Apprentissage d'estimateurs sans modèle avec peu de mesures - Application à la mécanique des fluides

This thesis deals with sparsity promoting techniques in order to produce efficient estimators relying only on a small amount of measurements given by sensors. These sensor locations are crucial to the estimators and have to be chosen meticulously. The proposed methods do not require dynamical models and are instead based on a collection of snapshots of the field of interest. This learning sequence can be acquired through measurements on the real system or through numerical simulation. By relying only on a learning sequence, and not on dynamical models, the proposed methods become general and applicable to a variety of systems.These techniques are illustrated on the 2-D fluid flow around a cylindrical body. The pressure field in the neighbourhood of the cylinder has to be estimated from a limited amount of surface pressure measurements. For a given arrangement of the sensors, efficient estimators suited to these locations are proposed. These estimators fully harness the information given by the limited amount of sensors by manipulating sparse representations and classes. Cases where the measurements are no longer made on the field to be estimated can also be considered. A sensor placement algorithm is proposed in order to improve the performances of the estimators.Multiple extensions are discussed : incorporating past measurements, past control inputs, recovering a field non-linearly related to the measurements, estimating a vectorial field, etc.