Space partitioning in engineering design via metamodel acceptance score distribution

Abstract

Metamodels for simulators are used to reduce computational costs in engineering system design. In general, metamodels have different fit accuracy levels over different regions in the design variables space, especially for highly nonlinear responses over wide spaces. A metamodeling strategy should place less emphasis on sub regions in the design variables space requiring relatively less complex metamodels. In this paper, we present a graphically based methodology that can be used to partition the space for piecewise metamodel building. The method is based on analyzing an initial global metamodel for acceptability in terms of prediction accuracy over the whole space; then generating acceptance score distribution (ASD) plots. Visual inspection of the ASD plots is used as a guidance to partition the design variables space, leading to a metamodel with fair prediction accuracy on a piece-by-piece basis, not just globally on average. The proposed methodology is general and can be applied to various metamodel types. It is tested on a number of problems, including some of the most highly nonlinear test problems used in the literature.