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Hilbert-Huang Transform(HHT)

Hilbert-Huang Transform(HHT). Presenter: Yu-Hao Chen ID:R98943021 2010/05/07. Outline. Author Motivation Hilbert Transform Instantaneous frequency(IF) Flow chart Theory Intrinsic Mode Function(IMF) Empirical Mode Decomposition(EMD) Time–Frequency analysis Application Problem

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Hilbert-Huang Transform(HHT)

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  1. Hilbert-Huang Transform(HHT) Presenter: Yu-Hao Chen ID:R98943021 2010/05/07

  2. Outline • Author • Motivation • Hilbert Transform • Instantaneous frequency(IF) • Flow chart • Theory • Intrinsic Mode Function(IMF) • Empirical Mode Decomposition(EMD) • Time–Frequency analysis • Application • Problem • Summary

  3. Norden E. Huang (黃鍔) • Career and Experience • Research Scientist, NASA (1975-2006) • National Academy of Engineering (2000) • Academia Sinica (2006) • NASA Goddard Space Flight Center (2000-2006) • Research Center for Adaptive Data Analysis (2006) • Research topic • Engineering Sciences • Applied Mathematical Sciences • Applied Physical Sciences

  4. Motivation • To deal with nonlinear and non-stationarysignal • To get Instantaneous frequency(IF) [5]

  5. Hilbert Transform • The Hilbert transform can be thought of as the convolution of s(t) with the function h(t) = 1/(πt) • Derive the analytic representation of a signal

  6. Instantaneous Frequency(IF) • s(t) = β + cos(t) • (1) β = 0: IF is the constant • (2) 0 < β < 1: IF has been oscillating • (3) β > 1: IF has been negative [3] [3] [3]

  7. Flow Chart [1] [4]

  8. Intrinsic Mode Function(IMF) • The number of extrema and zero-crossings must either be equal or differ at most by one. • The mean value of the upper envelope and the lower envelope is zero. [5]

  9. Empirical Mode Decomposition(EMD)(1/8) [1]

  10. Empirical Mode Decomposition(EMD)(2/8) [1]

  11. Empirical Mode Decomposition(EMD)(3/8) [1]

  12. Empirical Mode Decomposition(EMD)(4/8) [1]

  13. Empirical Mode Decomposition(EMD)(5/8) [1]

  14. Empirical Mode Decomposition(EMD)(6/8) • SD<0.1 => IMF [4] [1]

  15. Empirical Mode Decomposition(EMD)(7/8) [1] Sifting Process

  16. Empirical Mode Decomposition(EMD)(8/8) [4]

  17. Example [5]

  18. Time–Frequency Analysis • Fast Fourier Transform (FFT) • Wavelet Transform • Hilbert-Huang Transform (HHT)

  19. Application • Geoscience • Biomedical applications • Multimodal Pressure Flow (MMPF) • Financial applications • Image processing • Audio processing • Structural health monitoring

  20. Geoscience • Length of day 1章年(19年) [5]

  21. Biomedical(1/2) • Multimodal Pressure Flow (MMPF) [5]

  22. Biomedical(2/2) • Doppler blood flow signal analysis [14] • Detection and estimation of Doppler shift [15]

  23. Image Processing • Edge detection [10] • Image denoise [11] • Image fusion [12] a b c a. EMD b. Sobel c. Canny

  24. Problems of HHT • P1: Stopping criterion • P2: End effect problem • Hilbert Transform • EMD • P3: Mode mixing problem • Ensemble EMD (EEMD) • Post-processing of EEMD • P4: Speed of computing • P5: Spline

  25. P1: Stopping Criterion [1] • Standard deviation(SD) • SD ≤ 0.2~0.3 • S number criterion • 3 ≤ S ≤ 5 • Three parameter method(θ1,θ2, α) • Mode amplitude： • Evaluation function： • σ(t)< θ1 in (1- α) σ(t)< θ2 in α • α ≒ 0.05, θ1 ≒0.05, θ2 ≒ 10θ1 [2] [3]

  26. P2: End Effect Problem • End effect of Hilbert Transform [1] • End effect of EMD

  27. minima maxima P2: Solutions for End Effects • End effect of Hilbert Transform • Adding characteristics waves • End effect of EMD • Extension with linear spline fittings near the boundaries [6]

