Mode mixing suppression algorithm for empirical mode decomposition based on self-filtering method
Keywords:empirical mode decomposition, time-frequency analysis, mode mixing, multi-component signal, self-filtering
AbstractThe Hilbert-Huang transform (HHT) is a classic method in time-frequency analysis field which was proposed in 1998. Since it is not limited by signal type, it is generally applied in medicine, target detection and so on. Empirical mode decomposition (EMD) is a pre-processing part of HHT. However, EMD still has many imperfect aspects, such as envelope fitting, the endpoint effect, mode mixing and other issues, of which the most important issue is the mode mixing. This paper proposes a mode mixing suppression algorithm based on self-filtering method using frequency conversion. The proposed algorithm focuses on the instantaneous frequency estimation and the false components removing procedures, which help the proposed algorithm to update or purify the designated intrinsic mode function (IMF). According the simulation results, the proposed algorithm can effectively suppress the mode mixing. Comparing with ensemble empirical mode decomposition (EEMD) and mask method, the suppression performance is increased by 26%.
Stankovic, L.; Stankovic, S.; Dakovic, M. “From the STFT to the Wigner distribution [Lecture Notes],” IEEE Signal Proces. Mag., v.31, n.3, p.163, 2014. DOI: https://doi.org/10.1109/MSP.2014.2301791.
Awal, M.A.; Ouelha, S.; Dong, S.Y.; Boashash, B. “A robust high-resolution time-frequency representation based on the local optimization of the short-time fractional Fourier transform,” Digital Signal Processing, v.70, p.125, Nov. 2017. DOI: https://doi.org/10.1016/j.dsp.2017.07.022.
Daubechies, I. “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory, v.36, n.5, p.961, 1990. DOI: https://doi.org/10.1109/18.57199.
Boashash, B. “Note on the use of the Wigner distribution for time-frequency signal analysis,” IEEE Trans. Acoustics, Speech, Signal Processing, v.36, n.9, p.1518, 1988. DOI: https://doi.org/10.1109/29.90380.
Claasen, T.; Mecklenbrauker, W. “Time-frequency signal analysis by means of the Wigner distribution,” Proc. of ICASSP’81. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, 30 Mar.-1 Apr. 1981, Atlanta, USA. IEEE, 1981, p.69-72. DOI: https://doi.org/10.1109/ICASSP.1981.1171331.
Chan, D. “A non-aliased discrete-time Wigner distribution for time-frequency signal analysis,” Proc. of ICASSP’82. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, 3-5 May 1982, Paris, France. IEEE, 1982, p.1333-1336. DOI: https://doi.org/10.1109/ICASSP.1982.1171451.
Hu, H. “Time-frequency DOA estimate algorithm based on SPWVD,” Proc. of 2005 IEEE Int. Symp. on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications, 8-12 Aug. 2005, Beijing, China. IEEE, 2005, v.2, p.1253-1256. DOI: https://doi.org/10.1109/MAPE.2005.1618151.
Sorokin, O.Y. “Increase of efficiency of spread spectrum radio signals application in communication systems,” Radioelectron. Commun. Syst., v.55, n.1, p.38, 2012. DOI: https://doi.org/10.3103/S0735272712010062.
Barkat, B.; Boashash, B. “A high-resolution quadratic time-frequency distribution for multicomponent signals analysis,” IEEE Trans. Signal Processing, v.49, n.10, p.2232, 2001. DOI: https://doi.org/10.1109/78.950779.
Gvozdak, A.P. “Detection of nonstationary components of signals with the use of distributions based on kernels with affine transforms,” Radioelectron. Commun. Syst., v.48, n.8, p.31, 2005. URI: http://radioelektronika.org/article/view/S0735272705080066.
Martin, W.; Flandrin, P. “Wigner-Ville spectral analysis of nonstationary processes,” IEEE Trans. Acoustics, Speech, and Signal Processing, v.33, n.6, p.1461, 1985. DOI: https://doi.org/10.1109/TASSP.1985.1164760.
Chan, H.-L.; Huang, H.-H.; Lin, J.-L. “Time-frequency analysis of heart rate variability during transient segments,” Annals Biomedical Engineering, v.29, n.11, p.983, Nov. 2001. DOI: https://doi.org/10.1114/1.1415525.
Hang, H. “Time-frequency DOA estimation based on Radon-Wigner transform,” Proc. of 2006 8th Int. Conf. on Signal Processing, 16-20 Nov. 2006, Beijing, China. IEEE, 2006, p.1. DOI: https://doi.org/10.1109/ICOSP.2006.344553.
Amirmazlaghani, M.; Amindavar, H. “Modeling and denoising Wigner-Ville distribution,” Proc. of 2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop, 4-7 Jan. 2009, Marco Island, USA. IEEE, 2009, p.530-534. DOI: https://doi.org/10.1109/DSP.2009.4785980.
