Multi-fidelity approaches for general constrained Bayesian optimization with application to aircraft design

Abstract

Aircraft design relies heavily on solving challenging and computationally expensive Multidisciplinary Design Optimization problems. In this context, there has been growing interest in multi-fidelity models for Bayesian optimization to improve the MDO process by balancing computational cost and accuracy through the combination of high- and low-fidelity simulation models, enabling efficient exploration of the design process at a minimal computational effort. In the existing literature, fidelity selection focuses only on the objective function to decide how to integrate multiple fidelity levels, balancing precision and computational cost using variance reduction criteria. In this work, we propose novel multi-fidelity selection strategies. Specifically, we demonstrate how incorporating information from both the objective and the constraints can further reduce computational costs without compromising the optimality of the solution. We validate the proposed multi-fidelity optimization strategy by applying it to four analytical test cases, showcasing its effectiveness. The proposed method is used to efficiently solve a challenging aircraft wing aero-structural design problem. The proposed setting uses a linear vortex lattice method and a finite element method for the aerodynamic and structural analysis respectively. We show that employing our proposed multi-fidelity approach leads to $86\%$ to $200\%$ more constraint compliant solutions given a limited budget compared to the state-of-the-art approach.

Figures (6)

• Figure 1: Multi-fidelity BO frameworks comparison. Analytical problems convergence results for the Rosenbrock, Branin, Sasena and Gano problems with two different cost ratios. Each optimization framework was run on 25 DoE.
• Figure 2: Fidelity criteria comparison. Analytical problems convergence results for the MF Rosenbrock, MF Branin, MF Sasena and MF Gano problems with two different cost ratios. Each fidelity criterion was run on 25 DoE.
• Figure 3: CRM multi-fidelity VLM mesh comparison. The LF and HF meshes use $4 \times 4$ panels and $6 \times 30$ panels respectively. The cost ratio between the 2 levels is 30.
• Figure 4: Fidelity criteria comparison on the wing aerostructural optimization problem. $\epsilon$ and $\tau$ denote the absolute constraint tolerance and the relative objective tolerance respectively. Each fidelity criterion was run on 25 DoE.
• Figure 5: Comparison of the best solutions found with MFSEGO and SLSQP for wing twist, tubular spar thickness, lift distribution and structural safety factor.