Robust optimization using NURBs based metamodels

Abstract

The subject of uncertainty is a prevalent factor in engineering and design. Real-world engineering systems are susceptible to uncontrollable dynamics or variations that influence their real-time performance and long-term consistency or reliability. Therefore designers and engineers desire to deliver system solutions that are both optimal and dependable. Robust design, in particular robust optimization has emerged as a promising methodology to address the problems of dealing with system uncertainty. The goal of robust optimization is to arrive at the optimized system configuration for a design objective (performance/objective function) that is tolerant to uncertain system variables through a strategy of minimizing the sensitivity of the system’s performance to the uncertain variables. The robust optimization approach creates representations of system perturbations/randomness, and develops measures of randomness and the designer’s risk aversion tolerance which are incorporated into identifying a robust optimal solution. This thesis presents a method for robust optimization that identifies robust regions and eliminates non-robust regions based on evaluations that estimate the gradients of the performance space topology across subspaces of NURBs based metamodel representations of a system’s design space. The thesis advances a new approach towards exploiting design space by searching for sections that could potentially hold robust solutions through analysis of the gradients across proximate clusters of control points in the control point networks inherent in NURBs metamodels and selectively optimizing only within the section(s) with the desired sensitivity profile to uncover robust optimal solutions. The HyPerROB algorithm is implemented in C++ and tested to prove the validity of its results in comparison to alternative methods in literature. This robust optimization framework is applied to formulate unconstrained robust optimization problems from three test functions and a constrained robust optimization problem from a practical engineering design problem.