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邱志平, 陈吉云, 王晓军. 结构鲁棒优化的非概率集合理论凸方法[J]. 力学学报, 2005, 37(3): 295-300. DOI: 10.6052/0459-1879-2005-3-2003-347
引用本文: 邱志平, 陈吉云, 王晓军. 结构鲁棒优化的非概率集合理论凸方法[J]. 力学学报, 2005, 37(3): 295-300. DOI: 10.6052/0459-1879-2005-3-2003-347
Robust optimization for structures using non-probabilistic convex method of set theory[J]. Chinese Journal of Theoretical and Applied Mechanics, 2005, 37(3): 295-300. DOI: 10.6052/0459-1879-2005-3-2003-347
Citation: Robust optimization for structures using non-probabilistic convex method of set theory[J]. Chinese Journal of Theoretical and Applied Mechanics, 2005, 37(3): 295-300. DOI: 10.6052/0459-1879-2005-3-2003-347

结构鲁棒优化的非概率集合理论凸方法

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

  • 摘要: 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.

     

    Abstract: Based on the conventional structural optimal theory andconsidering the uncertainties of structural parameters, we present robustoptimal method for structures using non-probabilistic convex set theory. Wemodel the uncertain parameters which exist in the object function andconstraint conditions as convex set, and need not know their detailedstatistical information bur bounds of uncertainties. The proposed method canendure the variation of structural performance resulting from the variationof uncertain parameters. According to the variation range of them, we candetermine the range or interval of optimal solution. In this sense, theoptimal solution is one domain rather than a point. Numerical example often-bar truss is used to illustrate the method using non-probabilisticrobust optimization, which shows both the feasibility and superioritycompared with conventional methods.

     

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