基于区间模型的结构非概率稳健优化设计

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。

Non-probabilistic robust optimization design of structures based on interval model

The structural robust optimization with uncertain parameters described by interval models is investigated. Comparing with the traditional optimization design, the non-probabilistic reliability index has been involved as an constraint condition in the robust optimization model. The relationship between the target of non-probabilistic reliability index and the fluctuation range of uncertain parameters is described by the geometric meaning of the reliability index. The non-probabilistic robust optimization design model is 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 index 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 describe as the target value of non-probabilistic reliability index with explicit expression, and therefore the two-level robust optimization is 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. Numerical examples show the validity and efficiency of the proposed method.