Nonparametric Response Correction Techniques

Abstract

The response correction techniques described in Chap. 6 utilized explicit formulation where the relationship between the high-fidelity model and the surrogate is quantified by a number of parameters that need to be extracted in order to identify the model. In this chapter, we focus on nonparametric methods, where the relationship between the low- and high-fidelity models is identified, or better said, directly extracted from the model responses; however, it is not explicitly given by any formula. In particular, in the optimization context, the surrogate model prediction may be obtained by tracking the response changes of the low-fidelity model and applying these changes to the known high-fidelity model response at a certain reference design. The formulation of nonparametric techniques is generally more complex and involves more restrictive assumptions regarding their applicability. However, these methods are normally characterized by a better generalization capability than the parametric techniques (cf. Chap. 6). The particular techniques described in this chapter are adaptive response correction, adaptive response prediction, and shape-preserving response prediction. We provide their formulations and illustrate their performance using design problems that involve airfoil shapes, and microwave devices, as well as antenna structures.