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Inférence bayésienne pour la reconstruction d'écoulements complexes - Application au profil NACA0012

Abstract : This thesis takes place in the framework of the calibration of low order models from experimental sequences acquired by time resolved PIV around at profil NACA0012 with various angles of attack and numbers of Reynolds. A reduced-order modelling approach issued from the Galerkin projection of the incompressible flow Navier-Stokes equations onto a low-dimensional basis extracted by Proper Orthogonal Decomposition (POD) is used. A state space model governing the evolution of the state variables of the reduced-order model POD-Galerkin and mapping directly or indirectly a part or the whole of these state variables is then used to solve the problem of the estimation of the state of the reduced-order model POD-Galerkin during time. The Bayesian inference on the reduced-order model POD-Galerkin depending on different sets of observations is proposed. The first part is devoted to the application of Bayesian estimators from the assimilation of sequential data on the linear and quadratic reduced-order models POD-Galerkin in the case where time resolved observations are available. The Bayesian estimators used are the linear Kalman filters and the ensemble Kalman filter (EnKF). These Kalman filters are experimentally validated on the flow fields. They allow the reduced-order model to describe the dynamics of the considered flow in time and reproduce a significant percentage of the flow. The second part deals with the reconstruction of missing velocity fields after under-sampling the experimental data. The missing coefficients are reconstructed using the EM algorithm which proceeds by maximization of a likelihood calculated with a Kalman filter and smoother. Different types of under-sampling of the snapshots were then tested. A last part is devoted to the stochastic filtering of the reduced-order model POD-Galerkin with the EnKF filter using observations of different physical nature. The signal used for the observations is a voltage signal obtained by hot film anemometry downstream of the NACA0012 profile. Due to the very high collinearity of the signals obtained by hot film, the PLSR has been used to define a linear operator of observations in the Kalman filter EnKF. Results concerning the use and application of the PLSR with the EnKF filter are presented. The application of these methods for the reconstruction of velocity fields is then validated on experimental data.
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Contributor : Romain Leroux <>
Submitted on : Monday, December 17, 2012 - 9:49:35 PM
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Romain Leroux. Inférence bayésienne pour la reconstruction d'écoulements complexes - Application au profil NACA0012. Mécanique des fluides [physics.class-ph]. Université de Poitiers, 2012. Français. ⟨tel-00766239⟩

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