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Annals of the Assembly for International Heat Transfer Conference 13

ISBN 1-56700-225-0 / CD 1-56700-226-9

Volumes per year:

various

Year 2006

DOI: 10.1615/IHTC13.p9

THE MODAL IDENTIFICATION METHOD IN NONLINEAR HEAT TRANSFER PROBLEMS

O. Balima
Laboratoire d'Etudes Thermiques, U.M.R. C.N.R.S. 6608, Université de Poitiers, ENSMA, Teleport 2, 1 avenue Clément Ader, BP 40109, 86961 Futuroscope Cedex, France

Y. Favennec
Laboratoire d'Etudes Thermiques, U.M.R. C.N.R.S. 6608, Université de Poitiers, ESIP, 40 avenue du recteur Pineau, 86022 POITIERS Cedex, France

M. Girault
Laboratoire d'Energétique et de Mécanique Théorique et Appliquée, U.M.R. n°7563 C.N.R.S.-I.N.P.L.-U.H.P., 2 avenue de la Forêt de Haye, BP 160, 54504, Vandoeuvre-Les-Nancy, France

Daniel Petit
Laboratoire d'Etudes Thermiques, U.M.R. C.N.R.S. 6608, Université de Poitiers, ENSMA, Teleport 2, 1 avenue Clément Ader, BP 40109, 86961 Futuroscope Cedex, France

J. B. Saulnier
Laboratoire d'Etudes Thermiques, U.M.R. C.N.R.S. 6608, Université de Poitiers, ENSMA, Teleport 2, 1 avenue Clément Ader, BP 40109, 86961 Futuroscope Cedex, France

ABSTRACT

The Modal Identification Method (MIM) has been developed to identify Reduced Models (RM) for linear and then for nonlinear systems, from numerical or experimental data. The MIM consists in defining a modal structure for the RM equations. Then, all the RM parameters are identified through an optimization problem [2,1,8]. This approach is particularly interesting when compared to classical truncation methods such POD-Galerkin or Litz methods [7,5]. The obtained RMs can be used for solving inverse problems or for control purposes as they are stable and less time consuming than the related Detailed Models. Furthermore, the RM state formulation is well suited for automatics. Several applications are presented in the paper: i) an example of direct modeling of a conductive system with a thermo-dependency of the conductivity coefficient, ii) an example of direct modeling of a natural convective system, and iii) an optimal control resolution on a nonlinear conductive problem. All treated examples show that these RMs are well suited to simulate and control such nonlinear systems with accuracy.