Stochastic Kriging for random simulation metamodeling with finite sampling

As a metamodeling method, Kriging has been intensively developed for deterministic design in the past few decades. However, Kriging is not able to deal with the uncertainty of many engineering processes. By incorporating the uncertainty of data, Stochastic Kriging methods has been developed to analyze and predict random simulation results, but the results cannot fit the problem with uncertainty well. In this paper, deterministic Kriging are extended to stochastic space theoretically, where a novel form of Stochastic Kriging that fully considers the intrinsic uncertainty of data and number of replications is proposed on the basis of finite inputs. It formulates a more reasonable optimization problem via a stochastic process, and then derives the spatial correlation models underlying a random simulation. The obtained results are more general than Kriging, which can fit well with many uncertainty-based problems. Three examples will illustrate the method's application through comparison with the existing methods: the novel method shows that the results are much closer to reality.