径向基代理模型中形状参数对精度的影响

代理模型方法是复杂系统优化设计的一种有效方法,讨论了以多二次函数为核函数的径向基（radial basis function, RBF）代理模型中形状参数h对精度的影响,在此基础上探讨了一种获得最优h值的方法。在该方法中,将RBF代理模型的标准均方根误差表达为形状参数h的函数,通过极小化该标准均方根误差,得到最优h值。在样本点给定的情况下,采用该最优h值所构造代理模型与采用其他h值所构造的代理模型相比,其精度更高。一维和二维数值算例验证了采用本方法确定h值的有效性,并应用该方法求解了战术导弹的气动外型优化设计问题。

Study on shape parameter selection for surrogate model -constructed by using radial basis function

The effect of shape parameter selection on the accuracy of the surrogate model constructed by using the radial basis function (RBF) is discussed, based on which an alternative method for determining the optimal value of the shape parameter is investigated. In this method, the normalized root-mean-square error (NRMSE) of the surrogate model is expressed as a function with respect to the shape parameter. Consequently a minimization optimization problem is constructed, in which the NRMSE is the objective and the shape parameter is the decision variable. Then the optimization is solved to obtain the optimal shape parameter. For a set of given sample points, the RBF surrogate model using this optimal shape parameter is more accurate than those using other shape parameters. Two numerical test examples, a one dimension problem and a two dimension problem, show the effectiveness of this method. A tactical missile aerodynamic shape optimization problem is also solved successfully by using this method.