Résolution numérique en électromagnétisme statique de problèmes aux incertitudes géométriques par la méthode de transformation : application aux machines électriques

Abstract : The numerical models that are more and more used as virtual prototypes require information on the input data as the geometrical dimensions, the physical characteristics of materials and the external solicitations. At present, the models available are very close to the physics they represent and the gap met with the reality can come now partially from a lack of information on the input data. The probabilistic approach which consists in modelling the uncertain quantities by variables or random fields is the solution which was chosen in this thesis to take into account the uncertainties on the geometrical dimensions. To resolve the problem, the transformation method, allowing transposing a problem with uncertainties on the geometry to a problem with uncertainties on the behaviour laws, was chosen. As there are an infinite number of possible transformations, various methods to determine the transformation were implemented and compared. In particular, an a-priori error estimator has been proposed which gives a criterion for the transformation choice. It was also shown that the transformation method can take into account naturally the discontinuities at the stochastic level of the electromagnetic fields. Finally, the method was used to study the influence of the geometrical uncertainties of a stator on the performances of an electrical machine. This study is based on a set of measurements made on a batch of stators.
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Duy Hung Mac. Résolution numérique en électromagnétisme statique de problèmes aux incertitudes géométriques par la méthode de transformation : application aux machines électriques. Electromagnétisme. Arts et Métiers ParisTech, 2012. Français. ⟨NNT : 2012ENAM0005⟩. ⟨pastel-00685277⟩

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