分析了径向基插值代理模型的特点,为了提高代理模型的推广能力,引入了结构风险最小化基本原理;指出基函数满足Mercer条件的径向基插值代理模型,本质上也是一类高维分类超平面;文中推导了径向基插值的VC维度与构成径向基插值函数的常数项的导数关系,为此提出了基于结构风险最小化的径向基插值。最后若干函数测试表明基于结构风险最小化的径向基插值提高了代理模型的推广能力。

The characteristic of radial basis function (RBF) was analyzed in this paper. In order to improve the generalization ability of surrogate model, the structural risk minimization (SRM) principle was introduced into the RBF surrogate model. It was pointed out that the RBF surrogate model is essentially one of the high-dimensional classifiers when the interpolation basis functions satisfy the Mercer condition. The relationship between VC dimension and the constant parameter of the interpolation basis functions was derived, thus the structural risk minimization based RBF surrogate model was put forward. Finally, several function tests were utilized to validate that the generalization ability had been improved by the structural risk minimization based RBF surrogate model.