Multidimensional sequential sampling for NURBs-based metamodel development

Adaptive design of experiments approaches are intended to overcome the limitations of a priori experimental design by adapting to the results of prior runs so that subsequent runs yield more significant information. Such approaches are valuable in engineering applications with metamodels, where efficiently collecting a dataset to define an unknown function is important. While a variety of approaches have been proposed, most techniques are limited to sampling for only one phenomenon at a time. We propose a multicriteria optimization approach that effectively simultaneously samples for multiple phenomena. In addition to determining the next sequential sampling point, such an algorithm also can be formulated to support conclusions about the adequacy of the experiment through the use of convergence criteria. A multicriteria adaptive sequential sampling algorithm, along with convergence metrics, is defined and demonstrated on five trial problems of engineering interest. The results of these five problems demonstrate that a multicriteria sequential sampling approach is a useful engineering tool for modeling engineering design spaces using NURBs-based metamodels.