Abstract: Reliability optimization design of key structure for complex products focuses on searching the optimal values of the design variables on the premise of meeting the reliability requirements,which is an important way to ensure product performance and improve human experience.It is worth noting that uncertainty factors are ubiquitous and diverse in the process of structural design,especially interval uncertainty and random uncertainty often exist at the same time and have high parameter dimensions,making traditional design methods no longer applicable.Therefore,a novel method of reliability optimization design for product key structure based on integration dimension-reduction was put forward that taken the high-dimensional heterogeneous uncertainties including random factors and interval factors into consideration.With the Kriging approximation modeling and the multi-objective particle swarm intelligence algorithm,the efficient double-layer nesting computing framework of reliability optimization for high-dimensional heterogeneous uncertainties product key structure was established.The inner layer was reliability analysis with integration dimension-reduction,where the random variables and interval variables in performance function for key structure were analyzed according to univariate dimension-reduction and Taylor expansion respectively.The upper and lower limits of performance function for key structure were obtained by the superposition of the low-dimensional integrations which were converted with the Gaussian integration to calculate the reliability of the key structure quickly.The outer layer was the iterative optimization with a multi-objective particle swarm optimization algorithm based on the reliability analysis results in inner layer,and the design vectors that could meet the reliability requirements were optimized by objective functions to obtain the optimal design vector.The calculation cost of reliability optimization design for product key structures with high-dimensional heterogeneous uncertainties could be reduced in this way.The rationality and superiority of the proposed method were verified by a case study of beam design for a large hydraulic press.

Key words: high-dimensional heterogeneous uncertainties, integration dimension-reduction, reliability optimization design, product key structure, double-layer nesting computing

摘要： 在产品可靠性中注入优化设计思想,在满足可靠度要求的前提下寻找能够使目标性能最优的关键结构设计变量取值,是保障产品性能和提升人类使用感受的重要途径。值得注意的是,不确定因素在结构设计过程中无处不在且品种多样,特别是区间不确定和随机不确定往往同时存在,并具有较高的参数维度,使得传统的设计方法不再适用。针对此问题,先引入积分降维来提升产品关键结构可靠性的分析速度,再通过Kriging近似建模技术和多目标粒子群智能算法,建立高维混合不确定产品关键结构可靠性优化设计的高效循环嵌套计算架构。内层计算聚焦于考虑高维混合不确定变量的产品关键结构功能函数降维积分以快速获取其上下界函数表征及对应的可靠性范围,外层计算则根据内层的可靠性分析结果来判断当前的结构设计变量是否满足可靠性要求并借助多目标粒子群智能算法进行搜索更新,有效减小了产品关键结构可靠性优化设计过程的计算工作量,并通过工程实例验证了所提方法的合理性与有效性。

关键词: 高维混合不确定, 降维积分, 可靠性优化设计, 产品结构, 双层嵌套计算