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An Improved EMD Method Based on Utilizing Certain Inflection Points in the Construction of Envelope Curves

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The empirical mode decomposition (EMD) algorithm is widely used as an adaptive time-frequency analysis method to decompose nonlinear and non-stationary signals into sets of intrinsic mode functions (IMFs). In the traditional EMD, the lower and upper envelopes should interpolate the minimum and maximum points of the signal, respectively. In this paper, an improved EMD method is proposed based on the new interpolation points, which are special inflection points (SIPn) of the signal. These points are identified in the signal and its first (n − 1) derivatives and are considered as auxiliary interpolation points in addition to the extrema. Therefore, the upper and lower envelopes should not only pass through the extrema but also these SIPn sets of points. By adding each set of SIPi (i = 1, 2, n) to the interpolation points, the frequency resolution of EMD is improved to a certain extent. The effectiveness of the proposed SIPn-EMD is validated by the decomposition of synthetic and experimental bearing vibration signals.
Rocznik
Strony
389--401
Opis fizyczny
Bibliogr. 36 poz., rys., tab., wykr.
Twórcy
autor
  • Mechanical Engineering Group, Pardis College, Isfahan University of Technology Isfahan, Iran
  • Mobarakeh Steel Company Isfahan, Iran
autor
  • Mobarakeh Steel Company Isfahan, Iran
  • Department of Mechanical Engineering, Isfahan University of Technology Isfahan, Iran
Bibliografia
  • 1. Bouchikhi A., Boudraa A.-O. (2012), Multicomponent AM–FM signals analysis based on EMD-B-splines ESA, Signal Processing, 92(9): 22142228, doi: 10.1016/j.sigpro.2012.02.014.
  • 2. Case Western Reserve University (n.d.), Bearing Data Center, https://engineering.case.edu/bearingdatacenter/download-data-file (access date: 21.02.2023).
  • 3. Chen Q., Huang N., Riemenschneider S., Xu Y. (2006), A B-spline approach for empirical mode decompositions, Advances in Computational Mathematics, 24(1): 171-195, doi: 10.1007/s10444-004-7614-3.
  • 4. Chu P.C., Fan C., Huang N. (2012), Compact empirical mode decomposition: An algorithm to reduce mode mixing, end effect, and detrend uncertainty, Advances in Adaptive Data Analysis, 4(3): 1250017, doi: 10.1142/S1793536912500173.
  • 5. Deering R., Kaiser J.F. (2005), The use of a masking signal to improve empirical mode decomposition, [in:] Proceedings (ICASSP’05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 4: 485-488, doi: 10.1109/ICASSP.2005.1416051.
  • 6. Egambaram A., Badruddin N., Asirvadam V.S., Begum T. (2016), Comparison of envelope interpolation techniques in empirical mode decomposition (EMD) for eyeblink artifact removal from EEG, [in:] 2016 IEEE EMBS Conference on Biomedical Engineering and Sciences (IECBES), pp. 590-595, doi: 10.1109/IECBES.2016.7843518.
  • 7. Guo T., Deng Z. (2017), An improved EMD method based on the multi-objective optimization and its application to fault feature extraction of rolling bearing, Applied Acoustics, 127: 46-62, doi: 10.1016/j.apacoust.2017.05.018.
  • 8. Huang N.E et al. (1998), The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 454(1971): 903-995, doi: 10.1098/rspa.1998.0193.
  • 9. Huang N.E. et al. (2003), A confidence limit for the empirical mode decomposition and Hilbert spectral analysis, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 459(2037): 2317-2345, doi: 10.1098/rspa.2003.1123.
  • 10. Kopsinis Y., McLaughlin S. (2007), Investigation and performance enhancement of the empirical mode decomposition method based on a heuristic search optimization approach, [in:] IEEE Transactions on Signal Processing, 56(1): 113, doi: 10.1109/TSP.2007.901155.
  • 11. Kopsinis Y., McLaughlin S. (2008), Improved EMD using doubly-iterative sifting and high order spline interpolation, EURASIP Journal on Advances in Signal Processing, 2008(1): 128293, doi: 10.1155/2008/128293.
  • 12. Lei Y., Lin J., He Z., Zuo M.J. (2013), A review on empirical mode decomposition in fault diagnosis of rotating machinery, Mechanical Systems and Signal Processing, 35(1–2): 108-126, doi: 10.1016/j.ymssp.2012.09.015.
  • 13. Li H., Qin X., Zhao D., Chen J.,Wang P. (2018), An improved empirical mode decomposition method based on the cubic trigonometric B-spline interpolation algorithm, Applied Mathematics and Computation, 332: 406--419, doi: 10.1016/j.amc.2018.02.039.
  • 14. Li H., Wang C., Zhao D. (2015a), An improved EMD and its applications to find the basis functions of EMI signals, Mathematical Problems in Engineering, 2015: 150127, doi: 10.1155/2015/150127.
  • 15. Li Y., Xu M., Wei Y., Huang W. (2015b), An improvement EMD method based on the optimized rational Hermite interpolation approach and its application to gear fault diagnosis, Measurement, 63: 330-345, doi:10.1016/j.measurement.2014.12.021.
