응용통계연구 (The Korean Journal of Applied Statistics)

  • 제26권2호
  • /
  • Pages.335-347
  • /
  • 2013
  • /
  • 1225-066X(pISSN)
  • /
  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

이차 미분을 이용한 경험적 모드분해법

Empirical Mode Decomposition using the Second Derivative

  • Park, Min-Su (Department of Statistics, Seoul National University) ;
  • Kim, Donghoh (Department of Applied Mathematics, Sejong University) ;
  • Oh, Hee-Seok (Department of Statistics, Seoul National University)
  • 투고 : 2013.02.25
  • 심사 : 2013.04.02
  • 발행 : 2013.04.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

다양한 분야에서 시그널(signal) 형태로 자료들이 표현된다. 예를 들면 심전도(electrocardiogram)는 심근에서 발생하는 활동 전류를 나타내는데, 심장의 박동에 따라 수축과 이완을 반복하는 과정을 시간에 따른 활동 전류량의 변동으로 나타낸다. 현실세계에서 측정하거나 관찰되는 시그널에는 다양한 형태의 시그널들이 혼합되어 있는 경우가 흔하다. 예를 들어 오케스트라 연주의 아름다운 선율은 고유한 주파수(frequency)를 지닌 악기들의 다양한 소리로 구성되어 있으며, 각기 다른 음조(note)가 하나로 모여 완벽한 하모니를 형성하게 된다. 시그널이 정상인(stationary) 경우에 혼합된 시그널들을 분해하여 분석하는 방법에 대해 현재까지 다양하게 연구되어 왔다. 자료가 비정상(non-stationary)일 경우에는 기존의 방법론들을 적용시키기에는 한계가 있다. 비정상성 자료를 다루기 위해 Huang 등 (1998)은 경험적 모드분해법(empirical mode decomposition)이라는 방법을 제안하였다. 자료에 내포되어 있는 국소적인 파동(oscillation)을 국소 극값들(local extrema)을 식별하여 자료 적응적으로 추출한다. 경험적 모드분해법은 잡음(error)에 의해 자료가 오염되어 있는 경우에는 국소 극값들을 통하여 국소적인 파동을 추정하기 어려우며, 자료의 크기가 커짐에 따라 계산량도 크게 늘어나는 단점 등이 있다. 본 연구에서는 이차 미분을 이용하여 국소적인 파동을 식별하고 추정하는 새로운 방법론을 제시하고자 한다.

There are various types of real world signals. For example, an electrocardiogram(ECG) represents myocardium activities (contraction and relaxation) according to the beating of the heart. ECG can be expressed as the fluctuation of ampere ratings over time. A signal is a composite of various types of signals. An orchestra (which boasts a beautiful melody) consists of a variety of instruments with a unique frequency; subsequently, each sound is combined to form a perfect harmony. Various research on how to to decompose mixed stationary signals have been conducted. In the case of non-stationary signals, there is a limitation to use methodologies for stationary signals. Huang et al. (1998) proposed empirical mode decomposition(EMD) to deal with non-stationarity. EMD provides a data-driven approach to decompose a signal into intrinsic mode functions according to local oscillation through the identification of local extrema. However, due to the repeating process in the construction of envelopes, EMD algorithm is not efficient and not robust to a noise, and its computational complexity tends to increase as the size of a signal grows. In this research, we propose a new method to extract a local oscillation embedded in a signal by utilizing the second derivative.

