Optimizing aerodynamic shape of benchmark problems using an improved Gaussian process regression algorithm

doi:10.1080/19942060.2025.2456500

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Optimizing aerodynamic shape of benchmark problems using an improved Gaussian process regression algorithm

2025-01-30

DOI：10.1080/19942060.2025.2456500

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Abstract

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The current challenges encountered in Surrogate-Based Optimization (SBO) primarily stem from the substantial number of function calls essential for accurate evaluations. A promising approach to alleviate this problem is to leverage Gaussian Process Regression (GPR) models integrated with Automatic Kernel Construction (AKC) algorithms, known for their superior fitting precision with reduced sample sizes. This study introduces an SBO framework tailored for Gaussian process regression models, featuring an automatic kernel construction algorithm coupled with a beam search strategy (AKC-GPR). The primary aim of this framework is to explore the efficiency enhancements achievable through AKC-GPR. By using the benchmark two-dimensional Rosenbrock function for comprehensive evaluation, the results show that when optimizing this function, the AKC-GPR model reduces the number of actual function calls by 45%, and the optimization results are closer to the true value. In addition, to further demonstrate the effectiveness of the framework, a benchmark optimization of aerodynamic shape for drag minimization of a RAE2822 wing under transonic viscous flow, proposed by the American Institute of Aeronautics and Astronautics (AIAA) Aerodynamic Design Optimization Discussion Group (ADODG), was conducted. Compared to the conventional GPR-based SBO approach, our AKC-GPR framework significantly reduces the number of required computational fluid dynamics (CFD) simulations by 27.7% while improving drag reduction by 2.83%. Qualitative and approximate comparative analysis of the results with other research groups on the same benchmark case validates the robustness and effectiveness of our proposed optimization framework.

Keywords:

Aerodynamic shape optimization

surrogate-based optimization

Gaussian process regression

automatic kernel construction