应用试验模态参数修正理论模型的最佳矩阵逼近法

A Best Matrix Approximation Technique to Update Analytical Model through Identified Model Parameters

本文从特征方程和模态正交条件出发，给出了一种应用模态参数识别结果修正理论模型的最佳矩阵逼近方法。该方法通过对识别出的模态矩阵进行奇异值分解并结合特征方程和模态正交条件导出了修正理论模型的通解表达式。在此基础上，给出了最佳逼近解的定义，研究了最佳逼近解的存在性和唯一性，给出了最佳修正质量矩阵和刚度矩阵的具体表达式，讨论了保证修正后的质量矩阵和刚度矩阵仍具有带状性质的方法．数值计算表明，本文方法具有较高的修正精度，对于大误差模型也有较好的修正能力。

From the eigenequation and the orthogonality conditions a best matrix approximation technique for updated analytical model based on test identified modal parameters is presented in this paper. The identified modal matrix is decomposed by means of singular-value decomposition technique combining with the eigenequation and modal orthogonality relations, and thus general modified equation for the analytical model is obtained.Based on the results,the definition of the best approximation solution for the problem is presented,the existence and uniqueness of the best approximation relative to the analytical model are stud-ied, and the concrete form of the best modification is presented. The method to keep the modified mass ma-trix and stiffness matrix with the same strip width as the initial matrices is studied.Examples demonstrate that the modification methods developed in this paper possesses higher modificatory accurancy and it is also suitable to modify models of the larger error.