基于证据理论的结构非概率可靠性拓扑优化设计  

Approach of non-probabilistic reliability topology optimization using evidence theory

作　　者：苏瑜 唐和生[2] 薛松涛[2] 苏骏[1] SU Yu;TANG HeSheng;XUE SongTao;SU Jun(School of Civil Engineering, Architecture and Environment,Hubei University of Technology, Wuhan 430068, China;Research Institute of Structural Engineering and Disaster Reduction, Tongji University,Shanghai 200092,China)

机构地区：[1]湖北工业大学土木建筑与环境工程学院,武汉430068 [2]同济大学结构工程与防灾研究所,上海200092

出　　处：《中国科学：技术科学》2019年第3期320-330,共11页Scientia Sinica(Technologica)

基　　金：科技部国家重点实验室基金项目(编号:SLDRCE14-B-03);湖北省自然科学基金青年项目(编号:2018CFB287)资助

摘　　要：考虑数据信息较少以及认知水平有限情况下的不确定性对于结构拓扑优化具有重要意义.本文引入证据理论处理不精确的数据信息,采用证据理论的不确定测度克服精确概率约束模型建立的困难,并结合拓扑优化策略,形成了基于证据理论的可靠性拓扑优化设计模型.为了提高不确定测度的计算效率,提出了仿生智能优化算法和不精确极值思想相结合的改进优化算法来降低焦元数目和极限状态函数极值求解所导致的计算量.通过两个桁架算例对所提方法进行验证,结果表明,确定性优化结果可能是不确定情况下的失效解,虽然基于证据理论的最优设计在重量和拓扑形式上相对于确定性优化结果偏保守,但具备抵抗不确定波动的能力.It is of great importance to consider uncertainty due to insufficient data or imprecise information in topology optimization design.In this paper,evidence theory is presented to handle the imprecise data situation.The plausibility measure based on evidence theory is introduced to overcome the difficulty of constructing the precise probabilistic constraint.Furthermore,the topology problem in this evidence-based optimization design is solved by combined strategy of the differential evolution and superior topology technique.In order to overcome the difficulty of intensive computational cost in calculating plausibility measure,an improved method of evolutionary optimization design integrating with imprecise extremum idea is proposed.Two truss examples are given to demonstrate the proposed approach.The research indicates that deterministic results may be the failure solutions under epistemic uncertainty.Although evidence-based optimum topology designs are more conservative than deterministic results in aspects of weight and optimal structural topology layout,it gains a more robust design under epistemic uncertainty.

关 键 词：证据理论 拓扑优化 微分演化 不确定分析 

分 类 号：TB114.3[理学—概率论与数理统计]