Huang, N.E.; Shen, Z.; Long, S.R.; Wu, M.C.; Shih, H.H.; Zheng, Q.; Yen, N.-C.; Tung, C.C.; Liu, H.H. “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. Royal Soc. A - Math. Phys. Engineering Sci., v.454, n.1971, p.903, Mar. 1998. DOI: https://doi.org/10.1098/rspa.1998.0193.
Cheng, B.L.; Kubrak, A.N. “Modernized method of estimating the parameters of LFM signals based on the time-frequency distribution correction and the use of the Hough transformation,” Radioelectron. Commun. Syst., v.52, n.6, p.295, 2009. DOI: https://doi.org/10.3103/S0735272709060028.
Zheng, J.D.; Cheng, J.S.; Yang, Y. “Partly ensemble empirical mode decomposition: An improved noise-assisted method for eliminating mode mixing,” Signal Processing, v.96, Part B, p.362, Mar. 2014. DOI: https://doi.org/10.1016/j.sigpro.2013.09.013.
Quan, H.; Liu, Z.; Shi, X. “A new processing method for the end effect problem of empirical mode decomposition,” Proc. of 2010 3rd Int. Congress on Image and Signal Processing, 16-18 Oct. 2010, Yantai, China. IEEE, 2010, p.3391-3394. DOI: https://doi.org/10.1109/CISP.2010.5647347.
Kovalenko, P.Y.; Bliznyuk, D.I.; Berdin, A.S. “Improved extrema detection algorithm for the generalized empirical mode decomposition,” Proc. of 2nd Int. Conf. on Industrial Engineering, Applications and Manufacturing, ICIEAM, 19-20 May 2016, Chelyabinsk, Russia. IEEE, 2016, p.1-5. DOI: https://doi.org/10.1109/ICIEAM.2016.7911546.
Wang, Peng; Chen, Guo-chu; Xu, Yu-fa; Yu, Jin-shou. “Improved empirical mode decomposition and its application to wind power forecasting,” Control Engineering China, v.18, n.4, p.588, 2011. URI: https://caod.oriprobe.com/articles/28044593/Improved_Empirical_Mode_Decomposition_and_its_Appl.htm.
Zhang, Zhi-meng; Liu, Chen-chen; Liu, Bo-sheng; Tian, Bao-jing. “Simulation analysis of envelops fitting algorithms in EMD,” J. System Simulation, v.21, n.23, p.7690, 2009. URI: http://caod.oriprobe.com/articles/38656675/jing_yan_mo_tai_fen_jie_zhong_de_bao_luo_xian_ni_he_suan_fa_fang_zhen_.htm.
Lazorenko, O.V.; Chernogor, L.F. “System spectral analysis of infrasonic signal generated by Chelyabinsk meteoroid,” Radioelectron. Commun. Syst., v.60, n.8, p.331, 2017. DOI: https://doi.org/10.3103/S0735272717080015.
Svoboda, M.; Matiu-Iovan, L.; Frigura-Iliasa, F.M.; Andea, P. “B-spline interpolation technique for digital signal processing,” Proc. of 2015 Int. Conf. on Information and Digital Technologies, 7-9 Jul. 2015, Zilina, Slovakia. IEEE, 2015, p.366-371. DOI: https://doi.org/10.1109/DT.2015.7222998.
Chen, Q.; Huang, N.; Riemenschneider, S.; Xu, Y. “A B-spline approach for empirical mode decompositions,” Adv. Comput. Math., v.24, n.1-4, p.171, 2006. DOI: https://doi.org/10.1007/s10444-004-7614-3.
Yang, J.H. Shixi; Wu, Zhaotong; et al. “Study of empirical mode decomposition based on high-order spline interpolation,” J. Zhejiang University: Engineering Sci., v.38, n.3, p.267, 2004.
Ding, H.; Lv, J. “Comparison study of two commonly used methods for envelope fitting of empirical mode decomposition,” Proc. of 2012 5th Int. Congress on Image and Signal Processing, 16-18 Oct. 2012, Chongqing, China. IEEE, 2012, p.1875-1878. DOI: https://doi.org/10.1109/CISP.2012.6469862.
Huang, D.J.; Zhao, J.P.; Su, J.L. “Practical implementation of Hilbert-Huang Transform algorithm,” Acta Oceanologica Sinica, v.22, n.1, p.1, 2003. URI: http://www.hyxb.org.cn/aoscn/ch/reader/view_abstract.aspx?file_no=20030101&flag=1.