  • 16. Pegram G.G.S., Peel M.C., McMahon T.A. (2008), Empirical mode decomposition using rational splines: An application to rainfall time series, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464(2094): 1483-1501, doi: 10.1098/rspa.2007.0311.
  • 17. Qin S.R., Zhong Y.M. (2006), A new envelope algorithm of Hilbert–Huang Transform, Mechanical Systems and Signal Processing, 20(8): 1941-1952, doi: 10.1016/j.ymssp.2005.07.002.
  • 18. Rilling G., Flandrin P. (2007), One or two frequencies? The empirical mode decomposition answers, [in:] IEEE Transactions on Signal Processing, 56(1): 85-95, doi: 10.1109/TSP.2007.906771.
  • 19. Rilling G., Flandrin P., Gonçalvès P. (2003), On empirical mode decomposition and its algorithms, [in:] IEEE-EURASIP workshop on nonlinear signal and image processing, 3(3): 8-11, Grado.
  • 20. Shu L., Deng H., Liu X., Pan Z. (2022), A Comprehensive working condition identification scheme for rolling bearings based on modified CEEMDAN as well as modified hierarchical amplitude-aware permutation entropy, Measurement Science and Technology, 33(7): 075111, doi: 10.1088/1361-6501/ac5b2c.
  • 21. Singh P., Joshi S.D., Patney R.K., Saha K. (2014), Some studies on nonpolynomial interpolation and error analysis, Applied Mathematics and Computation, 244: 809-821, doi: 10.1016/j.amc.2014.07.049.
  • 22. SKF (n.d.), Bearing Select, https://www.skfbearingselect.com/#/bearing-selection-start (access date: 21.02.2023).
  • 23. Smith W.A., Randall R.B. (2015), Rolling element bearing diagnostics using the Case Western Reserve University data: A benchmark study, Mechanical Systems and Signal Processing, 6465: 100-131, doi: 10.1016/j.ymssp.2015.04.021.
  • 24. Sun Y., Li S., Wang X. (2021), Bearing fault diagnosis based on EMD and improved Chebyshev distance in SDP image, Measurement, 176: 109100, doi:10.1016/j.measurement.2021.109100.
  • 25. Torres M.E., Colominas M.A., Schlotthauer G., Flandrin P. (2011), A complete ensemble empirical mode decomposition with adaptive noise, [in:] 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4144-4147, doi:1109/ICASSP.2011.5947265.
  • 26. Wang J., Du G., Zhu Z., Shen C., He Q. (2020), Fault diagnosis of rotating machines based on the EMD manifold, Mechanical Systems and Signal Processing, 135: 106443, doi: 10.1016/j.ymssp.2019.106443.
  • 27. Wang J.-L., Li Z.-J. (2013), Extreme-point symmetric mode decomposition method for data analysis, Advances in Adaptive Data Analysis, 5(3): 1350015, doi: 10.1142/S1793536913500155.
  • 28. Wang Z., Yang J., Guo Y. (2022), Unknown fault feature extraction of rolling bearings under variable speed conditions based on statistical complexity measures, Mechanical Systems and Signal Processing, 172: 108964, doi: 10.1016/j.ymssp.2022.108964.
  • 29. Wu Z., Huang N.E. (2009), Ensemble empirical mode decomposition: A noise-assisted data analysis method, Advances in Adaptive Data Analysis, 1(1): 1-41, doi: 10.1142/S1793536909000047.
  • 30. Xu Z., Huang B., Li K. (2010), An alternative envelope approach for empirical mode decomposition, Digital Signal Processing, 20(1): 77-84, doi: 10.1016/j.dsp.2009.06.009.
  • 31. Yang L., Yang Z., Zhou F., Yang L. (2014), A novel envelope model based on convex constrained optimization, Digital Signal Processing, 29(1): 138-146, doi: 10.1016/j.dsp.2014.02.017.
  • 32. Yeh J.-R., Shieh J.-S., Huang N.E. (2010), Complementary ensemble empirical mode decomposition: A novel noise enhanced data analysis method, Advances in Adaptive Data Analysis, 2(2): 135-156, doi: 10.1142/S1793536910000422.
  • 33. Yuan J., He Z., Ni J., Brzezinski A.J., Zi Y. (2013), Ensemble noise-reconstructed empirical mode decomposition for mechanical fault detection, Journal of Vibration and Acoustics, 135(2): 021011, doi: 10.1115/1.4023138.
  • 34. Yuan J., Xu C., Zhao Q., Jiang H., Weng Y. (2022), High-fidelity noise-reconstructed empirical mode decomposition for mechanical multiple and weak fault extractions, ISA Transaction, 129(Part B): 380-397, doi: 10.1016/j.isatra.2022.02.017.
  • 35. Zhao D., Huang Z., Li H., Chen J., Wang P. (2017), An improved EEMD method based on the adjustable cubic trigonometric cardinal spline interpolation, Digital Signal Processing, 64: 41-48, doi: 10.1016/j.dsp.2016.12.007.
  • 36. Zheng J., Cao S., Pan H., Ni Q. (2022), Spectral envelope-based adaptive empirical Fourier decomposition method and its application to rolling bearing fault diagnosis, ISA Transactions, 129(Part B): 476-492, doi: 10.1016/j.isatra.2022.02.049.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023). (PL)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-e472b400-8c4f-49b2-9a7e-6dce29e66190
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