Impact of Optimality Criteria on Metamodeling Accuracy Under Scarce Sampling Plans

Metamodeling has been widely used in place of complex numerically intensive simulations to perform design reliability assessment and optimization. Due to cost and time constraints, most complex simulations can only afford a limited number of runs with a relatively large number of factors. The accuracy of a metamodel is affected by the degree of the underlying non-linearity, the sample size, the sampling strategy, and the type of the metamodel. In this study, the effect of the DOE optimality criteria on the accuracy of the Kriging metamodel is investigated under scarce sampling plans. Uniformity optimization is performed using some of the most popular uniformity measures, such as Centered Discrepancy (CL₂), Maximin, and Entropy criteria. Case studies consist of eight analytical closed-form functions drawn mostly from real engineering applications with five to seven factors each and various degrees of non-linearity. The percent improvements in Relative Root Mean Square Error (RRMSE) over random Latin Hypercube Sampling (LHS) and S/N ratio are used to evaluate the performance and robustness of each criterion. Based on the results of the case studies investigated, it is concluded that the Entropy, E(2,1)¹, and Maximin, M(5,1), have yielded the best results in terms of overall performance and consistency.