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Régression polynomiale par morceaux pour la propagation de fissures

Florine Greciet 1, 2, 3
Abstract : An aircraft engine is made up of several families of materials that undergo multiple degradation mechanisms from their manufacture but also during their flight cycle (take-off, landing, pressurization, pilot manoeuvring,...) or during its rest on the ground. One of these mechanisms is related to the phenomenon of fatigue which represents the degradation of a piece due to repeated cyclic stresses. This degradation results in the initiation of a crack and its propagation until the piece ruptures. The prediction of the propagation lifetime of parts is therefore a very sensitive point since it impacts both the dimensioning (step prior to the design of the pieces) and the maintenance procedures (repair or change of the piece). Propagation lifetime calculations are partly based on the laws of phenomenological evolution describing the rate of progress of the crack in a material as a function of the stress applied. In order to study these data, which are likely to be modelled continuously and which allow several propagation regimes to be observed, we propose a polynomial regression model with several regimes, subject to regularity assumptions (continuity and/or differentiability). Following this, we developed inference methods to estimate the number of regimes, transition times and parameters of each regime. These results will only be usable by the engineering office if they are obtained within reasonable calculation times, i.e. in the order of a few minutes. Each new method has therefore been designed to reduce the computation time required to estimate the model parameters. Moreover, since the number of regimes present in the data is not known a priori, the last two methods we propose do not use any a priori on this number to estimate the model parameters. The work presented in this thesis is the subject of a collaboration between the Probability and Statistics team of the Institut Elie Cartan of the University of Lorraine, the BIGS team of Inria Nancy Grand Est and Safran Aircraft Engines.
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Florine Greciet. Régression polynomiale par morceaux pour la propagation de fissures. Mathématiques [math]. Université de Lorraine, 2020. Français. ⟨NNT : 2020LORR0004⟩. ⟨tel-02510850⟩

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