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Ensemble Empirical Mode Decomposition (EEMD) for Noise-Assisted Signal Analysis

Explore the innovative EEMD method for data analysis, utilizing white noise to solve mode mixing issues and improve signal quality. Learn the procedures, definitions, and benefits of incorporating noise in signal decomposition.

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Ensemble Empirical Mode Decomposition (EEMD) for Noise-Assisted Signal Analysis

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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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