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Analyse topologique des données dans la mécanique numérique

Abstract : The present thesis focuses on the applications of numerical topology for mechanical systems. We will deal with the analysis, the characterization, and the exploration of data with high topological content, such as mechanical deformations, microstructures, times series, and dynamical systems trajectories.This data often contains heterogeneous information, difficult to measure, and is not suitable for classical approaches and metric. Hence, it is necessary to have a general approach with invariance properties, allowing to extract the topological and geometrical information of the data, measure it, then use it as topological descriptors.Therefore, our approach is to adapt the use of homology and topological persistence to physics and engineering issues. This approach is purely data driven, and consists in the computation of robust descriptors, relying on optimal transport among others, to summarize the information contained within the physical system into a graph, a diagram, or an image. These descriptors are then used for machine learning, in clustering, classification and regression.We will present four published applications of our methodology. The first one is the identification of deformation modes of a metallic structure, from the topology of the associated deformed mesh. The second is the characterization of rough polymers surfaces profiles in order to predict quantities of interest. The third is the prediction of a driver state from the time series associated to the head movement, which is induced by vibrations of the road. The fourth is the topological signature extracted from real data of an autonomous robot trajectories, in order to improve its predictive maintenance.
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Submitted on : Monday, May 30, 2022 - 5:26:25 PM
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  • HAL Id : tel-03682117, version 1


Tarek Frahi. Analyse topologique des données dans la mécanique numérique. Acoustique [physics.class-ph]. HESAM Université; Université CEU Cardinal Herrera, 2021. Français. ⟨NNT : 2021HESAE046⟩. ⟨tel-03682117⟩



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