An inverse eigenvalue problem in symmetric sparse quadratic model updating

In this paper, symmetric sparse quadratic model updating problem (SSQMUP) is considered from the perspective of an inverse eigenvalue problem. This problem attempts to update the analytical model (stiffness and damping matrices), so that it agrees with the measured eigendata and preserves the symmetric and sparsity structure of the original model. In this paper, a necessary and sufficient condition for the existence of solution of SSQMUP is derived. In addition, we present the expressions of the class of all solutions to this problem explicitly. Moreover, we proposed an optimization-based approach to find the solution of this problem which is nearest to the analytical model. Validity of the our proposed method is illustrated with results on numerical experiments on a spring mass problem.