Reducible Uncertain Interval Design by Kriging Metamodel Assisted Multi-Objective Optimization

Abstract

Sources of reducible uncertainty present a particular challenge to engineering design problems by forcing designers to make decisions about how much uncertainty to consider as acceptable in final design solutions. Many of the existing approaches for design under uncertainty require potentially unavailable or unknown information about the uncertainty in a system’s input parameters, such as probability distributions, nominal values, and/or uncertain intervals. These requirements may force designers into arbitrary or even erroneous assumptions about a system’s input uncertainty. In an effort to address these challenges, a new approach for design under uncertainty is presented that can produce optimal solutions in the form of upper and lower bounds (which specify uncertain intervals) for all input parameters to a system that possess reducible uncertainty. These solutions provide minimal variation in system objectives for a maximum allowed level of input uncertainty in a multi-objective sense and furthermore guarantee as close to deterministic Pareto optimal performance as possible with respect to the uncertain parameters. The function calls required by this approach are kept to a minimum through the use of a kriging metamodel assisted multi-objective optimization technique performed in two stages. The capabilities of this approach are demonstrated through three example problems of varying complexity.