摘要
提出了在概率不确定性和非概率不确定性同时存在时的约束函数鲁棒性和目标函数鲁棒性的实现策略及结构鲁棒设计方法。将传统优化设计问题的约束条件改造成为能同时反映两类不确定性量波动变化影响的约束条件,以实现约束函数的鲁棒性;在传统优化设计问题目标函数中增加若干个关于目标函数灵敏度的新目标函数,构成一个多目标函数设计问题,以实现目标函数的鲁棒性。所提方法应用于一个10杆桁架结构设计,采用宽容排序法求解。计算结果表明,在相同的结构总质量限制条件下,目标函数鲁棒性程度随着变量不确定性程度的增加而降低;在相同的变量不确定性程度条件下,增加结构总质量能提高目标函数鲁棒性的程度。
The paper describes the strategies for constraint function robustness and objective function robustness respectively subject to probabilistic and non-probabilistic uncertainties and proposes an approach to robust design of structures with probabilistic and non-probabilistic uncertainties. The robustness of constraint functions is achieved by adding some items reflecting the variation of the constraint function due to uncertain variables to the original constraint function. The robustness of objective function is guaranteed by adding several new objective functions about the sensitivities of the original objective function and performing a multi-objective optimization. The proposed method is applied to the design of a 1 O-bar truss structure and the modified lexicographic method is employed to find the optimal solution. Numerical results show that the degree of objective function robustness decreases as the uncertainty degree of variables increases for the same structural weight while the degree of objective function robustness increases as the structural weight increases for the same uncertainty degree of variables.
出处
《工程力学》
EI
CSCD
北大核心
2005年第4期10-14,42,共6页
Engineering Mechanics
关键词
概率不确定性
非概率不确定性
鲁棒设计
约束函数鲁棒性
目标函数鲁棒性
probabilistic uncertainty
non-probabilistic uncertainty
robust design
constraint function robustness
objective function robustness
