To solve the design problems of engineering structures with multiple conflicting performance indices under uncertainties, a non-probabilistic optimization model which takes into consideration the correlation of uncertainties was proposed in this paper. The multidimensional parallelepiped model was utilized to describe the uncertainties and deal with their correlation. Further, a novel concept of feasible discriminant of interval constraints was proposed to identify the feasible solutions, and a competitive strategy for design vectors was proposed to achieve equilibrium design of structures. To improve the efficiency of optimization and promote its applications in engineering, a direct solution framework was constructed in this paper. This framework was based on response surface model and integrated the interval analysis with the genetic algorithm. The effectiveness and superiority of the proposed approach were illustrated by two numerical examples. Finally, the proposed method was applied to structural design of the upper and lower beams of forming machine, and the design of lightweight and equilibrium were achieved. This structural design example demonstrated the applicability and effectiveness of the proposed method in engineering.

为解决不确定性下多性能指标冲突的工程结构设计问题，提出一种考虑不确定性相关性的非概率优化模型。利用多维平行六面体模型来描述不确定性并处理它们的相关性。此外，提出了区间约束可行判别的新概念来识别可行解，并提出设计向量的竞争策略以实现结构的平衡设计。为提高优化效率，促进其在工程中的应用，本文构建了直接求解框架。该框架基于响应面模型，将区间分析与遗传算法相结合。通过两个数值例子说明了所提出方法的有效性和优越性。最后，将该方法应用于成型机上下梁的结构设计，实现了轻量化和平衡设计。这个结构设计实例证明了所提出的方法在工程中的适用性和有效性。