Collecting data to characterize an unknown space presents a series of challenges. Where in the space should data be collected? What regions are more valuable than others to sample? When have sufficient samples been acquired to characterize the space with some level of confidence? Sequential sampling techniques offer an approach to answering these questions by intelligently sampling an unknown space. Sampling decisions are made with criteria intended to preferentially search the space for desirable features. However, N-dimensional applications need efficient and effective criteria. This paper discusses the evolution of several such criteria based on an understanding of the behaviors of existing criteria, and desired criteria properties. The resulting criteria are evaluated with a variety of planar functions, and preliminary results for higher dimensional applications are also presented. In addition, a set of convergence criteria, intended to evaluate the effectiveness of further sampling are implemented. Using these sampling criteria, an effective metamodel representation of the unknown space can be generated at reasonable sampling costs. Furthermore, the use of convergence criteria allows conclusions to be drawn about the level of confidence in the metamodel, and forms the basis for evaluating the adequacy of the original sampling budget.
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