키워드

참고문헌

  1. Blanco-Velasco, M., Weng, B. and Barner, K. E. (2008). ECG signal denoising and baseline wander correction based on the empirical mode decomposition, Computers in Biology and Medicine, 38, 1-13. https://doi.org/10.1016/j.compbiomed.2007.06.003
  2. Campolo, M., Labate, D., La Foresta, F., Morabito, F. C., Lay-Ekuakille, A. and Vergallo, P. (2011). ECGderived respiratory signal using empirical mode decomposition, In Proceedings of the IEEE International Symposium on Medical Measurements and Applications (MeMeA '11), article 5966727.
  3. Coughlin, K. T. and Tung, K.-K. (2004). 11-year solar cycle in the stratosphere extracted by the empirical mode decomposition method, Advances in Space Research, 34, 323-329. https://doi.org/10.1016/j.asr.2003.02.045
  4. Deering, R. and Kaiser, J. F. (2005). The use of a masking signal to improve empirical mode decomposition, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 4, 485-488.
  5. Huang, N. E. and Shen, S. S. P. (2005). Hilbert-Huang Transform and Its Applications, World Scientific, Singapore.
  6. Huang, N. E., Shen, Z., Long, S. R., Wu, M. L., Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C. and Liu, H. H. (1998). The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis, Proceedings of the Royal Society London A, 454, 903-995. https://doi.org/10.1098/rspa.1998.0193
  7. Huang, N. E., Wu, M.-L. C., Qu, W., Long, S. R., Shen, S. S. P. and Zhang, J. E. (2003). Applications of Hilbert-Huang transform to non-stationary financial time series analysis, Applied Stochastic Models in Business and Industry, 19, 245-268. https://doi.org/10.1002/asmb.501
  8. Huang, W., Sher, Y.-P., Peck, K. and Fung, Y. C. (2002). Matching gene activity with physiological functions, Proceedings of the National Academic of Sciences of the United States of America, 99, 2603-2608. https://doi.org/10.1073/pnas.042684399
  9. Kim, D., Kim, K. O. and Oh, H. S. (2012a). Extending the scope of empirical mode decomposition using smoothing, EURASIP Journal on Advances in Signal Processing, 2012:168. https://doi.org/10.1186/1687-6180-2012-168
  10. Kim, D. and Oh, H. S. (2006). Hierarchical Smoothing Technique by Empirical Mode Decomposition, The Korean Journal of Applied Statistics, 19, 319-330. https://doi.org/10.5351/KJAS.2006.19.2.319
  11. Kim, D. and Oh, H. S. (2009a). A multi-resolution approach to non-stationary financial time series using the Hilbert-Huang transform, The Korean Journal of Applied Statistics, 22, 499-513. https://doi.org/10.5351/KJAS.2009.22.3.499
  12. Kim, D. and Oh, H. S. (2009b). EMD: A package for empirical mode decomposition and Hilbert spectrum, The R Journal, 1, 40-46.
  13. Kim, D. and Oh, H. S. (2013). EMD: Empirical mode decomposition and Hilbert spectral analysis, http://cran.r-project.org/web/packages/EMD/index.html
  14. Kim, D., Park, M. and Oh, H. S. (2012b). Bidimensional statistical empirical mode decomposition, IEEE Signal Processing Letters, 19, 191-194. https://doi.org/10.1109/LSP.2012.2186566
  15. Liu, Z.-F., Liao, Z.-P. and Sang, E.-F. (2005). Speech enhancement based on Hilbert-Huang transform, Proceedings of 2005 International Conference on Machine Learning and Cybernetics, 8, 4908-4912.
  16. Nason, G. (2012). wavethresh: Wavelets statistics and transforms, http://cran.r-project.org/web/packages/ wavethresh/index.html
  17. Priestley, M. B. (1981). Spectral Analysis and Time Series Vols. 1 and 2, Academic Press, New York.
  18. Rilling, G., Flandrin, P. and Goncalves, P. (2003). On empirical mode decomposition and its algorithm, IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP-03.
  19. Wu, Z. and Huang, N. E. (2009). Ensemble empirical mode decomposition: a noise assisted data analysis method, Advances in Adaptive Data Analysis, 1, 1-49. https://doi.org/10.1142/S1793536909000047
  20. Yi, K. H., Park, S. B. and Yoon, H. R. (2006). Real time ECG derived respiratory extraction from heart rate for single lead ECG measurement using conductive textile electrode, The Transactions of the Korean Institute of Electrical Engineers, 55, 335-343.
  21. Zeng, K. and He, M.-X. (2004). A simple boundary process technique for empirical mode decomposition, Proceedings of 2004 IEEE International Geoscience and Remote Sensing Symposium, 6, 4258-4261.
  22. Zhang, R. R., Ma, S., Safak, E. and Hartzell, S. (2003). Hilbert-Huang transform analysis of dynamic and earthquake motion recordings, Journal of Engineering Mechanics, 129, 861-875. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:8(861)

피인용 문헌

  1. Duplicated ECG signal decomposition vol.19, pp.2, 2015, https://doi.org/10.6109/jkiice.2015.19.2.414
  2. A Study on Fault Diagnosis Algorithm for Rotary Machine using Data Mining Method and Empirical Mode Decomposition vol.15, pp.4, 2016, https://doi.org/10.14775/ksmpe.2016.15.4.023