中文摘要：

研究了一类广义中心对称结构的有限元模型修正的数学理论和方法．首先将模型修正问题处理为约束矩阵的最佳逼近问题，给出最佳逼近解的表达式．重点讨论了逼近解的扰动理论，并对稀疏结构的模型给出了保结构的算法．数值例子表明该方法是行之有效的．

英文摘要：

Some mathematical theories and methods are studied based on finite element analytical model updating problem of a class of generalized centrosymmetric structure. At first, the model updating problem is treated as a constraints matrix approximation problem. An expression of the best approxi- mation solution is provided. Emphasis is to establish a perturbation theory on the solution. Finally, a method is presented to preserve the sparsity of the model. The numerical examples show that the method is feasible and effective.