On Using Kriging Models as Probabilistic Models in Design

Kriging models are frequently used as metamodels during system design optimization. In many applications, a kriging model is used as a deterministic model of a computationally expensive analysis or simulation. In this paper, a kriging model is employed as a probabilistic model on a one-dimensional and two two-dimensional test problems. A probabilistic model is a model in which the parameters are random variables resulting in a probability distribution of the output rather than a deterministic value. A probabilistic model can be used in design to quantify the knowledge designers have about a subsystem and the lack of knowledge or uncertainty in the model. Using a kriging model as a probabilistic model requires that the correlation of observations is only a function of the distance between the observations and that the observations have a Gaussian probability distribution. This paper will provide some methods to satisfy these requirements when using kriging models as probabilistic models.