1. Empirical Mode Decompositionand Hilbert-Huang Transform Emine Can 2010

3. Wavelet Analysis

4. Wigner-Ville Distribution (Heisenberg wavelet)

5. Evolutionary spectrum

6. EmpiricalOrthogonalFunction Expansion (EOF)

7. Other methodsEnergy-frequency distributions =Spectrum≈Fourier Transform of the data Restrictions: * the system must be linear * the data must be strictly periodic or stationary 10.2010 2 Empirical Mode Decomposition and Hilbert-Huang Transform Modifications of Fourier SA

8. Hilbert Transform Instantaneous Frequency 10.2010 3 Empirical Mode Decomposition and Hilbert-Huang Transform Empirical Mode Decomposition Complicated Data Set Intrinsic Mode Functions (Energy-Frequency-Time)

9. A method that any complicated data set can be decomposedinto a finiteand oftensmallnumber of `intrinsicmode functions' that admitwell-behaved HilbertTransforms. 10.2010 4 Empirical Mode Decomposition and Hilbert-Huang Transform Emperical Mode Decomposition (EMD) Intrinsic Mode Functions(IMF) IMF is a function that satisfies two conditions: 1- In the whole data set, the number of extrema and the number of zero crossings musteither equal or differ at most by one 2-At any point, the mean value of theenvelope defined by the local maxima and the envelope defined by the local minima is zero

10. The empirical mode decomposition method: the sifting process 10.2010 Empirical Mode Decomposition and Hilbert-Huang Transform 5

11. 10.2010 Empirical Mode Decomposition and Hilbert-Huang Transform 6

12. The sifting process Complicated Data Set x(t)

13. The sifting process 1. identify all upperextrema of x(t).

14. The sifting process 2. Interpolate the local maxima to form an upper envelope u(x).

15. The sifting process 3. identify all lowerextrema of x(t).

16. The sifting process 4. Interpolate the local minima to form an lower envelope l(x).

17. The sifting process 5. Calculate the mean envelope: m(t)=[u(x)+l(x)]/2.

18. The sifting process 6. Extract the mean from the signal: h(t)=x(t)-m(t)

19. The sifting process 7. Check whether h(t) satisfies the IMF condition. YES: h(t) is an IMF, stop sifting. NO: let x(t)=h(t), keep sifting.

20. The sifting process

21. The sifting process

22. The sifting process

23. The sifting process

24. The sifting process

25. The sifting process

26. 10.2010 Empirical Mode Decomposition and Hilbert-Huang Transform 21

27. 10.2010 Empirical Mode Decomposition and Hilbert-Huang Transform 22 The signal is composed of a “high frequency” triangular waveform whose amplitude is slowly (linearly) growing. a “middle frequency”sine wave whose amplitude is quickly (linearly) decaying a “low frequency” triangular waveform

28. 10.2010 Empirical Mode Decomposition and Hilbert-Huang Transform 23 The sifting process Stop criterion A criterionfor the sifting process to stop: Standard deviation, SD, computed from the two consecutive sifting results is in limited size. :residue after the kth iteration of the 1st IMF A typical value for SD can be set between 0.2 and 0.3.

29. 10.2010 Empirical Mode Decomposition and Hilbert-Huang Transform 24 Hilbert Transform * Analytic Signal: Instantaneous Frequency:

30. Advantages *Adaptive,highly efficient,applicable to nonlinear and non-stationary processes. 10.2010 25 Empirical Mode Decomposition and Hilbert-Huang Transform

31. Applications of EMD 10.2010 Empirical Mode Decomposition and Hilbert-Huang Transform 26 nonlinear wave evolution, climate cycles, earthquake engineering, submarine design, structural damage detection, satellite data analysis, turbulence flow, blood pressure variations and heart arrhythmia, non-destructive testing, structural health monitoring, signal enhancement, economic data analysis, investigation of brain rythms Denoising …

32. References “The empirical mode decomposition and theHilbert spectrum for nonlinear and non-stationary time series analysis”Huanget al., The Royal Society, 4 November 1996. Rilling Gabriel, FlandrinPatrick ,Gon¸calv`es Paulo, “On Empirical Mode Decomposition and Its Algorithms” Stephen McLaughlin and YannisKopsinis.ppt “Empirical Mode Decomposition:A novel algorithm for analyzingmulticomponent signals” Institute of Digital Communications (IDCOM) “Hilbert-Huang Transform(HHT).ppt” Yu-HaoChen, ID:R98943021, 2010/05/07 10.2010 27 Empirical Mode Decomposition and Hilbert-Huang Transform