结构计算模型修正的二次约束最小二乘算法

提出了一种结构计算模型修正的二次约束最小二乘方法。该方法是在质量矩阵和刚度矩阵满足正交性条件和特征方程的约束下，使修正矩阵的范数最小，将模型修止问题转化为一个带二次约束的最小二乘问题。应用奇异值分解，给出了在振型需要和不需要扩充两种情况下结构计算模型修正的数值算法，并进行了数值实验。计算结果表明：新算法精度较高，能保证修正模型的前m阶模态参数与实测值有较好的吻合。

Least Square Method with Quadratic Constraints for Structural Computational Model Updating

A computational model updating algorithm with the least squares under quadratic constraints is proposed. The new updating method is to minimize the error matrix norm under the condition of a quadratic constraint under which the mode orthogonality should be satisfied and the mass and stiffness matrices should be fitted into the eigen equation. The updating problem of structural calculational model is then transformed into a least square problem with quadratic constraints. Singular value decomposition is utilized to solve the problem, and numerical examples are presented to testify the feasibility and effectiveness of the proposed method.