用幂基多项式拟合频响函数的几点技巧

Several Techniques for the Frequency Response Function Fitting by Ordinary Power Polynomials

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 。

Several techniques are set forth in the paper for the frequency response functions (FRFs)fitting by ordinary power polynomials.The formulas for the FRFs fitting by power polynomials are derived using the least square method and the linear equations for the solution are achieved.In order to improve the condition in the coefficient matrix of the equations,the variables of the frequency domain and the coefficient matrix is normalized.The fitting variables are normalized from original ones to a 0～1 domain and the norm of each column of two correlative matrices are normalized to 1.The linear equations are solved by singular value decomposition method to obtain the coefficients of the power polynomials.A simulating example of a cantilever beam is presented and the results show that the accuracy of the algorithm is satisfied.