Reducible Uncertain Interval Design (RUID) by Kriging Meta-Model Assisted Multi-Objective Optimization

Optimization under uncertainty can be a difficult and computationally expensive problem driven by the need to consider the degrading effects of system variations. Sources of uncertainty that may be reducible in some fashion present a particular challenge because designers must determine how much uncertainty to accept in the final design. Many of the existing approaches for design under input uncertainty require potentially unavailable or unknown information about the uncertainty in a system's input parameters; such as probability distributions, nominal values or uncertain intervals. These requirements may force designers into arbitrary or even erroneous assumptions about a system's input uncertainty when attempting to estimate nominal values and/or uncertain intervals for example. These types of assumptions can be. especially degrading during the early stages in a design process when limited system information is available. In an effort to address these challenges a new design approach 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 dramatically reduced through the use of a kriging meta-model assisted multi-objective optimization technique performed in two stages. The capabilities of the approach are demonstrated through three example problems of varying complexity.