Sensitivity of the Empirical Mode Decomposition to Interpolation Methodology and Data Non-stationarity
Empirical mode decomposition (EMD) is a commonly used method in environmental science to study environmental variability in specific time period. Empirical mode decomposition is a sifting process that aims to decompose non-stationary and non-linear data into their embedded modes based on the local extrema. The local extrema are connected by interpolation. The results of EMD strongly impact the environmental assessment and decision making. In this paper, the sensitivity of EMD to different interpolation methods, linear, cubic, and smoothing-spline, is examined. A range of non-stationary data, including linear, quadratic, Gaussian, and logarithmic trends as well as noise, is used to investigate the method’s sensitivity to different types of non-stationarity. The EMD method is found to be sensitive to the type of non-stationarity of the input data, and to the interpolation method in recovering low-frequency signals. Smoothing-spline interpolation gave overall the best. The accuracy of the method is also limited by the type of non-stationarity: if the data have an abrupt change in amplitude or a large change in the variance, the EMD method cannot sift correctly.
KeywordsEmpirical mode decomposition Non-linear and non-stationary data Time series analysis Sensitivity analysis Interpolation method
The authors would like to thank Peter McIntyre for help with proof reading. The authors are also indebted to the anonymous reviewer whose comments resulted in a significantly improved version of the manuscript.
This study was financially supported by the School of Physical, Environmental and Mathematical Sciences at the University of New South Wales Canberra.
- 1.Bahri, F.M., & Sharples, J.J. (2015). Sensitivity of the Hilbert-Huang transform to interpolation methodology: examples using synthetic and ocean data. In MODSIM2015, 21st international congress on modelling and simulation. Modelling and simulation society of Australia and New Zealand (pp. 1324–1330).Google Scholar
- 4.Deering, R, & Kaiser, JF. (2005). The use of a masking signal to improve empirical mode decomposition. In IEEE international conference, acoustics, speech, and signal processing, 2005. Proceedings. (ICASSP’05) (Vol. 4, p. iv–485).Google Scholar
- 5.Donnelly, D. (2006). The fast Fourier and Hilbert-Huang transforms: a comparison. Computational Engineering in Systems Applications, 1, 84–88.Google Scholar
- 7.Duffy, DG. (2005). The application of Hilbert-Huang transforms to meteorological datasets. Hilbert-Huang Transform and Its Applications (pp. 129–147).Google Scholar
- 8.Ezer, T, Atkinson, LP, Corlett, WB, Blanco, JL. (2013). Gulf Stream’s induced sea level rise and variability along the US mid-Atlantic coast. Journal of Geophysical Research: Oceans, 118, 685–697.Google Scholar
- 11.Huang, NE, & Shen, SS. (2005). Hilbert-Huang transform and its applications. Singapore: World Scientific.Google Scholar
- 12.Huang, NE, & Wu, Z. (2008). A review on Hilbert-Huang transform: method and its applications to geophysical studies. Reviews of Geophysics, 46.Google Scholar
- 13.Huang, NE, Shen, Z, Long, SR, Wu, MC, Shih, HH, Zheng, Q, Yen, N-C, Tung, CC, Liu, HH. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 454, 903–995.CrossRefGoogle Scholar
- 17.Pachori, RB. (2008). Discrimination between ictal and seizure-free EEG signals using empirical mode decomposition. Research Letters in Signal Processing, 14.Google Scholar
- 18.Parzen, E. (1999). Stochastic processes. SIAM, 24.Google Scholar
- 20.Peel, MC, McMahon, TA, Pegram, G.G.S. (2009). Assessing the performance of rational spline-based empirical mode decomposition using a global annual precipitation dataset. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 465, 1919–1937.CrossRefGoogle Scholar
- 21.Peel, MC, McMahon, TA, Srikanthan, R, Tan, KS. (2011). Ensemble empirical mode decomposition: testing and objective automation. In Proceedings of the 34th world congress of the international association for hydro-environment research and engineering: 33rd hydrology and water resources symposium and 10th conference on hydraulics in water engineering (p. 702).Google Scholar
- 25.Priestley, MB. (1988). Non-linear and non-stationary time series analysis. London: Academic Press.Google Scholar
- 30.Torres, ME, Colominas, M, Schlotthauer, G, Flandrin, P, et al. (2011). A complete ensemble empirical mode decomposition with adaptive noise. In 2011 IEEE international conference on acoustics, speech and signal processing (ICASSP) (Vol. 2011, pp. 4144–4147).Google Scholar
- 34.Yang, C, Zhang, J, Fan, G, Huang, Z, Zhang, C. (2012). Time-frequency analysis of seismic response of a high steep hill with two side slopes when subjected to ground shaking by using HHT. In Sustainable transportation systems: plan, design, build, manage, and maintain.Google Scholar