自适应设计空间扩展的高效代理模型气动优化设计方法

对基于Kriging模型气动优化的加点方法和设计空间的构建问题进行了研究。首先，针对高效全局优化（EGO）方法收敛缓慢的问题，提出了一种混合加点方法，该方法通过引入期望提高（EI）阈值控制EI和最小预测值（MP）加点准则，利用先全局再局部的优化思想，提高了EGO方法在确定设计空间内的收敛性。其次，针对设计空间的构建问题，对比了扩大设计变量范围和多轮优化两种不同的设计空间构建方法，分析了设计变量范围对设计空间大小和样本密度的影响，进而提出了自适应设计空间扩展的代理模型优化方法。相对于传统固定设计空间的方法，自适应设计空间扩展的方法在动态的设计空间中进行优化搜索，只在有潜力的维度扩展设计变量范围，通过构建自适应设计空间，实现了样本的高效配置。最后，通过ADODG标准翼型优化算例证实，自适应设计空间优化方法可以大幅提高气动优化设计效率。

Efficient surrogate-based aerodynamic design optimization method with adaptive design space expansion

The infill criterion and design space construction in Kriging-based aerodynamic shape optimization are studied in this paper. A hybrid infill method is proposed, which combines the Expected Improvement (EI) criterion and the Minimum Prediction (MP) criterion using an EI threshold. Global exploration is first implemented by the IE criterion, and local exploitation is then implemented by the MP criterion. Consequently, the convergence rate of Efficient Global Optimization (EGO) is accelerated in a certain design space. To find the global optimum in aerodynamic shape optimization, expansion of the design variable range and multi-round method are employed. Influence of the variable range on the size of design space and density of samples are discussed. To improve the efficiency of samples, an adaptive design space expansion method is proposed. In this method, the design space is dynamic and the range of design variable is expanded in potential dimensions. Accordingly, the samples are allocated efficiently through adaptive expansion of design space boundaries. ADODG airfoil optimization cases show that the adaptive design space expansion method has remarkable superiority over the conventional fixed design space method.