Using a Reduced Modal Basis to Update Acoustic Models V. Decouvreur 1 and Ph. Bouillard Structural and Material Computational Mechanics Department Universit ´ e Libre de Bruxelles, av. F. D. Roosevelt 50 CP 194/05, 1050 Brussels, Belgium e-mail: pbouilla@smc.ulb.ac.be A. Deraemaeker 2 and P. Ladev` eze Laboratoire de M ´ ecanique et Technologie, ENS-Cachan Universit ´ e Paris VI/CNRS, 61 av. Pr´ esident Wilson, 94235 Cachan, France e-mail: ladeveze@lmt.ens-cachan.fr Key words: Model Updating, Reduced Basis, Constitutive Relation Error, Acoustics Table of nomenclature Ω : acoustic domain ∂ Ω= ∂ 1 Ω+ ∂ 2 Ω+ ∂ 3 Ω : boundary of the acoustic domain Ω=Ω ∪ ∂ Ω ~v : particle velocity, v n = ~v ~ 1 n p : sound pressure, p : imposed pressure, ˜ p : measured pressure ρ : fluid density c = 343ms -1 : sound velocity at 15 0 C ω : angular frequency k = w/c : wave number t : time Z n : acoustic impedance A n = Z -1 n : acoustic admittance ξ 2 ω : constitutive relation error (CRE) L 2 = Z ∂2Ω dΓ L 3 = Z ∂3Ω dΓ γ,ζ,r : weighting factors S ad : set of admissible solutions s ω Π 1 , Π 2 : projection operators e 2 ω,rel : relative modified CRE z(ω) : weighting function e 0 : relative modified CRE threesold required to stop the updating process P , Q, R : pressure fields P, Q, R : nodal unknowns corresponding to the pressure fields P , Q, R p h = N t P : finite element approximation of the pressure [M]= 1 c 2 Z Ω N t NdΩ : acoustic mass matrix 1 research fellow supported by the F.R.I.A. foundation 2 presently Active Structures Laboratory, Universit´ e Libre de Bruxelles, av. F. D. Roosevelt 50, CP 165/42, 1050 Brussels, Belgium