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提出了用幂基多项式拟合频响函数的几点技巧。运用幂基多项式和最小二乘法对频响函数拟合的计算公式进行了推导 ,得到了用于问题求解的线性代数方程组。为改善该方程组系数矩阵的条件数 ,对频率变量和系数矩阵进行了规范化处理 ;频率变量被规范化到 0～ 1的无量纲正实数区域 ,两个相关矩阵的每列模长被规范为 1。然后用奇异值分解的方法求解该方程组 ,得到拟合频响函数所用的幂基多项式的系数。最后 ,根据幂基多项式的系数 ,求出系统的极点和留数 ,从而识别出系统的模态参数。文中给出了一个悬臂梁模拟算例 ,结果表明本文算法具有较好的计算精度
Several techniques for fitting frequency response functions by power polynomials are proposed. The power frequency polynomial and least square method are used to deduce the formula of frequency response function fitting, and the linear algebraic equations for solving the problem are obtained. In order to improve the condition number of the coefficient matrix of the system, the frequency variable and the coefficient matrix are normalized. The frequency variable is normalized to a dimensionless real real region of 0 ~ 1. The length of each column of the two correlation matrices is defined as 1 . Then, the system of equations is solved by the singular value decomposition to obtain the coefficients of the polynomial of the power base used to fit the frequency response function. Finally, according to the power of the polynomial coefficients, find the system poles and remainders, and thus identify the modal parameters of the system. A simulation example of cantilever beam is given in this paper. The results show that the proposed algorithm has good calculation accuracy