Journal of Korean Society of Industrial and Systems Engineering (산업경영시스템학회지)

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
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Control Limits of Time Series Data using Hilbert-Huang Transform : Dealing with Nested Periods

힐버트-황 변환을 이용한 시계열 데이터 관리한계 : 중첩주기의 사례

  • Suh, Jung-Yul (School of Industrial Engineering, Kumoh National Institute of Technology) ;
  • Lee, Sae Jae (School of Industrial Engineering, Kumoh National Institute of Technology)
  • 서정열 (금오공과대학교 산업공학부) ;
  • 이세재 (금오공과대학교 산업공학부)
  • Received : 2014.08.11
  • Accepted : 2014.11.10
  • Published : 2014.12.31
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Abstract

Real-life time series characteristic data has significant amount of non-stationary components, especially periodic components in nature. Extracting such components has required many ad-hoc techniques with external parameters set by users in a case-by-case manner. In this study, we used Empirical Mode Decomposition Method from Hilbert-Huang Transform to extract them in a systematic manner with least number of ad-hoc parameters set by users. After the periodic components are removed, the remaining time-series data can be analyzed with traditional methods such as ARIMA model. Then we suggest a different way of setting control chart limits for characteristic data with periodic components in addition to ARIMA components.

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References

  1. Chui, C.K., An introduction to Wavelets. San Diego : Academic Press, 1992.
  2. Daubechies, I., Ten lectures on Wavelets, Society for Industrial and Applied Mathematics, 1992.
  3. Flandrin, P., Rilling, G., and Goncalves, P., Empirical mode decomposition as a filter bank. IEEE Signal Proc Lett., 2003, Vol. 11, p 112-114.
  4. Huang, C., Sachin T., and Shin, Y.J., Wavelet-based Real Time Detection of Network Traffic Anomalies, Securecomm and Workshops, 2006, p 1-7.
  5. Huang, N., Shen, Z., Long, S., Wu, M., Shih, H., Zheng, Q., Yen, N., Tung, C., and Liu, H., The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. London, 1998, A454, p 903-995.
  6. Huang, N. and Attoh-Okine, N.O., The Hilbert-Huang transform in engineering, Taylor and Francis, 2005.
  7. Huang, N.E. and Shen, S.P., Hilbert-Huang transform and its applications, London : World Scientific, 2005.
  8. Jacobsen, E. and Lyons, R., The sliding DFT. Signal Processing Magazine, 2003, Vol. 20, No. 2, p 74-80.
  9. Lee, S.J. and Suh, J.Y., Evaluating Efficacy of Hilbert- Huang Transform in Analyzing Manufacturing Time Series Data with Periodic Components. J. Soc. Korea Ind. Syst. Eng., 2012, Vol. 35, No. 2, p 106-112.
  10. Little, M., McSharry, P., Roberts, S., Costello, D., and Moroz, I., Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection. Biomed Eng Online, 2007, Vol. 6, No. 1, p 23. https://doi.org/10.1186/1475-925X-6-23
  11. Lomb, N.R., Least-squares frequency analysis of unequally spaced data. Astrophysics and Space Science, 1976, Vol. 39, p 447-462. https://doi.org/10.1007/BF00648343
  12. Reynolds, Jr., Marion R., and Lu, C., Control charts for monitoring processes with autocorrelated data. Nonlinear Analysis, Theory, Methods and Applications, 1997, Vol. 30, No. 7, p 4059-4067. https://doi.org/10.1016/S0362-546X(97)00011-4
  13. Scargle, J.D., Studies in astronomical time series analysis II : Statistical aspects of spectral analysis of unevenly spaced data. Astrophysical Journal, 1982, Vol. 263, p 835-853. https://doi.org/10.1086/160554
  14. Sheu, S.H., Huang, C.J., and Hsu, T.S., Extended maximum generally weighted moving average control chart for monitoring process mean and variability. Computers and Industrial Engineering, 2012, Vol. 62, p 216-225. https://doi.org/10.1016/j.cie.2011.09.009
  15. Stark, J., Broomhead, D., Davies, M., and Huke, J., Takens embedding theorems for forced and stochastic systems. Nonlinear Analysis-Theory Methods and Applications, 1997, Vol. 30, No. 8, p 5303-5314. https://doi.org/10.1016/S0362-546X(96)00149-6
  16. Vanicek, P., Approximate Spectral Analysis by Leastsquares Fit. Astrophysics and Space Science, 1969, Vol. 4, p 387-391. https://doi.org/10.1007/BF00651344
  17. Wei, L. and Ghorbani, A.A., Network Anomaly Detection Based on Wavelet Analysis. EURASIP Journal on Advances in Signal Processing, 2009, p 16.