基于活跃子空间降维的飞行器不确定性多学科设计优化方法研究

Advanced flight vehicle design of high reliability and strong robustness has been a hotspot issue in the research field of aviation and aerospace. Flight vehicle design usually involves multiple closely coupled disciplines, complex time-consuming disciplinary models, and various uncertainty factors, which demands a suitable Uncertainty-Based Multidisciplinary Design Optimization (UMDO) approach to fully handle the disciplinary couplings and the uncertainty influences, achieving reliable, accurate, and robust ability of practical flight vehicle designs. In this project, a novel UMDO architecture, i.e. ’dimension reduction quantification, unified propagation, and density-matching optimization', will be proposed to conquer the costly computational burden, limited analysis accuracy, and engineering implementation difficulty. Specifically, the project will try to establish a dimension reduction method based on generalized active subspaces, in order to tackle the approximate modeling and solving challenges of high-dimensional uncertainty problems. The propagation and analysis efficacy of mixed uncertainties will be largely enhanced through building an effective adaptive surrogate model in the reduced subspace. Moreover, a joint density-matching optimization procedure and highly constrained multi-objective optimization solving algorithms will be developed. Through the research of this project, a relatively systematic and general UMDO approach will be established, which can lay a solid foundation for the theoretical development and extended application of UMDO.

高可靠性、强稳健性先进飞行器设计已成为航空航天领域广泛关注的热点问题。现代飞行器设计通常涉及多个紧密耦合的学科关系、复杂费时的学科模型和多种多样的不确定性因素，急需研究相适应的飞行器不确定性多学科设计优化（UMDO）方法，以充分考虑学科耦合与不确定性影响，提升可靠性、精确性和鲁棒性方面的飞行器实际设计能力。为克服现有UMDO计算成本高昂、分析精度受限、工程实现困难等瓶颈问题，本项目拟提出“降维量化、统一传播、匹配优化”的UMDO理论新框架，试图建立一种广义活跃子空间降维方法，解决高维不确定性问题近似建模与求解难题，通过构建合理有效的降维空间自适应代理模型，提升混合不确定性传播分析效率和精度。同时探讨基于密度匹配的联合优化过程，发展不确定性条件下的多约束多目标优化高效求解算法。通过本项目的研究，将形成一套较为系统、通用的UMDO方法，为 UMDO 理论发展及其推广应用奠定良好的基础。

现代飞行器设计通常涉及多个紧密耦合的学科关系、复杂费时的学科模型和多种多样的不确定性因素，急需研究相适应的飞行器不确定性多学科设计优化（UMDO）方法，以提升可靠性、精确性和鲁棒性方面的飞行器实际设计能力，具有重要理论和工程价值。为克服现有UMDO计算成本高昂、分析精度受限、工程实现困难等瓶颈问题，本项目从“降维量化、统一传播、匹配优化”三个层面对飞行器UMDO技术开展了系统研究，提出了一种适用于线性和非线性问题、随机和认知不确定性条件的广义活跃子空间降维方法，克服高维问题近似建模与求解瓶颈；提出了降维空间自适应代理模型，解决混合不确定性条件的传播分析复杂性难题，保证混合不确定性传播分析效率与精度；提出了基于累积分布匹配的不确定性优化设计方法，发展了不确定性条件下优化组织求解算法，为复杂可靠性与稳健性设计优化问题提供了有效解决途径。通过本项目的研究，初步形成了一套较为系统、普适的UMDO方法，可在实际飞行器部件级与总体级设计问题中推广应用。