Bayesian Inspired Multi-Fidelity Optimization with Aerodynamic Design

In most engineering design problems, there exist multiple models of varying fidelities for use in predicting a single system response such as Computational Fluid Dynamics (CFD) models constructed using Potential Flow, Euler equations, or full physics Navier Stokes implementation. Engineering design is constantly pushing the forefront of the field through imposing stricter and more complex constraints on system performance, thus elevating the need for use of high-fidelity models in the design process. Increasing fidelity level often correlates to an increase in cost (financial, computational time, and computational resources). Traditional design processes rely upon low-fidelity models for expedience and resource savings. However, the reduced accuracy and reliability of low-fidelity tools often lead to design defects or inadequacies due to a failure in capturing the true underlying physics governing the system. It is proposed that the solution to achieving accurate yet computationally efficient designs lies in the development of multi-fidelity design techniques. Multi-fidelity design is a methodology which aims to mitigate deficits and/or impediments associated with traditional design techniques by leveraging the accuracy of high-fidelity models against the computational efficiency of low-fidelity models. This work discusses a novel approach, Bayesian Inspired Multi-Fidelity Optimization (BIMFO), for solving complex optimization requiring computationally expensive simulations. BIMFO aims to minimize computational cost in achieving accurate high-fidelity results through the use of low-fidelity (computationally cheaper) models in combination with a surrogate correction model. 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 optimization to that of optimization with multiple fidelity objective and constraint functions. The proposed solution technique allows for utilization of commercial optimizers and is demonstrated on analytical and physics-based optimization problems