END EFFECTS MITIGATION FOR EMPIRICAL MODE DECOMPOSITION WITH NONLINEAR GRAY MODEL

2012 ◽  
Vol 04 (01n02) ◽  
pp. 1250002 ◽  
Author(s):  
ZHI HE ◽  
YI SHEN ◽  
QIANG WANG ◽  
YAN WANG
Keyword(s):  
Empirical Mode Decomposition ◽  
Mirror Symmetry ◽  
Real Data ◽  
Data Series ◽  
Gray Model ◽  
End Effects ◽  
Synthetic Signal ◽  
Novel Approach ◽  
Mode Decomposition ◽  
Mirror Extension

To mitigate end effects of empirical mode decomposition (EMD), a novel approach inspired by the nonlinear gray model (GM) termed as GM(1,1,α) is presented. Other than traditional linear or mirror extension on the boundary, the GM(1,1,α) model is applied to predict two extrema at both ends of the data. It is worth noting that our GM(1,1,α) model is particularly useful for predicting uncertainty data. According to numerical experiments on synthetic signal as well as real data series, the proposed method gives very comparable results with other three generally acknowledged methods, including the linear extension (LE), window function (WF), and mirror symmetry (MS) based methods. That is, the proposed method can reduce end effects and improve decomposition results of EMD significantly.

An Extrema Extension Method Based on Support Vector Regression for Restraining the End Effects in Empirical Mode Decomposition

2013 ◽  
Vol 404 ◽  
pp. 526-532 ◽  
Author(s):  
Xiao Ming Xue ◽  
Jian Zhong Zhou ◽  
Yong Chuan Zhang ◽  
Xiao Jian ◽  
Xue Min Wang
Keyword(s):  
Support Vector Regression ◽  
Empirical Mode Decomposition ◽  
Original Data ◽  
Lower Envelope ◽  
Support Vector ◽  
Data Series ◽  
End Effects ◽  
Extension Method ◽  
Mode Decomposition ◽  
Emd Method

The end effects is a serious problem in the applications of the empirical mode decomposition (EMD) method. To deal with this problem, an extrema extension method based on the support vector regression (SVR) is proposed in this paper. In each iterating process of the EMD method, the SVR method is employed to predict one maximum and a minimum point respectively at the both ends of the original data series to form the relatively true upper and lower envelope, thus the end effects can be restrained effectively. The prediction of an extrema point includes two parts, the forecast of the extreme value and location. In contrast with other traditional extrema extension methods, such as the extrema mirror extension and linear fitting extension method, the decomposed results from the simulation and actual signals demonstrated that this proposed method has a better performance in eliminating the end effects related to the empirical mode decomposition.

scholarly journals Trivariate Empirical Mode Decomposition via Convex Optimization for Rolling Bearing Condition Identification

Sensors ◽  
2018 ◽  
Vol 18 (7) ◽  
pp. 2325 ◽  
Author(s):  
Yong Lv ◽  
Houzhuang Zhang ◽  
Cancan Yi
Keyword(s):  
Convex Optimization ◽  
Empirical Mode Decomposition ◽  
Dimensional Space ◽  
Real Data ◽  
Rolling Bearing ◽  
Low Rank ◽  
Data Matrix ◽  
Mode Decomposition ◽  
Uniform Sample ◽  
Local Mean

As a multichannel signal processing method based on data-driven, multivariate empirical mode decomposition (MEMD) has attracted much attention due to its potential ability in self-adaption and multi-scale decomposition for multivariate data. Commonly, the uniform projection scheme on a hypersphere is used to estimate the local mean. However, the unbalanced data distribution in high-dimensional space often conflicts with the uniform samples and its performance is sensitive to the noise components. Considering the common fact that the vibration signal is generated by three sensors located in different measuring positions in the domain of the structural health monitoring for the key equipment, thus a novel trivariate empirical mode decomposition via convex optimization was proposed for rolling bearing condition identification in this paper. For the trivariate data matrix, the low-rank matrix approximation via convex optimization was firstly conducted to achieve the denoising. It is worthy to note that the non-convex penalty function as a regularization term is introduced to enhance the performance. Moreover, the non-uniform sample scheme was determined by applying singular value decomposition (SVD) to the obtained low-rank trivariate data and then the approach used in conventional MEMD algorithm was employed to estimate the local mean. Numerical examples of synthetic defined by the fault model and real data generated by the fault rolling bearing on the experimental bench are provided to demonstrate the fruitful applications of the proposed method.

B-SPLINE ANALYTICAL REPRESENTATION OF THE MEAN ENVELOPE FOR EMPIRICAL MODE DECOMPOSITION

2010 ◽  
Vol 08 (02) ◽  
pp. 175-195 ◽  
Author(s):  
TIANXIANG ZHENG ◽  
LIHUA YANG
Keyword(s):  
Empirical Mode Decomposition ◽  
Basic Concept ◽  
Spline Functions ◽  
Mathematical Foundation ◽  
Knot Insertion ◽  
B Spline ◽  
Explicit Formulation ◽  
Novel Approach ◽  
Mode Decomposition ◽  
The Mean

This paper investigates how the mean envelope, the subtrahend in the sifting procedure for the Empirical Mode Decomposition (EMD) algorithm, represents as an expansion in terms of basis. To this end, a novel approach that gives an alternative analytical expression using B-spline functions is presented. The basic concept lies mainly on the idea that B-spline functions form a basis for the space of splines and have refined-node representations by knot insertion. This newly-developed expression is essentially equivalent to the conventional one, but gives a more explicit formulation on this issue. For the purpose of establishing the mathematical foundation of the EMD methodology, this study may afford a favorable opportunity in this direction.

scholarly journals Elastic-Net Regression based on Empirical Mode Decomposition for Multivariate Predictors

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Abdullah Suleiman Al-Jawarneh ◽  
Mohd. Tahir Ismail
Keyword(s):  
Empirical Mode Decomposition ◽  
Real Data ◽  
Elastic Net ◽  
Predictor Variables ◽  
Response Variable ◽  
Mode Function ◽  
Mode Decomposition ◽  
Finite Set ◽  
Nonlinear Signal ◽  
Emd Method

The empirical mode decomposition (EMD) method is used to decompose the non-stationary and nonlinear signal into a finite set of orthogonal non-overlapping time scale components that include several intrinsic mode function components and one residual component. Elastic net (ELN) regression is a statistical penalized method used to address multicollinearity among predictor variables and identify the necessary variables that have the most effect on the response variable. This study proposed the use of the ELN method based on the EMD algorithm to identify the decomposition components of multivariate predictor variables with the most effect on the response variable under multicollinearity problems. The results of the numerical experiments and real data confirmed that the EMD-ELN method is highly capable of identifying the decomposition components with the presence or absence of multicollinearity among the components. The proposed method also achieved the best estimation and reached the optimal balance between the variance and bias. The EMD-ELN method also improved the accuracy of regression modeling compared with the traditional regression models.

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