Aerodynamic shape design optimization method based on novel high⁃dimensional surrogate model

With the ever-increasing demands for the performance of modern aircraft，the refined aerodynamic shape design optimization of aircraft requires higher-fidelity CFD numerical analysis and more independent design variables，thus significantly reducing the efficiency of surrogate-based global optimization algorithm，particularly with an excessive number of design variables，Therefore，meeting the advanced demands for complex engineering problems becomes challenging. Furthermore，with complex modeling process and prohibitive computational costs，popular high-dimensional surrogate models，lack good adaptability to a wide range of engineering problems，This paper proposes a Supervised Nonlinear Dimension-Reduction Surrogate Modeling（SN-DRSM）method to alleviate the problem of high-dimensional variables in the process of surrogate-based design optimization. This method，integrates and trains the Kernel Principal Component Analysis（KPCA）nonlinear dimension-reduction model and the Gaussian regression pro⁃ cess model as a whole，A new high-dimensional surrogate model is adaptively constructed，continuously studied in depth and improved during the optimization process，to establish an accurate mapping from high-dimensional inputs to outputs，thereby effectively solving the problems of high training cost and poor adaptability of traditional high-dimensional surrogate models. Then，an efficient high-dimensional global design optimization platform for complex aerodynamic configuration of aircraft is developed based on this novel surrogate model，and applied to two standard transonic optimization cases defined by AIAA aerodynamic optimization group. A comprehensive comparison with the traditional surrogate optimization methods，proves that the new method can significantly improve the global optimiza⁃ tion efficiency and ability of high-dimensional aircraft variables. © 2023 AAAS Press of Chinese Society of Aeronautics and Astronautics. All rights reserved.