**48**, 3, pp. 389–401, 2023

**10.24425/aoa.2023.145245**

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

**Keywords**: empirical mode decomposition (EMD); interpolation points; envelope curve; inflection points; rolling element bearing fault diagnosis

**Full Text:**PDF

#### References

Bouchikhi A., Boudraa A.-O. (2012), Multicomponent AM–FM signals analysis based on EMD-B-splines ESA, Signal Processing, 92(9): 2214–2228, doi: 10.1016/j.sigpro.2012.02.014.

Case Western Reserve University (n.d.), Bearing Data Center, https://engineering.case.edu/bearingdatacenter/download-data-file (access date: 21.02.2023).

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.

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.

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.

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.

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.

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.

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.

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): 1–13, doi: 10.1109/TSP.2007.901155.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

SKF (n.d.), Bearing Select, https://www.skfbearingselect.com/#/bearing-selection-start (access date: 21.02.2023).

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, 64–65: 100–131, doi: 10.1016/j.ymssp.2015.04.021.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

DOI: 10.24425/aoa.2023.145245