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Empirical Mode Decomposition

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Empirical Mode Decomposition

1. 1. Empirical Mode Decompositionand Hilbert-Huang Transform<br />Emine Can 2010<br />
2. 2. nonlinear process<br />Data Analysis<br />Fourier Spectral Analysis <br />Data Processing Methods<br /><ul><li> Spectrogram
3. 3. Wavelet Analysis
4. 4. Wigner-Ville Distribution (Heisenberg wavelet)
5. 5. Evolutionary spectrum
6. 6. EmpiricalOrthogonalFunction Expansion (EOF)
7. 7. Other methods</li></ul>Energy-frequency distributions =Spectrum≈Fourier Transform of the data<br />Restrictions: * the system must be linear<br /> * the data must be strictly periodic or stationary<br />10.2010<br />2<br />Empirical Mode Decomposition and Hilbert-Huang Transform<br />Modifications of Fourier SA<br />
8. 8. Hilbert <br />Transform<br />Instantaneous <br />Frequency<br />10.2010<br />3<br />Empirical Mode Decomposition and Hilbert-Huang Transform<br />Empirical Mode Decomposition<br />Complicated <br />Data Set<br />Intrinsic Mode Functions<br />(Energy-Frequency-Time)<br />
9. 9. A method that any complicated data set can be decomposedinto<br />a finiteand oftensmallnumber of `intrinsicmode functions' that<br />admitwell-behaved HilbertTransforms. <br />10.2010<br />4<br />Empirical Mode Decomposition and Hilbert-Huang Transform<br />Emperical Mode Decomposition (EMD)<br />Intrinsic Mode Functions(IMF)<br />IMF is a function that satisfies two conditions:<br /> 1- In the whole data set, the number of extrema and the number of zero crossings musteither equal or differ at most by one<br /> 2-At any point, the mean value of theenvelope defined by the local maxima and the envelope defined by the local<br />minima is zero<br />
10. 10. The empirical mode decomposition method: the sifting process<br />10.2010<br />Empirical Mode Decomposition and Hilbert-Huang Transform<br />5<br />
11. 11. 10.2010<br />Empirical Mode Decomposition and Hilbert-Huang Transform<br />6<br />
12. 12. The sifting process<br />Complicated Data Set x(t)<br />
13. 13. The sifting process<br />1. identify all upperextrema of x(t).<br />
14. 14. The sifting process<br />2. Interpolate the local maxima to form an upper envelope u(x).<br />
15. 15. The sifting process<br />3. identify all lowerextrema of x(t).<br />
16. 16. The sifting process<br />4. Interpolate the local minima to form an lower envelope l(x).<br />
17. 17. The sifting process<br />5. Calculate the mean envelope: m(t)=[u(x)+l(x)]/2.<br />
18. 18. The sifting process<br />6. Extract the mean from the signal: h(t)=x(t)-m(t)<br />
19. 19. The sifting process<br />7. Check whether h(t) satisfies the IMF condition. <br /> YES: h(t) is an IMF, stop sifting. NO: let x(t)=h(t), keep sifting.<br />
20. 20. The sifting process<br />
21. 21. The sifting process<br />
22. 22. The sifting process<br />
23. 23. The sifting process<br />
24. 24. The sifting process<br />
25. 25. The sifting process<br />
26. 26. 10.2010<br />Empirical Mode Decomposition and Hilbert-Huang Transform<br />21<br />
27. 27. 10.2010<br />Empirical Mode Decomposition and Hilbert-Huang Transform<br />22<br />The signal is composed of <br />a “high frequency” triangular waveform whose amplitude is slowly (linearly) growing. <br />a “middle frequency”sine wave whose amplitude is quickly (linearly) decaying <br />a “low frequency” triangular waveform<br />
28. 28. 10.2010<br />Empirical Mode Decomposition and Hilbert-Huang Transform<br />23<br />The sifting process<br />Stop criterion<br />A criterionfor the sifting process to stop: Standard deviation, SD, computed from the two consecutive sifting results is in limited size.<br />:residue after the kth iteration of the 1st IMF<br />A typical value for SD can be set between 0.2 and 0.3.<br />
29. 29. 10.2010<br />Empirical Mode Decomposition and Hilbert-Huang Transform<br />24<br />Hilbert Transform <br />*<br />Analytic Signal:<br />Instantaneous Frequency:<br />
30. 30. Advantages<br />*Adaptive,highly efficient,applicable to<br />nonlinear and non-stationary processes.<br />10.2010<br />25<br />Empirical Mode Decomposition and Hilbert-Huang Transform<br />
31. 31. Applications of EMD<br />10.2010<br />Empirical Mode Decomposition and Hilbert-Huang Transform<br />26<br />nonlinear wave evolution,<br />climate cycles,<br />earthquake engineering,<br />submarine design,<br />structural damage detection,<br />satellite data analysis,<br />turbulence flow,<br />blood pressure variations and heart arrhythmia,<br />non-destructive testing,<br />structural health monitoring,<br />signal enhancement,<br />economic data analysis,<br />investigation of brain rythms<br />Denoising<br />…<br />
32. 32. References<br />“The empirical mode decomposition and theHilbert spectrum for nonlinear and non-stationary time series analysis”Huanget al., The Royal Society, 4 November 1996.<br />Rilling Gabriel, FlandrinPatrick ,Gon¸calv`es Paulo, “On Empirical Mode Decomposition and Its Algorithms”<br />Stephen McLaughlin and YannisKopsinis.ppt “Empirical Mode Decomposition:A novel algorithm for analyzingmulticomponent signals” Institute of Digital Communications (IDCOM)<br />“Hilbert-Huang Transform(HHT).ppt” Yu-HaoChen, ID:R98943021, 2010/05/07<br />10.2010<br />27<br />Empirical Mode Decomposition and Hilbert-Huang Transform<br />