An approach to eliminating end effects of EMD through mirror extension coupled with support vector machine method

  • Jian Wang
  • Wenyuan LiuEmail author
  • Shuai Zhang
Original Article


The mirror extension is a basic algorithm to treat the end effects in the empirical mode decomposition (EMD) of signals. It must meet the requirements of the specular position at the local extremum, but the actual signal is very difficult to implement. For this reason, its decomposition can lead to severe distortion. This paper proposed a new approach to the performance improvement of end effect elimination in EMD method through the data extension on the basis of traditional mirror extension technique coupled with the function regression method of support vector machine (SVM). Some data outside of both ends of an original signal are firstly predicted by means of the relationships obtained by the function regression method of SVM, from which one or more extreme points outside each end are captured. And then the mirror extension algorithm is used to inhibit the end effects possibly occurring in operation of EMD method. The application examples of the simulated signal show that the proposed method can effectively eliminate the end effect of the EMD method.


Empirical mode decomposition (EMD)  End effects Mirror extension Support vector machine 



  1. 1.
    Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen NC, Tung CC, Liu HH (1998) The empirical mode decomposition and the Hilbert spectrum for non-linear and non-stationary time series analysis. Proc R Soc Lond A 454(12):903–995MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Yan J, Lu L (2014) Improved Hilbert–Huang transform based weak signal detection methodology and its application on incipient fault diagnosis and ECG signal analysis. Signal Process 98:74–87CrossRefGoogle Scholar
  3. 3.
    Chu PC, Fan C, Huang N (2014) Derivative-optimized empirical mode decomposition for the Hilbert–Huang transform. J Comput Appl Math 259:57–64MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Liu X, Bo L, Luo H (2015) Bearing faults diagnostics based on hybrid LS-SVM and EMD method. Measurement 59:145–166CrossRefGoogle Scholar
  5. 5.
    Han J, Zheng P, Wang H (2014) Structural modal parameter identification and damage diagnosis based on Hilbert-Huang transform. Earthq Eng Eng Vib 13(1):101–111CrossRefGoogle Scholar
  6. 6.
    An FP, Lin DC, Li YA, Zhou XW (2015) Edge effects of BEMD improved by expansion of support-vector-regression extrapolation and mirror-image signals. Opt Int J Light Electron Opt 126(21):2985–2993CrossRefGoogle Scholar
  7. 7.
    He Z, Shen Y, Wang Q (2012) Boundary extension for Hilbert–Huang transform inspired by gray prediction model. Signal Process 92(3):685–697CrossRefGoogle Scholar
  8. 8.
    Zhang M, Tang J, Zhang X, Zhang J (2016) Intelligent diagnosis of short hydraulic signal based on improved EEMD and SVM with few low-dimensional training samples. Chin J Mech Eng 29(2):396–405MathSciNetCrossRefGoogle Scholar
  9. 9.
    He Z, Wang Q, Shen Y, Jin J, Wang Y (2013) Multivariate gray model-based BEMD for hyperspectral image classification. IEEE Trans Instrum Meas 62(5):889–904CrossRefGoogle Scholar
  10. 10.
    Zhang Z, Gu L, Zhu Y (2013) Intelligent fault diagnosis of rotating machine based on SVMs and EMD method. Open Autom Control Syst J 5:219–230CrossRefGoogle Scholar
  11. 11.
    Han KL, Thomas SVM, Koontz SM, Changpriroa CM, Ha SK, Malech HL, Kang EM (2013) Adenosine A2A receptor agonist–mediated increase in donor-derived regulatory T cells suppresses development of graft-versus-host disease. J Immunol 190(1):458–468CrossRefGoogle Scholar
  12. 12.
    Rilling R, Flandrin P, Goncalvès P (2003) On empirical mode decomposition and its algorithms. In: IEEE-EURASIP workshop on nonlinear signal and image processing, Grado(I). pp 1–5Google Scholar
  13. 13.
    Lee YS, Tsakirtzis S, Vakakis AF, Bergman LA, McFarland DM (2009) Physics-based foundation for empirical mode decomposition. AIAA J 47(12):2938–2963CrossRefGoogle Scholar
  14. 14.
    Mandic DP, ur Rehman N, Wu Z et al (2013) Empirical mode decomposition-based time-frequency analysis of multivariate signals: the power of adaptive data analysis. IEEE Signal Process Mag 30(6):74–86CrossRefGoogle Scholar
  15. 15.
    Bin GF, Gao JJ, Li XJ, Dhillon BS (2012) Early fault diagnosis of rotating machinery based on wavelet packets—empirical mode decomposition feature extraction and neural network. Mech Syst Signal Process 27:696–711CrossRefGoogle Scholar
  16. 16.
    Vapnik VN (1995) The nature of statistical learning theory. Springer-Verlag, NewYorkCrossRefzbMATHGoogle Scholar
  17. 17.
    Qi Z, Tian Y, Shi Y (2013) Robust twin support vector machine for pattern classification. Pattern Recogn 46(1):305–316CrossRefzbMATHGoogle Scholar
  18. 18.
    Orrù G, Pettersson-Yeo W, Marquand AF, Sartori G, Mechelli A (2012) Using support vector machine to identify imaging biomarkers of neurological and psychiatric disease: a critical review. Neurosci Biobehav Rev 36(4):1140–1152CrossRefGoogle Scholar
  19. 19.
    Yang JN, Lei Y, Lin S, Huang N (2004) Hilbert-Huang based approach for structural damage detection. ASCE J Eng Mech 130(1):85–95CrossRefGoogle Scholar
  20. 20.
    Pradhan B (2013) A comparative study on the predictive ability of the decision tree, support vector machine and neuro-fuzzy models in landslide susceptibility mapping using GIS. Comput Geosci 51:350–365CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Information Science and EngineeringYanshan UniversityQinhuangdaoChina
  2. 2.The First Hospital of QinhuangdaoQinhuangdaoChina
  3. 3.Hebei Normal University of Science &TechnologyQinhuangdaoChina

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