Parameter estimation in a structural acoustic system with fully nonlinear coupling conditions (Q1914935)

The authors give a methodology for estimating physical parameters in a class of structural acoustic systems. The differential model (partial differential equations) considered in this paper is weakly nonlinear due to the manner in which the structural vibrations couple with the interior acoustic fields. A discretization method is outlined and a brief algorithm for carrying out the discretization of the nonlinear component is given. Then a parameter estimation scheme is presented and results on convergence and continuous dependence on data are proved. Finally, numerical examples are treated with the techniques described in this paper. Global optimization methods (such as ALIENOR) coupled with decomposition methods of Adomian could be very useful for solving these kinds of identification problems. They could avoid the discretization of PDE and the functional to be minimized would depend explicitly on unknown parameters.