A Preconditioning Framework for the Empirical Mode Decomposition Method

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.

[1]  N. Huang,et al.  A new view of nonlinear water waves: the Hilbert spectrum , 1999 .

[2]  Di Zhao,et al.  A New Signal Classification Method Based on EEMD and FCM and its Application in Bearing Fault Diagnosis , 2014 .

[3]  James F. Kaiser,et al.  The use of a masking signal to improve empirical mode decomposition , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[4]  Zhi-Yong Tao,et al.  Local Integral Mean-Based Sifting for Empirical Mode Decomposition , 2009, IEEE Signal Processing Letters.

[5]  Stéphane Mallat,et al.  A Wavelet Tour of Signal Processing - The Sparse Way, 3rd Edition , 2008 .

[6]  Di Zhao,et al.  Preconditioning Toeplitz-plus-diagonal linear systems using the Sherman-Morrison-Woodbury formula , 2017, J. Comput. Appl. Math..

[7]  Hongyi Li,et al.  An Improved EMD and Its Applications to Find the Basis Functions of EMI Signals , 2015 .

[8]  Yanli Yang,et al.  An improved empirical mode decomposition by using dyadic masking signals , 2015, Signal Image Video Process..

[9]  Norden E. Huang,et al.  Complementary Ensemble Empirical Mode Decomposition: a Novel Noise Enhanced Data Analysis Method , 2010, Adv. Data Sci. Adapt. Anal..

[10]  María Eugenia Torres,et al.  Improved complete ensemble EMD: A suitable tool for biomedical signal processing , 2014, Biomed. Signal Process. Control..

[11]  Li Lin,et al.  Signal feature extraction based on an improved EMD method , 2009 .

[12]  Hongyi Li,et al.  An explicit formula for the inverse of a pentadiagonal Toeplitz matrix , 2015, J. Comput. Appl. Math..

[13]  Xiaohua Xie.  Illumination preprocessing for face images based on empirical mode decomposition , 2014, Signal Process..

[14]  Feipeng Da,et al.  Regenerated Phase-Shifted Sinusoid-Assisted Empirical Mode Decomposition , 2016, IEEE Signal Processing Letters.

[15]  Danilo P. Mandic,et al.  Emd via mEMD: multivariate noise-Aided Computation of Standard EMD , 2013, Adv. Data Sci. Adapt. Anal..

[16]  Danilo P. Mandic,et al.  Filter Bank Property of Multivariate Empirical Mode Decomposition , 2011, IEEE Transactions on Signal Processing.

[17]  Qing Zhao,et al.  Pseudo-fault signal assisted EMD for fault detection and isolation in rotating machines , 2016 .

[18]  Hongyi Li,et al.  Improved Schur complement preconditioners for block-Toeplitz systems with small size blocks , 2017, J. Comput. Appl. Math..

[19]  Hongyi Li,et al.  Reconstruction and basis function construction of electromagnetic interference source signals based on Toeplitz-based singular value decomposition , 2017, IET Signal Process..

[20]  Norden E. Huang,et al.  Ensemble Empirical Mode Decomposition: a Noise-Assisted Data Analysis Method , 2009, Adv. Data Sci. Adapt. Anal..

[21]  Mei Li,et al.  An Improved EMD Method for Time–Frequency Feature Extraction of Telemetry Vibration Signal Based on Multi-Scale Median Filtering , 2015, Circuits Syst. Signal Process..

[22]  Lothar Reichel,et al.  Tikhonov regularization based on generalized Krylov subspace methods , 2012 .

[23]  Hongyi Li,et al.  An improved EEMD method based on the adjustable cubic trigonometric cardinal spline interpolation , 2017, Digit. Signal Process..

[24]  Abdelkhalek BOUCHIKHI,et al.  Multicomponent AM-FM signals analysis based on EMD-B-splines ESA , 2012, Signal Process..

[25]  Guanghui Sun,et al.  New Developments in Sliding Mode Control and Its Applications , 2014 .

[26]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.