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.

本文从特征值反问题的角度考虑了对称稀疏二次模型更新问题（SSQMUP）。该问题试图更新解析模型（刚度和阻尼矩阵），使其与测得的特征数据一致，并保留原始模型的对称性和稀疏性结构。本文推导了存在SSQMUP解的充要条件。此外，我们明确提出了该问题的所有解决方案的类的表达。此外，我们提出了一种基于优化的方法来找到最接近解析模型的该问题的解决方案。弹簧质量问题的数值实验结果说明了我们提出的方法的有效性。