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ENSEMBLE EMPIRICAL MODE DECOMPOSITION Noise Assisted Signal Analysis (nasa) Part II EEMD

ENSEMBLE EMPIRICAL MODE DECOMPOSITION Noise Assisted Signal Analysis (nasa) Part II EEMD. Zhaohua Wu and N. E. Huang: Ensemble Empirical Mode Decomposition: A Noise Assisted Data Analysis Method. Advances in Adaptive Data Analysis, 1, 1-41, 2009. The Ensemble Effects.

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ENSEMBLE EMPIRICAL MODE DECOMPOSITION Noise Assisted Signal Analysis (nasa) Part II EEMD

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  1. ENSEMBLE EMPIRICAL MODE DECOMPOSITIONNoise Assisted Signal Analysis (nasa)Part II EEMD Zhaohua Wu and N. E. Huang: Ensemble Empirical Mode Decomposition: A Noise Assisted Data Analysis Method. Advances in Adaptive Data Analysis, 1, 1-41, 2009

  2. The Ensemble Effects The true answer is not the one without perturbation of noise.

  3. EXAMPLE : ORIGINAL DATA

  4. “LOCAL” -> “LOCAL”

  5. Ensemble EMD Solves the mode mixing problem utilizing the uniformly distributed reference frame based on the white noise

  6. EXAMPLE : ORIGINAL DECOMP.

  7. Procedures for EEMD • Add a white noise series to the targeted data; • Decompose the data with added white noise into IMFs; • Repeat step 1 and step 2 again and again, but with different white noise series each time; and • Obtain the (ensemble) means of corresponding IMFs of the decompositions as the final result.

  8. Definition of Signal in EEMD The signal used in EEMD is given by :

  9. Definition of IMF in EEMD The truth defined by EEMD is given by the number of the ensemble approaching infinite:

  10. The Standard Deviation of EEMD With the truth defined, the discrepancy, Δ, should be in which E{ } is the expected value as given in Equation.

  11. Effect of the White Noise • The effects of the added white noise should decrease following the well established statistical rule:

  12. Data of the Noise Effects:Dotted line = theoretical; solid line = high frequency components; dashed line = low frequency components.

  13. Procedure for EEMD Illustration

  14. EXAMPLE : E1 DECOMP.

  15. EXAMPLE : E10 DECOMP.

  16. EXAMPLE : E100 DECOMP.

  17. EXAMPLE : Intermittence DECOMP.

  18. EXAMPLE : Difference Main IMF.

  19. EXAMPLE : Difference Intermittent Signal.

  20. EXAMPLE : Difference Intermittent Signal Details.

  21. EXAMPLE : Instantaneous Frequency from Main Signal.

  22. Summary: Numerical Data • From the intermittency Example, we see that the Ensemble EMD can generate IMFs with comparable quality as the ones through the Intermittence test. • More ensemble in the average will improve confidence in the EMD results. • The main advantage of Ensemble EMD is that we do not need to determine the ‘Intermittence test criteria’ subjectively, which could become impossible for complicated data.

  23. Example I : Geophysical DataSurface TemperatureData from Two Difference Satellite Radiometer channels

  24. EXAMPLE I: ORIGINAL DATA

  25. EXAMPLE I: DECOMPOSITION (I)

  26. EXAMPLE I: DECOMPOSITION (II)

  27. EXAMPLE I: NOISY DATA(added noise std=0.1)

  28. NOISY DATA DECOMPOSITION (I)(added noise std=0.1)

  29. NOISY DATA DECOMPOSITION (II)(added noise std=0.1)

  30. EXAMPLE I: NOISY DATA(added noise std=0.2)

  31. NOISY DATA DECOMPOSITION (I)(added noise std=0.2)

  32. NOISY DATA DECOMPOSITION (II)(added noise std=0.2)

  33. NOISY DATA DECOMPOSITION (II)(RSS_T2)

  34. NOISY DATA DECOMPOSITION (II)(RSS_T2)

  35. NOISY DATA DECOMPOSITION (II)(UAH_T2)

  36. NOISY DATA DECOMPOSITION (II)(UAH_T2)

  37. EXAMPLE I: CORR. COEF.’s

  38. Summary: Radiometer Data • Data from the two different channels should reflect a similar overall structure, especially for medium and long wave length. • Straightforward sifting will have severe mode mixing for medium scale IMFs. • It is impossible to select the proper scales for the ‘Intermittence test’ to separate the modes. • Ensemble EMD provided an automatic dyadic filter to separate the modes. • Ensemble EMD especially effective when the data contain intermittent signal as in UAH case as shown by the correlation coefficients between RSS and UAH series.

  39. Example II : Geophysical Data SOI and the Sea Surface temperature at Nino 34

  40. EXAMPLE II: ORIGINAL DATA

  41. EXAMPLE II: DECOMPOSITION (I)

  42. EXAMPLE II: DECOMPOSITION (II)

  43. EXAMPLE II: DECOMPOSITION (III)

  44. EXAMPLE II: NOISY DATA(added noise std=0.4)

  45. EXAMPLE II: DECOMPOSITION (I)(added noise std=0.4)

  46. EXAMPLE II: DECOMPOSITION (II)(added noise std=0.4)

  47. EXAMPLE II: DECOMPOSITION (III)(added noise std=0.4)

  48. CTI: DECOMPOSITION (I)

  49. CTI: DECOMPOSITION (II)

  50. CTI: DECOMPOSITION (III)

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