, the optimal combined forecasting model is developed to forecast the V-Modes. In the end, the final forecasting results are obtained by summing the forecasts of V-Modes. For illustration and comparison, the carbon price data from Shenzhen and Hubei Province in China are shown as numerical examples. The empirical results confirm that the proposed approach outperforms benchmark models in terms of some statistical measures and robustness. Therefore, the proposed hybrid approach can be utilized as an effective model for the forecasting of carbon price.
93 citations
TL;DR: A new methodology based on the Fourier decomposition method (FDM) to separate both BW and PLI simultaneously from the recorded ECG signal and obtain clean ECG data and has low computational complexity which makes it suitable for real-time pre-processing of ECG signals.
93 citations
TL;DR: In this article, a Hilbert-Huang transform (HHT) has been applied to transient response of a cracked rotor and few interesting results have been observed. And in all cases it has been found that HHT appears to be a better tool compared to fast Fourier transform and continuous wavelet transform for crack detection in a transient rotor.
93 citations
01 Jan 2015
TL;DR: In this article, Kriging et al. proposed a shapefile for SDS, which is based on the shapefile of a shape-file shapefile shape file this article.
Abstract: 沙和灰尘暴风雨(SDS ) 是在干旱、半干旱的区域的普通现象。在最近的年里， SDS 频率和紧张在伊朗显著地增加了。关于 SDS 来源的研究为理解灰尘产生的机制并且估计它的社会经济、环境的影响是重要的。在这篇论文，我们开发了一条新途径用九相关数据集的联合在伊朗识别 SDS 来源区域，也就是干旱事件，温度， 降水，沙的土壤的地点， SDS 频率，导致人的土壤降级( HISD )，人的影响索引( HII )，雨使用效率(后悔)和网主要生产率( NPP )损失。为了识别 SDS，采购区域，我们第一用兰伯特包括层设计在一致标准下面使这些数据集正常化保角的圆锥形的设计，到光栅的从 shapefile 的数据变换，有从 0 ～ 1 的数据范围的 Min 最大正规化，和由 Kriging 和图象采样(1 km 的分辨率) 的数据插值。在那以后，为 SDS 来源的可能性的 20 张地图通过在平均重量分配标准，每个项目同等地在获得了重量下面覆盖多重数据集被产生。在 20 张地图，越高分数，越多可能一个特定的区域能被认为是 SDS 来源区域。例外主要来自大城市，象德黑兰和伊斯法罕一样。作为结果，最后的 SDS 来源区域被畴划，并且 Al-Howizeh/Al-Azim 沼泽地和 Sistan 盆在伊朗作为主要 SDS 来源区域被识别。在 Al-Howizeh/Al-Azim 沼泽地的 SDS 来源区域仍然不停地膨胀。另外， Al-Howizeh/Al-Azim 沼泽地现在由于自然、导致人的因素正在承受快速的陆地降级并且在不久的将来可能完全消失。Sistan 盆也表明土壤降级和风侵蚀的影响。与适当紧张，持续时间，风速度和灰尘暴风雨的高度，从这个区域高举的沙粒子可能发展成极端灰尘暴风雨，特别在夏天期间。
93 citations
TL;DR: The MCSA is done with empirical mode decomposition from which a set of intrinsic mode functions (IMFs) is obtained and extracted features from two of the obtained IMFs form the basis of the proposed classification criterion.
Abstract: Induction motor is a ubiquitous machine. In industrial settings, online monitoring of motors’ health status in order to schedule maintenance operations with the goal of damage prevention has become an essential necessity. Broken rotor bar is one of the most common failures in the rotor of a squirrel cage motor. Motor current signature analysis (MCSA) has become a popular method for the detection of this failure because of its high reliability. Recent works have performed the MCSA with a combination of different signal processing techniques to identify the presence of broken bars. In this paper, the MCSA is done with empirical mode decomposition from which a set of intrinsic mode functions (IMFs) is obtained. The extracted features from two of the obtained IMFs form the basis of the proposed classification criterion; these are the samples between zero crossings (SBZCs) and the time between successive zero crossings (TSZCs). The standard deviation from the SBZCs and the TSZCs is used as a classification feature. Experimental results using our method show high accuracy in the detection of a broken and a half-broken rotor bar.
93 citations
Cites methods from "The empirical mode decomposition an..."
...The test results in [24] and [25] do not report a quantitative amount of accuracy of their own methods, on the other hand, the accuracy reported in [26] for one-broken-bar detection is 90%....
[...]
...To carry out EMD analysis described in [24], the extrema of the signal X (t) must be identified, the local maxima is then interpolated by a cubic spline as the upper envelope....
[...]
...EMD is a data analysis technique proposed in [24], where a complex signal, stationary or nonstationary, is decomposed in a finite series of simpler data sets called IMFs....
[...]
References
More filters
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…...
[...]
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)....
[...]