在结构可靠性分析和设计中,往往无法将所有不确定性参数均作为概率随机变量,存在部分不确定性分布特征不明确而仅知其扰动界限的情况。基于概率模型与多椭球模型的混合不确定性描述,以标准U空间中扩展定义的混合可靠性指标为约束条件,建立了随机不确定性和有界不确定性并存情况下的结构可靠性优化数学模型。利用功能测度方法对原优化模型进行等效转换后,结合序列近似规划方法,将嵌套优化问题简化为一系列确定性优化问题求解,提高了计算效率。通过数学优化问题及某导弹翼面结构设计算例对所提模型的合理性及算法的有效性进行了验证。
In the reliability analysis and design of structures, it is unreasonable to describe all the uncertain parameters as stochastic variables when the probabilistic distribution characteristic for some of them is unavailable and only their variation bounds are known. Based on the probabilistic model description and the multi-ellipsoid model description for different types of uncertainties, a reliability-based optimization model of structures combining stochastic and bounded uncertainties is mathematically formulated with constraints on mixed reliability indices defined in standard U-space. The performance measure approach is employed to transform the original model into its equivalent form for improving the convergence and the stability. Then the reformulated nested optimization problem is simplified into a series of deterministic ones by using the sequential approximate programming approach, which greatly facilitates the efficient solution. Two examples, a mathematic optimization problem and a design of missile wing structure, are given to illustrate the validity of the proposed model as well as the efficiency of the presented numerical techniques.
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