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.