关键词: 气动优化设计, 代理模型, 伴随方程, 维数灾难, GEK模型

Abstract: The integration of the adjoint method, capable of computing gradients at a cost independent of dimension, with Gradient-Enhanced Kriging (GEK) presents a promising solution to the “curse of dimensionality” in global optimization. However, existing research predominantly focuses on leveraging gradients to enhance modeling accuracy, often overlooking their potential in steering the optimi-zation trajectory. Consequently, this leads to only marginal improvements in optimization efficiency with substantial increases in training costs. To address these challenges, this paper proposes a novel high-dimensional global optimization framework combining the adjoint method and GEK. By exploiting sensitivity and function descent information inherent in sample gradients, the proposed method guides hyperparameter space reduction and design space exploration, thereby significantly enhancing model training and optimization efficiency. First, a gradient-sensitivity-based hyperparameter optimization method is introduced. This approach utilizes gradients to quantify variable sensitivities, establishing a mapping between the full set of hyperparameters and a reduced set of opti-mization parameters, achieving significant dimensionality reduction while preserving the distinct characteristics of each dimension. Second, a gradient-informed infill sampling criterion is proposed. By leveraging the gradient information to approximate the Hessian matrix and construct Quasi-Newton search directions, this method substantially improves local exploitation capabilities. The pro-posed method is validated using high-dimensional analytical benchmark functions and subsequently applied to the aerodynamic de-sign optimization of the ADODG Case 6 wing, a challenging multi-modal design problem. Results demonstrate that the proposed framework reduces the total optimization time by more than a factor of ten compared to conventional GEK-based optimization meth-od.

Key words: Aerodynamic design optimization, Surrogate model, Adjoint method, Curse of Dimensionality, Gradient-enhanced kriging