Application du contrôle optimal à l'identification d'un chargement thermique

Abstract

La détermination du champ de température sur certaines pièces d'un moteur est obtenue par la résolution d'un problème inverse. Une alternative aux méthodes expérimentales coûteuses utilisées aujourd'hui est la méthode du contrôle optimal qui permet d'estimer le champ de température à partir de quantités mesurées sur pièce. Différents tests préfigurent des possibilités de prédiction et de fiabilité de la méthode. ABSTRACT. We are faced with an inverse problem in the determination of some engine temperature concerning unreacheable pieces. To reduce the experimental costs, PSA tends to develop the theoretical method of optimal control. It allows us to approach the effective temperature using measured physical data and hard-and software possibilities. We collected mathematical and experimental results which provide us a way of evaluating the reliability and accuracy of the method.

Inverse problems in elasticity

“…Model updating is often treated as an inverse problem [17,27,41,57,100,107,126,142], in particular because corrections affect distributed parameters over a limited region of space which is not known beforehand. Identification of sources or inaccessible boundary values (i.e., Cauchy problems in elasticity) are also encountered [42,50,55,94,[109][110][111]. Finally, the identification of homogeneous constitutive properties is increasingly often made on the basis of measurements taken on structures, for which simplifying assumptions such as constant states of strain or stress are invalid, and inverse techniques are then developed for that purpose [51,64,69,108,137].…”

An iterative method for parameter identification and shape reconstruction

“…Inverse Problems in Science and Engineering 43 Figure 2(a) represents the values of the TD when i ¼ ;, a i ¼ a 0 and k i ¼ k 0 , computed using formula (4) (with u m and w m solving (5) and (6), respectively) at a sampling grid defined in the square region represented in Figure 1(b). Dark colours indicate the regions where the TD takes large negative values, where objects should be located.…”

“…The inverse problem consists in reconstructing the objects and their material parameters from measurements of the total field at different locations. Adjoint state approaches based on FEM techniques are discussed in [1] or [6], where a boundary temperature is determined from interior temperature measurements. Other methods assume particular shape functions for the parameter distribution.…”

Untitled

“…The solution proposed here is focused on the application of optimal control theory. An example of application is the steady-state heat conduction problem, where optimal control theory has been used to determine the history of heat sources [Delattre et al 2002].…”