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A Preconditioning Framework for the Empirical Mode Decomposition Method

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Abstract

The empirical mode decomposition (EMD) is a useful method for processing nonlinear and nonstationary signals. However, it usually suffers from the mode mixing problem due to the existence of intermittence and interferences of noises in signals. In this paper, a preconditioning framework for the EMD method is proposed in order to alleviate the mode mixing problem. The key points of the preconditioning before implementing the EMD method lie in two aspects: On the one hand, the interferences of noises in the original signal are reduced by filtering; on the other hand, the assisted signals are added to the denoised signal to improve properties of the signal data. Under this framework, the preconditioned forms of the complementary ensemble empirical mode decomposition method and the masking signal-assisted empirical mode decomposition method are presented, respectively. The effectiveness of the proposed methods is illustrated by numerical simulations and applications to real-world signals.

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References

  1. A. Bouchikhi, A. Boudraa, Multicomponent AM–FM signals analysis based on EMD-B-splines ESA. Signal Process. 92, 2214–2228 (2012)

    Article  Google Scholar 

  2. M. Colominas, G. Schlotthauer, M. Torres, Improved complete ensemble EMD: a suitable tool for biomedical signal processing. Biomed. Signal Process. Control 14, 19–29 (2014)

    Article  Google Scholar 

  3. R. Deering, J. Kaiser, The use of a masking signal to improve empirical mode decomposition. In Proceedings of IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP05), vol. 4 (Philadelphia, Pennsylvania, USA, 2005), pp. 485–488

  4. I. Daubechies, Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics (SIAM, Philadelphia, PA, USA, 1992)

  5. N.E. Huang et al., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. A 454, 903–995 (1998)

    Article  MathSciNet  Google Scholar 

  6. N.E. Huang, Z. Shen, A new view of nonlinear water waves: the Hilbert spectrum. Fluid Mech. 31, 417–457 (1999)

    Article  MathSciNet  Google Scholar 

  7. H. Hong, X. Wang, Z. Tao, Local integral mean-based sifting for empirical mode decomposition. IEEE Signal Process. Lett. 16, 841–844 (2016)

    Article  Google Scholar 

  8. X. Jin, Preconditioning Techniques for Toeplitz systems (Higher Education Press, Beijing, 2010)

    Google Scholar 

  9. H. Li, C. Wang, D. Zhao, An improved EMD and its applications to find the basis functions of EMI Signals. Math. Probl. Eng. (2015). https://doi.org/10.1155/2015/150127

    MATH  Google Scholar 

  10. L. Lin, H. Ji, Signal feature extraction based on an improved EMD method. Measurement 42, 796–803 (2008)

    Article  Google Scholar 

  11. M. Li, X. Wu, X. Liu, An improved EMD method for time–frequency feature extraction of telemetry vibration signal based on multi-scale median filtering. Circuits Syst. Signal Process. 34, 815–830 (2015)

    Article  Google Scholar 

  12. H. Li et al., Reconstruction and basis function construction of electromagnetic interference source signals based on Toeplitz-based singular value decomposition. IET Signal Process. 11(1), 59–65 (2016). https://doi.org/10.1049/iet-spr.2016.0307

    Article  Google Scholar 

  13. S. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way, 3rd edn. (Elsevier, New York, 2009)

    MATH  Google Scholar 

  14. B. Ning, D. Zhao, H. Li, Improved Schur complement preconditioners for block-Toeplitz systems with small size blocks. J. Comput. Appl. Math. 311, 655–663 (2016)

    Article  MathSciNet  Google Scholar 

  15. J. Proakis, D. Manolakis, Digital Signal Processing, 4th edn. (Pearson Education Limited, New York, 2006)

    Google Scholar 

  16. N. Rehman et al., EMD via MEMD: multivariate noise-aided computation of standard EMD. Adv. Adapt. Data Anal. 5, 1350007 (2013)

    Article  MathSciNet  Google Scholar 

  17. N. Rehman, D. Mandic, Filter bank property of multivariate empirical mode decomposition. IEEE Trans. Signal Process. 59, 2421–2426 (2011)

    Article  MathSciNet  Google Scholar 

  18. L. Reichel, F. Sgallari, Q. Ye, Tikhonov regularization based on generalized Krylov subspace methods. Appl. Numer. Methods 62, 1215–1228 (2012)

    Article  MathSciNet  Google Scholar 

  19. D. Singh, Q. Zhao, Pseudo-fault signal assisted EMD for fault detection and isolation in rotating machines. Mech. Syst. Signal Proc. 81, 202–218 (2016)

    Article  Google Scholar 

  20. C. Wang, H. Li, D. Zhao, A new signal classification method based on EEMD and FCM and its application in bearing fault diagnosis. Appl. Mech. Mater. 602–605, 1803–1806 (2014)

    Google Scholar 

  21. Z. Wu, N.E. Huang, Ensemble empirical mode decomposition: a noise assisted data analysis method. Adv. Adapt. Data Anal. 1, 1–41 (2009)

    Article  Google Scholar 

  22. C. Wang, Q. Kemao, F. Da, Regenerated phase-shifted sinusoid-assisted empirical mode decomposition. IEEE Signal Process. Lett. 23, 556–560 (2016)

    Article  Google Scholar 

  23. C. Wang, H. Li, D. Zhao, Preconditioning Toeplitz-plus-diagonal linear systems using the Sherman–Morrison–Woodbury formula. J. Comput. Appl. Math. 309, 312–319 (2017)

    Article  MathSciNet  Google Scholar 

  24. C. Wang, H. Li, D. Zhao, An explicit formula for the inverse of a pentadiagonal Toeplitz matrix. J. Comput. Appl. Math. 278, 12–18 (2015)

    Article  MathSciNet  Google Scholar 

  25. X. Xie, Illumination preprocessing for face images based on empirical mode decomposition. Signal Process. 103, 250–257 (2014)

    Article  Google Scholar 

  26. J. Yeh, J. Shieh, N.E. Huang, Complementary ensemble empirical mode decomposition: a novel noise enhanced data analysis method. Adv. Adapt. Data Anal. 2, 135–156 (2010)

    Article  MathSciNet  Google Scholar 

  27. Y. Yang, J. Deng, D. Kang, An improved empirical mode decomposition by using dyadic masking signals. Signal Image Video Process. 9, 1–5 (2015)

    Google Scholar 

  28. D. Zhao, Z. Huang, H. Li, An improved EEMD method based on the adjustable cubic trigonometric cardinal spline interpolation. Digit. Signal Prog. 64, 41–48 (2017)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. LMIB, School of Mathematics and System Science, Beihang University, Beijing, 100191, People’s Republic of China

    Chaojie Wang, Hongyi Li & Di Zhao

Authors
  1. Chaojie Wang
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  2. Hongyi Li
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  3. Di Zhao
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Corresponding author

Correspondence to Di Zhao.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant 61771001), the scholarship of China Scholarship Council (No. 201606020068).

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Wang, C., Li, H. & Zhao, D. A Preconditioning Framework for the Empirical Mode Decomposition Method. Circuits Syst Signal Process 37, 5417–5440 (2018). https://doi.org/10.1007/s00034-018-0821-9

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  • DOI: https://doi.org/10.1007/s00034-018-0821-9

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