高维复杂系统的降阶建模表征方法与多精度近似优化策略研究

Aiming at the computational complexity difficulty in solving high dimensional complex system optimization, the order-reduction based modeling representation methods and multi-fidelity approximation optimization strategies are studied. The main research tasks of this project are summarized as follows. (1) A novel order reduced high dimensional modeling representation method (notated as KRG-HDMR) is proposed by using variation estimation of Gaussian process to improve the approximation accuracy and construction efficiency of the order reduced model; (2) a machine learning based design space branch reduction strategy is developed to identify the significant design regions, where the sequential bias sampling process is performed to enhance the optimization efficiency and global convergence capability; (3) penalty-independent constraint handling mechanisms are explored, which employ KS function to decrease the number of constraints, and construct adaptive KS filter to consecutively improve the optimality and feasibility of samples; (4) a KRG-HDMR correction method is proposed based on the multi-fidelity modeling concept to integrate KRG-HDMR in the adaptive metamodel based optimization framework; (5) KRG-HDMR based multi-fidelity approximation optimization strategies are finally developed to alleviate the computational cost of high dimensional complex system optimization, and upgrade the convergence property of solving constrained optimization problems with large scale expensive constraints. The research approaches of this project are novel and unique, and the research achievements are expected to break through several bottleneck techniques in high dimensional complex system optimization field, which can provide advanced design theories for complex equipment development.

针对高维复杂系统优化的计算复杂性问题，开展降阶建模表征方法与多精度近似优化策略研究。主要内容包括：①提出基于高斯过程方差估计的新型高维问题降阶建模表征方法(KRG-HDMR)，提高降阶模型的近似精度与构造效率；②提出基于机器学习的设计空间分支缩减策略以辨识重点设计域，通过序列有偏采样改善优化效率与全局收敛性；③探索不依赖于罚函数的大规模高精度约束处理机制，利用KS函数实现约束条件降维，构造自适应KS过滤器持续改善样本点的最优性与可行性；④采用多精度建模思想发展一种KRG-HDMR修正方法，实现KRG-HDMR与自适应代理模型优化框架的有机融合；⑤发展一套基于KRG-HDMR的多精度近似优化策略，降低高维复杂系统优化的计算成本，改善求解大规模耗时约束优化问题的收敛特性。本项目技术途径具有创新性，研究成果能够突破高维复杂系统优化领域的多项瓶颈技术，可以为复杂装备研制提供先进的设计理论支持。

以航空航天系统为代表的现代高精端装备本质上都是高维复杂工程系统，其系统性能由多个学科的海量设计变量综合影响决定。采用优化设计技术挖掘系统设计潜力，对于提高总体设计性能、缩短设计周期等方面具有重要意义。然而，设计变量高维度、模型计算高耗时以及学科之间强耦合等问题，严重加剧了优化任务的计算复杂性。如何缓解高维复杂工程系统优化过程所面临的计算复杂性难题，成为了工程优化理论研究与实践中亟待解决的关键问题。.针对高维复杂系统优化的计算复杂性问题，本项目开展降阶建模表征方法与多精度近似优化策略研究，主要研究工作总结如下：①针对高维系统近似降阶表征难题，提出了基于高斯过程的高维模型表征方法，引入比例采点策略和方差驱动的序列采样机制，提高了组元Kriging构造效率，并通过模型修正策略改善了高维问题全局近似精度；②针对大规模高耗时黑箱约束问题，引入过滤器技术，推导了黑箱约束问题的约束概率改善度函数，提出了基于KS方程的并行综合可行期望改善填充准则，在不依赖罚函数的情况下有效权衡了优化过程的可行性和最优性；③发展了一套基于空间映射与整数规划的高效序列Maximin-LHD方法，提出了基于机器学习的设计空间缩减技术和特征准则驱动的序列填充采样技术，形成了一套近似优化策略族，并开发了一套近似优化工具包；④基于多源模型响应信息，研究了基于最小二乘的低精度代理模型修正策略和基于高斯过程的多模型融合残差修正方法，提升了多模型融合建模精度和构造效率，提出了一种基于双采样的Co-Kriging优化方法，并定制了一种基于聚类分析和改进Pareto适应度的多精度填充采样机制，有效平衡了多精度优化过程中局部搜索与全局探索。此外，项目组已将上述理论研究成果用于求解全电推进卫星平台等多种飞行器工程设计优化问题，检验了研究成果的有效性与实用性。.本项目已发表论文18篇，其中SCI论文12篇，EI论文6篇；申请国家发明专利16项，已授权5项；获得国家软件著作权2项；获得国防技术发明二等奖1项；研究工作达到了预期目标。

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