基于Vandermode矩阵GFRF的一维数值解

广义频率响应函数（GFRF）表征非线性系统涉及多维变换，具体求解十分困难。基于Vandermode矩阵，借助MATLAB符号运算法，得到了多维核函数的关系表达式，代入输入和输出的频域采样值，将复杂的高阶核函数表示成一维数值解的形式。实验结果表明：该方法建模简单，运算量小，在误差允许范围完全可以表征非线性系统，具有一定的可行性和实用性。

One-dimensional numerical solution expression of GFRF based on Vandermode matrix

Aimed at seeking replacement of generalized frequency response function （GFRF） which involves muhi-dimensional transformation leading to difficult solution as in the ease of characterizing the nonlinear system, this paper introduees the relationship expression of multi-dimensional kernel function based on Vandermode matrix and symbolic operation by MATLAB and the expression of the complex high- er order kernel function into oneodimensional numerical solution form by substituting into the frequency domain sampling value of input and output. The simulation result shows that this method which gives more simple modeling , less computation and greater ability to completely characterize the nonlinear systern, as is allowed by error, features feasibility and practicality to a certain degree.