最小二乘复频域法实复系数矩阵的分析

摘要

In recent years, the least-square complex frequency-domain (LSCF) method for modal parameter identification has been developed. This method is proved to be effective in modal identification both in weak damping systems and strong damping systems. According to the theory and method of LSCF, there are two kinds of the coefficient matrix, namely real coefficient matrix and complex coefficient matrix. In this paper, the LSCF method was programmed and the corresponding user’s interface was designed using Matlab. The parameter set of the LSCF method in the two kinds of coefficient matrix and the improvement formula for the solution of system pole were provided. A test of aluminum sheets was accomplished to verify this method. It shows that the results from the two coefficient matrices are in consistency, but the complex coefficient has better numerical condition than the other. The correctness of the user’s interface was also verified.%　　最小二乘复频域法是近年来提出的频域模态识别的方法，该方法在强阻尼、弱阻尼下都具有很好的识别结果。依据最小二乘复频域法的理论与方法，其系数矩阵有两种形式：实系数矩阵形式、复系数矩阵形式。利用Matlab对最小二乘复频域法进行编程，并编制交互式的软件界面。指出最小二乘复频域法在两种系数矩阵下的参数设置，以及系统极点的求解修正公式。通过对铝板的实验分析，表明在两种系数矩阵下分析结果的一致性，并且复系数矩阵具有更好的数值条件，同时验证了程序的正确性。