考虑不确定性的多学科设计优化分解方法

Decomposition method for multidisciplinary design optimization considering uncertainty

为提高不确定性情况下多学科设计优化分解的合理性,研究不确定性因素对分解目标的影响,提出了考虑不确定性的多学科设计优化分解方法。首先将布尔型函数关系矩阵扩展为"相关性-规模"两层函数关系矩阵,给出了规模矩阵元素与设计变量不确定性的定量关系。然后针对该矩阵提出了任务规模、任务平均度和任务耦合度的概念,给出了三者的计算方法。在此基础上分析确定了优化目标、约束条件、优化变量,建立了整数规划模型,并应用遗传算法进行求解。最后以齿轮减速器为例进行分解,分解结果证明了本方法的合理性与先进性。

To improve rationality of decomposition for Muhidisciplinary Design Optimization （MDO） under uncertainty, influence of uncertain factors on decomposition subject was studied, and an optimal decomposition method for MDO considering uncertainty was proposed. Firstly, traditional Boolean Function Dependency Table （FDT） was extended to a Bi-layer FDT, which described relativity and scale separately. Relationships among elements of size-matrix and design variables＇ uncertainty were formulated. Secondly, based on Bi-layer FDT, concepts and formulations of task scale, task average degree and task coupling degree were defined. And their computation methods were also given out. An integer programming model was constructed after analyzing its optimization objectives, constraint relationships and optimization variables. Genetic algorithm was applied to resolve decomposition. Finally, the rationality and advantages of aforementioned method was verified by a case study of gear-reduce-box design.