Huang, N.E.; Shen, Z.; Long, S.R. “A new view of nonlinear water waves: The Hilbert spectrum,” Annual Review Fluid Mech., v.31, p.417, 1999. DOI: https://doi.org/10.1146/annurev.fluid.31.1.417.
Deering, R.; Kaiser, J.F. “The use of a masking signal to improve empirical mode decomposition,” Proc. of IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, 23 Mar. 2005, Philadelphia, USA. IEEE, 2005, v.4, p.iv/485-iv/488. DOI: https://doi.org/10.1109/ICASSP.2005.1416051.
Gao, Y.; Ge, G.; Sheng, Z.; Sang, E. “Analysis and solution to the mode mixing phenomenon in EMD,” Proc. of 2008 Congress on Image and Signal Processing, 27-30 May 2008, Sanya, Hainan, China. IEEE, 2008, p.223-227. DOI: https://doi.org/10.1109/CISP.2008.193.
Wu, Z.; Huang, N.E. “Ensemble empirical mode decomposition: A noise-assisted data analysis method,” Advances in Adaptive Data Analysis, v.01, n.01, p.1, 2009. DOI: https://doi.org/10.1142/S1793536909000047.
Senroy, N.; Suryanarayanan, S.; Ribeiro, P.F. “An improved Hilbert-Huang method for analysis of time-varying waveforms in power quality,” IEEE Trans. Power Systems, v.22, n.4, p.1843, Nov. 2007. DOI: https://doi.org/10.1109/TPWRS.2007.907542.
Huang, N.E.; Wu, M.-L.C.; Long, S.R.; Shen, S.S.P.; Qu, W.; Gloersen, P.; Fan, K.L. “A confidence limit for the empirical mode decomposition and Hilbert spectral analysis,” Proc. of Royal Soc. A - Math. Phys. Eng. Sci., v.459, n.2037, p.2317, Sep. 8 2003. DOI: https://doi.org/10.1098/rspa.2003.1123.
Stevenson, N.; Mesbah, M.; Boashash, B. “A sampling limit for the empirical mode decomposition,” Proc. of Eighth Int. Symp. on Signal Processing and Its Applications, 28-31 Aug. 2005, Sydney, Australia. IEEE, 2005, p.647-650. DOI: https://doi.org/10.1109/ISSPA.2005.1581021.
Rilling, G.; Flandrin, P. “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Signal Processing, v.56, n.1, p.85, Jan. 2008. DOI: https://doi.org/10.1109/TSP.2007.906771.
Boashash, B. “Estimating and interpreting the instantaneous frequency of a signal. II. Algorithms and applications,” Proc. IEEE, v.80, n.4, p.540, 1992. DOI: https://doi.org/10.1109/5.135378.
Cexus, J.-C.; Boudraa, A.-O. “Nonstationary signals analysis by Teager-Huang Transform (THT),” Proc. of 14th European Signal Processing Conf., 4-8 Sept. 2006, Florence, Italy. IEEE, 2006, p.1-5. URI: https://ieeexplore.ieee.org/document/7071680.
Benramdane, S.; Cexus, J.C.; Boudraa, A.O.; Astolfi, J.-A. “Time-frequency analysis of pressure fluctuations on a hydrofoil undergoing a transient pitching motion using Hilbert-Huang and Teager-Huang transforms,” Proc. of Asme Pressure Vessels and Piping Conf., 22-26 Jul. 2007, San Antonio, USA. IEEE, 2008, v.4: Fluid-Structure Interaction, p.199-207. DOI: https://doi.org/10.1115/PVP2007-26632.
Kaleem, M.F.; Sugavaneswaran, L.; Guergachi, A.; Krishnan, S. “Application of empirical mode decomposition and Teager energy operator to EEG signals for mental task classification,” Proc. of 2010 Annual Int. Conf. of IEEE Engineering in Medicine and Biology, 31 Aug.-4 Sept. 2010, Buenos Aires, Argentina. IEEE, 2010, p.4590-4593. DOI: https://doi.org/10.1109/IEMBS.2010.5626501.
Guo, J.; Qin, S.; Zhu, C. “The application of energy operator demodulation approach based on EMD in mechanical system identification,” Proc. of 19th Int. Conf. on Mechatronics and Machine Vision in Practice, M2VIP, 28-30 Nov. 2012, Auckland, New Zealand. IEEE, 2012, p.80-85. URI: https://ieeexplore.ieee.org/document/6484571.
Li, H.; Zheng, H.; Tang, L. “Gear fault diagnosis based on order tracking and Hilbert-Huang transform,” Proc. of 2009 Sixth Int. Conf. on Fuzzy Systems and Knowledge Discovery, 14-16 Aug. 2009, Tianjin, China. IEEE, 2009, p.468-472. DOI: https://doi.org/10.1109/FSKD.2009.220.