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基于自适应多可信度多项式混沌-Kriging模型的高效气动优化方法

ADAPTIVE MULTI-FIDELITY POLYNOMIAL CHAOS-KRIGING MODEL-BASED EFFICIENT AERODYNAMIC DESIGN OPTIMIZATION METHOD

  • 摘要: 多可信度代理模型已经成为提高基于代理模型的优化算法效率和可信度水平最有效的手段之一. 然而目前流行的co-Kriging和分层Kriging (HK)等多可信度代理模型泛化能力不足, 缺乏对高阶/高非线性建模问题的适应性, 难以广泛应用. 文章基于发展的自适应多可信度多项式混沌-Kriging (MF-PCK)代理模型, 在提高建模效率和对高阶/高非线性问题近似准确率的同时, 建立了基于该自适应MF-PCK模型的高效全局气动优化方法. 在发展的方法中, 提出了基于MF-PCK模型的新型变可信度期望改进加点方法, 使代理优化算法效率进一步提高. 为了验证发展方法的全面表现, 将其应用在经典的数值函数算例以及多个跨音速气动外形的确定性优化和稳健优化设计中, 并与基于Kriging和HK模型的代理优化算法进行了全面比较. 结果表明, 发展的新型多可信度全局气动优化方法其优化效率相对于基于Kriging和HK模型的优化效率显著提高, 结果更好也更加可靠, 并且稳健优化设计效率和结果也更符合工程应用需求, 证明了其相对于基于Kriging和HK模型的代理优化算法的显著优势.

     

    Abstract: The multi-fidelity surrogate-assisted global aerodynamic optimization method has become one of the most efficient means to improve the efficiency and reliability of surrogate-based optimization algorithms. However, currently popular multi-fidelity surrogate models, e.g., co-Kriging and hierarchical Kriging (HK) models, lack the generalization ability and the adaptability to complex engineering applications, so that it is very difficult to promote them to be widely utilized. In this paper, based on the developed adaptive multi-fidelity polynomial chaos-Kriging (MF-PCK) surrogate model, an efficient global aerodynamic optimization framework based on the novel adaptive MF-PCK model is proposed while improving the modeling efficiency and the global approximation accuracy for highly-nonlinear and high-order response problems. In the development framework, we proposed a new adaptive multi-fidelity polynomial chaos-Kriging-based variable-fidelity expected improvement (MF-PCK-VF-EI) infilling strategy that can adaptively select new samples of both low- and high-fidelity, which further improves the efficiency and ability of this optimization framework. The developed methodology is verified by one analytical function example and demonstrated by three engineering application problems, including the deterministic optimization and the robust design optimization of several transonic aerodynamic shapes, compared with the popular Kriging-based and HK-based optimization algorithms. The results show that the global aerodynamic optimization efficiency of the developed method based on the novel adaptive MF-PCK model is higher than that based on the HK model and more than twice that based on the Kriging model, meantime with better and more reliable results. More importantly, the efficiency and performance of robust aerodynamic design optimization (RADO) for transonic aerodynamic shapes are prone to satisfy the requirements for complex engineering applications, which proves a significant advantage of the developed method over the popular Kriging-based and HK-based optimization algorithms.

     

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