A variational inequality based stochastic approximation for estimating the flexural rigidity in random fourth-order models

This paper develops a stochastic approximation approach for estimating the flexural rigidity in the framework of variational inequalities. The nonlinear inverse problem is analyzed as a stochastic optimization problem using an energy least-squares formulation. A necessary and sufficient optimality condition for the optimization problem is a stochastic variational inequality solved by a stochastic auxiliary problem principle-based iterative scheme. Exhaustive convergence analysis for the proposed iterative scheme is given under quite general conditions on the random noise. Detailed computational results demonstrate the feasibility and the efficacy of the proposed methodology.