基于多层梯度增强Kriging模型的高维全局气动优化方法研究

梯度增强的代理模型，结合了代理模型方法与Adjoint方法的优点，是一种有望解决航空航天领域高维全局气动优化问题的新方法。但是目前该方法只能用于100维以下的中小规模优化问题，“维数灾难”仍是限制其进一步研究和应用的瓶颈。本项目拟运用“可信度分层”和“子模型加权”思想，提出一种多层梯度增强Kriging（MGEK）代理模型理论和算法；在此基础上通过引入多种可信度CFD分析和Adjoint梯度求解，建立一种适用于高维气动优化设计的全局优化框架，并发展出相应的统计学寻优机制、约束处理和多目标优化策略。通过解决“高维代理模型相关矩阵过大”和“多可信度设计空间中自适应加点”的关键问题，大幅度减小针对100维以上大规模优化的模型训练计算量和高可信度CFD分析次数，将代理优化适用的维数提高到至少200维，为飞行器精细全局气动优化及相关领域面临的“维数灾难”问题提供一种新的、更有效的解决途径。

Gradient-enhanced surrogate model, combining surrogate modeling and adjoint method, is a new method that may play an important role in solving the complex aerospace optimization problems with a large number of design variables. Although this method has been successfully used for the optimization problems with number of dimensions less than 100, it is still suffering from the prohibitive computational cost when applied to higher-dimensional (>100) aerodynamic shape optimizations based on high-fidelity CFD (computational fluid dynamics). Therefore, the “curse of dimensionality” is still a “bottleneck” that limits the further development and applications. . To ameliorate the “curse of dimensionality”, this project aims to propose a novel global optimization framework as well as the new infill-sampling criterion, constraint-handling and multiobjective optimization, by using multiple-level gradient-enhanced kriging model to simultaneously introduce multi-fidelity CFD analyses and the corresponding adjoint gradient evaluations. Through solving the problems associated with decomposing the extremely large correlation matrix of the surrogate model and searching the multi-level design spaces via adaptive sampling, the proposed theory and algorithms for high-dimensional surrogate modeling and design optimization, as the outcome of this project, may break the limitation of the conventional surrogate-based optimization (SBO) method regarding the number of dimensions, and the capability of SBO for high-dimensional global optimization is to be largely extended (up to 200 dimensions). This research may contribute not only the area of aerodynamic shape optimization, but also other areas relevant to design of aircraft or spacecraft.