Adjoint-based sensitivity analysis of fluid-structure interaction vibrations

Abstract

Adjoint-based sensitivity analysis for the cavity fluid-structure interaction vibrations problem, with the inclusion of prestress and internal pressurization, is considered. The formulation employs a continuum approach in which the adjoint model is defined by employing a new duality relation between the sensitivities and the adjoint variables. For complex problems, such as fluid-structure interaction, the new duality relation provides an unambiguous approach for the construction of the adjoint variational problem in contrast to the standard approach. It also provides useful insight into the interpretation of the adjoint method. The resulting adjoint formulation for sensitivities is based on evaluation of inner products of the adjoint and state variables and is efficient because it requires the calculation of the adjoint field only once, regardless of the number of decision variables. In order to assess the accuracy of the adjoint approach for sensitivities in fluid-structure interaction problems, a model problem is considered and exact and analytical adjoint sensitivities are compared. The method is then applied to a finite element human eye model to compute the sensitivities with respect to elasticity constants and intraocular pressure for application to inverse estimation of those properties. The results are presented using a particularly effective multidimensional visualization technique.