Analyse de l'invariance d'échelle de séries temporelles par la décomposition modale empirique et l'analyse spectrale de Hilbert

Yongxiang Huang (1, 2) , François G Schmitt (1) , Zhiming Lu (2) , Yulu Liu (2)

1 LOG - Laboratoire d’Océanologie et de Géosciences (LOG) - UMR 8187
2 SIAMM - Shanghai Institute of Applied Mathematics and Mechanics

In this paper, we propose an extended version of the Hilbert spectral analysis which is done in the framework of Empirical Mode Decomposition. This arbitrary order Hilbert spectral analysis is able to characterize the intermittency properties of multiscaling time series. The method is validated using simulations of fractional Brownian motion with many different values of the $H$ parameter, and with lognormal multifractal simulations. An application is shown to real data from the field of turbulence. The method proposed here works in the amplitude-frequency space, and is the first approach able to deal with intermittency exponents directly in the frequency space. It is also shown to be superior to the classical structure functions framework to retrieve backgraound scaling fluctuations in case of a strong periodic component.

Mots clés: Empirical mode decomposition; Hilbert spectral analysis; fractional Brownian motion; intermittency; multifractals

Domaines: Analyse de données, Statistiques et Probabilités [physics.data-an]; Traitement du signal et de l'image [eess.SP]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Traitement du signal et de l'image [eess.SP]

Yongxiang Huang, François G Schmitt, Zhiming Lu, Yulu Liu. Analyse de l'invariance d'échelle de séries temporelles par la décomposition modale empirique et l'analyse spectrale de Hilbert. Traitement du Signal, 2008, 25, pp.481-492. ⟨hal-00449081⟩