基于区间模型的结构非概率稳健优化设计  

NON-PROBABILISTIC ROBUST OPTIMIZATION DESIGN OF STRUCTURES BASED ON INTERVAL MODEL

作　　者：王敏容[1,2] 樊建平[1] 陈旭勇[3] 

机构地区：[1]华中科技大学土木工程与力学学院,武汉430074 [2]五邑大学土木建筑学院,江门529020 [3]武汉工程大学资源与土木工程学院,武汉430073

出　　处：《固体力学学报》2014年第6期583-589,共7页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(51408444);湖北省自然科学基金项目(2012FFB04712)资助

摘　　要：采用区间模型描述不确定参数,在考虑传统约束条件基础上,增加了可靠性指标作为约束条件,研究结构的稳健性优化设计.从非概率可靠性指标的几何意义出发,寻找非概率可靠性指标目标值与不确定参数的波动范围的关系,将非概率的稳健优化设计转化为两层优化模型.对于非线性功能函数,内层优化根据非概率可靠性指标的波动范围最小化功能函数,从而避免了内层优化直接计算非概率可靠性指标难的问题.对于线性功能函数,不确定性参数可以表示为非概率可靠性指标目标值的显示表达式,两层稳健优化转化为确定性的单层优化.该方法优化描述明确清晰,计算公式简便,计算效率高.算例验证了本文所提方法的可行性和正确性.The structural robust optimization with uncertain parameters which are described by inter- val models was investigated. Compared with the traditional optimization design, the robust optimization model involves the non-probabilistic reliability index as an constraint condition. In this contribution, the re- lationship between the target of non-probabilistic reliability index and the fluctuation range of uncertain pa- rameters was depicted by the geometric meaning of the reliability index. The non probabilistic robust opti- mization design model was converted into a two-level optimization model. The minimization for non-linear performance function was carried out according to the fluctuant range of the non-probabilistic reliability in- dex within the inner-lever optimization, so as to avoid the calculation of reliability index directly. For the linear performance function,the uncertain parameters could be described as the target value of non-probabi- listic reliability index with explicit expression, and therefore the two-level robust optimization was easily converted into a single level deterministic optimization. The advantages of the proposed method lie in clear geometric characterization, computing convenience and high calculation efficiency. Several numerical exam- ples are calculated, which show the proposed method is efficient.

关 键 词：结构可靠性 非概率可靠性指标 稳健优化 区间模型 

分 类 号：O211.1[理学—概率论与数理统计]