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Modélisation et détection de ruptures des signaux physiologiques issus de compétitions d'endurance

Abstract : This work focuses on the modeling and the estimation of relevant parameters characterizing instantaneous heart rate (HR) signals. We choose to focus especially in an exponent that can be called "Fractal", which indicates the local regularity of the path and the dependency between data. The asymptotic properties of the DFA (Detrended Fluctuation Analysis) function and the deduced estimator of H are studied in the case of fractional Gaussian noise (FGN) and extended to a general class of stationary semi-parametric long-range dependent processes with or without trend. We show that this method is not at all robust. We propose the modeling of HR data with a generalization of FGN, called locally fractional Gaussian noise. Such stationary process is built from a parameter called of local fractality which is a kind of Hurst parameter (that may take values in IR) in restricted band frequency. The estimation of local fractality parameter and also the construction of goodness-of-fit test can be made with wavelet analysis. We also show the relevance of model and an evolution of the parameter during the race. Then, change detection in this parameter can be extremely meaningful. We propose a method detecting multiple abrupt changes of long memory parameter (respectively self-similarity, local fractality). From a wavelet analysis, an estimator of the change points is proved to satisfy a limit theorem. A central limit theorem is established for the estimator of each parameter and a goodness-of-fit test is also built in each zona where the parameter does not change. Finally, we show the same evolution of local fractality parameter relating to HR time series.
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Contributor : Imen Kammoun Connect in order to contact the contributor
Submitted on : Thursday, December 20, 2007 - 6:36:00 PM
Last modification on : Wednesday, August 31, 2022 - 2:52:21 PM
Long-term archiving on: : Thursday, September 27, 2012 - 12:05:23 PM


  • HAL Id : tel-00200441, version 1



Imen Kammoun. Modélisation et détection de ruptures des signaux physiologiques issus de compétitions d'endurance. Mathématiques [math]. Université Panthéon-Sorbonne - Paris I, 2007. Français. ⟨tel-00200441⟩



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