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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 structural reliability analysis and design, it is often impossible to take all the uncertainty parameters as probabilistic random variables, and some of the uncertainty distribution features are not clear but only their perturbation boundaries are known. Based on the description of the mixed uncertainties of the probabilistic model and the multi-ellipsoidal model, the mixed reliability index defined by the extended U-space is used as the constraint condition, and the structural reliability under the condition of both the random uncertainty and the bounded uncertainty is established Optimize the mathematical model. After the original optimization model is equivalently transformed by the functional measure method, the nested optimization problem is reduced to a series of deterministic optimization problems by using the method of approximate sequence programming, which improves the computational efficiency. The rationality of the proposed model and the effectiveness of the algorithm are verified by the mathematical optimization problem and a missile wing structure design example.