Multi-Fidelity Optimization of Complex Physics Involved Engineering Systems

Abstract

This work presents an optimal design technique which allows for the use of multiple simulation models of varying physics and complexity (fidelity levels). An advancement of traditional Surrogate Based Optimization (SBO) techniques is intended to alleviate the computational cost associated with structural and multidisciplinary design optimization while maintaining a high degree of accuracy typically associated with fully coupled, nonlinear, complex physics-based models. This methodology, termed Bayesian Influenced Low-Fidelity Correction Approach to Multi-Fidelity Optimization, utilizes a combination of surrogate modeling, Bayesian statistics, and Trust Region Model Management (TRMM) techniques. A novel Bayesian Hybrid Bridge Function (BHBF) was developed to serve as the low-fidelity correction technique. This BHBF is a Bayesian weighted average of two standard bridge functions, additive and multiplicative. The correction technique is implemented in parallel with a modified Trust Region Model Management (TRMM) optimization scheme. It is shown that optimization on the corrected low-fidelity model converges to the same local optimum as optimization on the high-fidelity model in fewer high-fidelity function evaluations and ultimately lower computational cost. This work also extends the low-fidelity correction optimization beyond the traditional bi-fidelity (limited to 2 fidelity levels) optimization to that of a novel approach to handling optimization with multiple (2 or more) fidelity objective and constraint functions with commercial optimization solvers. It is shown that implementation of this Bayesian low-fidelity correction optimization approach results in high-fidelity results at a reduced computational cost. This is demonstrated on computationally different engineering design problems. First, a 27% computational savings over traditional optimization techniques is observed in the unconstrained minimization of thermally induced stresses in a quarter symmetric panel represented via 4 differing fidelity levels. Finally, a 71% reduction in computational cost is observed in an airfoil shape optimization in which both the objective and constraints are represented by 2 fidelity levels.