结构鲁棒优化的非概率集合理论凸方法

以传统的优化理论为基础，考虑含不确定结构参数的情况，提出了非概率凸集合理论的结构优化方法. 将结构优化列式中的目标函数与约束条件所含有的不确定参数用凸集合定量化，只需知道其所在范围的边界，降低了以往处理不确定性问题概率方法需要知道不确定参数的均值、方差或概率分布密度等详细统计信息的要求. 提出的鲁棒优化方法在使目标函数达到设计要求的同时，结构还能承受结构参数在其所在范围内变化引起结构性能的变异. 通过优化问题中普遍使用的10杆平面桁架和一个72杆空间桁架实例，给出了当结构参数为名义值时结构的优化结果，以及结构参数具有不确定性时的优化结果，力求表明所介绍的方法的可行性和优越性.

Robust optimization for structures using non-probabilistic convex method of set theory

Based on the conventional structural optimal theory and considering the uncertainties of structural parameters, we present robust optimal method for structures using non-probabilistic convex set theory. We model the uncertain parameters which exist in the object function and constraint conditions as convex set, and need not know their detailed statistical information bur bounds of uncertainties. The proposed method can endure the variation of structural performance resulting from the variation of uncertain parameters. According to the variation range of them, we can determine the range or interval of optimal solution. In this sense, the optimal solution is one domain rather than a point. Numerical example of ten-bar truss is used to illustrate the method using non-probabilistic robust optimization, which shows both the feasibility and superiority compared with conventional methods.