  28. P3: Mode Mixing • Ensemble EMD (EEMD) • Post-processing of EEMD [1]

  29. P3: Ensemble EMD (EEMD) • Noise n1-nm are identical independent distributed. • Ensemble EMD indeed enables the signals of similar scale collated together. • The ensemble EMD results might not be IMFs. [7] [8] EEMDIMF … … … … …

  30. P3: Post-Processing of EEMD • Post-processing EEMD can get real IMFs. … …

  31. P4: Speed of Computing • The processing time of HHT is dependent on complexity of the data and criterions of the algorithm • HHT data processing system(HHT-DPS) • Implementation of HHT based on DSP [13]

  32. P5: Spline • Cubic B-Spline [5]

  33. Conclusion • The definition of an IMF guarantees a well-behaved Hilbert transform of the IMF • IMF represents intrinsic signature of physics behind the data • Although there are still many problems in HHT,HHT has lots of applications in all aspects

  34. Reference(1/3) [1] N. E. Huang, Z. Shen, etc. “The empirical mode deomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proceedings of the Royal Society, vol. 454, no. 1971, pp. 903–995, March 8 1998. [2 ] N. E. Huang, M. C. Wu, S. R. Long, S. S. P. Shen, W. Qu, P. Gloersen and K. L. Fan, “A Confidence Limit for the Empirical Mode Decomposition and Hilbert Spectrum Analysis”, Proc. R. Soc. Lond. A, vol. 459, 2003, pp. 2317- 2345. [3] G. Rilling, P. Flandrin and P. Gonçalvés, “On Empirical Mode Decomposition and Its Algorithms”, IEEE-EURASIP Work- shop on Nonlinear Signal and Image Processing NSIP-03, Grado, Italy, 8-11 Jun. 2003. [4] J. Cheng, D. Yu and Y. Yang, “Research on the Intrinsic Mode Function (IMF) Criterion in EMD Method”, Mechanical Systems and Signal Processing, vol. 20, 2006, pp. 817-824. [5]Z. Xu, B. Huang and S. Xu, “Exact Location of Extrema for Empirical Mode Decomposition”, Electronics Letters, vol. 44, no. 8, 10 Apr. 2008, pp. 551-552. [6] 國立中央大學 數據分析研究中心 (RCADA) Available: http://rcada.ncu.edu.tw/intro.html

  35. Reference(2/3) [7]Z. WU and N. E. HUANG , “ENSEMBLE EMPIRICAL MODE DECOMPOSITION:A NOISE-ASSISTED DATA ANALYSIS METHOD”, Advances in Adaptive Data Analysis, Vol. 1, No. 1 pp 1–41,2009 [8] Master thesis: Applications of Ensemble Empirical Mode Decomposition (EEMD) and Auto-Regressive (AR) Model for Diagnosing Looseness Faults of Rotating Machinery [9] Y. Deng, W. Wang, C. Qian, Z. Wang and D. Dai, ”Boundary-Processing- Technique in EMD Method and Hilbert Transform”, Chinese Science Bulletin, vol. 46, no. 1, Jan. 2001, pp. 954-960. [10] J. Zhao and D. Huang, “Mirror Extending and Circular Spline Function for Empirical Mode Decomposition Method”, Journal of Zhejiang University, Science, vol. 2, no.3, July-Sep. 2001, pp. 247-252. [11] K. Zeng and M. He, “A simple Boundary Process Technique for Empirical Mode Decomposition”, IEEE International Geoscience and Remote Sensing Symposium IGARSS '04, vol. 6, 2004, pp. 4258-4261. [12] Z. Zhao and Y. Wang, “A New Method for Processing End Effect in Empirical Mode Decomposition”, IEEE International Conference on Circuits and Systems for Communications ICCSC 2007, 2007, pp. 841-845.

  36. Reference(3/3) • [13] H. Li and Z. Li, etc. ,” Implementation of Hilbert-Huang Transform (HHT) Based on DSP”, International Conference on Signal Processing, vol.1, 2004 • [14] Z. Zhidong and W. Yang ,”ANew Method for Processing End Effect In Empirical Mode Decomposition”, International Conference on Communications, Circuits and Systems,ICCCAS ,pp 841-845, July 2007

  37. Thank you

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