基于概率及证据理论的航天器不确定性多学科设计优化研究

To effectively prevent spacecraft failures, it is necessary to take uncertainties into account comprehensively in design phase so as to enhance spacecraft robustness and reliability. In the multidisciplinary spacecraft system design, there exist both aleatory uncertainties due to the inherent variation of the spacecraft and its operational environment, and epistemic uncertainties resulting from lack of knowledge and information. Due to the interdisciplinary cross propagation of the mixed aleatory and epistemic uncertainties, the uncertainty-based optimization is extremely complex to solve and entails huge computational cost which is unaffordable in practical engineering. Aiming to solve this problem, we propose to systematically study the Mixed Aleatory and Epistemic Uncertainty-based Multidisciplinary Design Optimization (MUMDO) method and its application in spacecraft system design based on probability and evidence theory. The research will be focused on two most important issues of MUMDO which need be addressed urgently, namely mixed uncertainty analysis and mixed uncertainty-based optimization, so as to improve the optimization efficiency and effectiveness of MUMDO and enable it to be applicable in practical engineering. The feasibility and effectiveness of the aforementioned methods will be validated and demonstrated in the system design problems of a single spacecraft and a multi-spacecraft system. To sum up, the research work in this project will develop MUMDO methods with practical value in engineering, initially form MUMDO-based design process for spacecraft system design, and provide beneficial foundation for the application of MUMDO in other areas as well.

为有效预防航天器在轨故障，需要在设计阶段充分考虑各类不确定性影响，提高航天器的稳健性和可靠性。在航天器设计过程中，既存在航天器及其运行环境固有的随机不确定性，也存在由于人员认识不足或信息缺乏导致的认知不确定性。航天器的多学科特性以及学科间各类不确定性混合交叉传递影响，导致考虑不确定性的航天器设计过程复杂、计算成本高昂、工程实现困难。为此，本项目将基于概率及证据理论，深入研究随机和认知不确定性混合条件下的多学科设计优化方法（MUMDO），并探索其在航天器设计中的应用。项目将以提高MUMDO的求解效率和优化效果为目标，重点突破混合不确定性分析和混合不确定性优化两项关键技术，并将其分别应用于单个航天器和多航天器系统的总体设计优化中，验证其可行性和有效性。通过本项目的研究，将形成工程实用性较强的MUMDO方法，初步建立基于MUMDO的航天器总体设计流程，并为MUMDO在其它领域的推广应用奠定基础。

本项目以提高航天器稳健性和可靠性为背景，基于概率及证据理论，对考虑随机和认知混合不确定性影响的航天器不确定性多学科设计优化方法（MUMDO）及其在航天器设计中的应用开展了系统研究。首先，在混合不确定性分析方法研究方面，提出了基于系统响应显式函数近似和约束边界隐式函数近似的不确定性分析方法，有效提高了计算效率，实现不确定性分析精度与效率的折中。然后，在混合不确定性优化方法研究方面，分别提出了基于泰勒展开进行不确定性优化问题转换的MUMDO序贯优化求解法和基于层次系统目标级联分析法的MUMDO分解协调求解法，算例表明上述两种方法都能有效获取满足可靠性要求的优化方案，同时提高优化效率。最后，对基于MUMDO方法的航天器总体设计应用开展了研究，分别以某对地观测小卫星和“在轨加注”多航天器系统为对象，对其不确定性总体设计优化问题进行了建模，基于前述不确定性分析和优化算法对MUMDO问题进行了求解，得到满足可靠性约束或可信性约束的最优方案，验证了本项目提出方法的有效性，为将来进一步推广应用奠定了基础。