Sequential design of mixture experiments with an empirically determined input domain and an application to burn-up credit penalization of nuclear fuel rods

Abstract

This paper proposes a sequential design for maximizing a stochastic computer simulator output, y(x), over an unknown optimization domain. The training data used to estimate the optimization domain are a set of (historical) inputs, often from a physical system modeled by the simulator. Two methods are provided for estimating the simulator input domain. An extension of the well-known efficient global optimization algorithm is presented to maximize y(x). The domain estimation/maximization procedure is applied to two readily understood analytic examples. It is also used to solve a problem in nuclear safety by maximizing the k-effective “criticality coefficient” of spent fuel rods, considered as one-dimensional heterogeneous fissile media. One of the two domain estimation methods relies on expertise-type constraints. We show that these constraints, initially chosen to address the spent fuel rod example, are robust in that they also lead to good results in the second analytic optimization example. Of course, in other applications, it could be necessary to design alternative constraints that are more suitable for these applications.