In this thesis, we present a sensor model comprised of a geometrically nonlinear beam coupled with a nonlinear viscoelastic Pasternak foundation via a distributed system of compliant elements. The governing equations of the system are obtained. By posing an inverse problem, the model is used to simulate the estimation of coupled substrates' material (constitutive) parameters. In the inverse problem, beam deformations are considered as measured parameters, and therefore an eventual hardware implementation would require measurements of these quantities. Different case studies are simulated to assess the robustness and applicability of this sensor model.