Estimation of material parameters in a dynamic nonlinear plate model

Abstract

The output-least-square estimation of flexural rigidity with observation of deformations is considered for a dynamic von Karman system. Since such equations may have multiple solutions, we develop a theory for the estimation of coefficients in systems with solution sets that are compact in suitable spaces. We provide a convergence theory based on Galerkin approximations and regularity of optimal estimators of the Galerkin systems. We also obtain stability results for the dependence of the optimal estimator upon the data. A numerical estimation algorithm is developed and the results of numerical experiments are reported.