Reliability-based design optimization (RBDO) under epistemic uncertainty (i.e., imprecise probabilistic information), especially in the presence of dependency of input variables, is a challenging problem. In this paper, we propose a dimension reduction-based RBDO framework considering dependent interval variables, which is pursued in a purely probabilistic manner. Most probable point (MPP) based dimension reduction method (DRM) is used for reliability evaluation due to its ability to circumvent the shortcomings of poor approximation by first order reliability method (FORM) and pronounced computational complexity by second order reliability method (SORM). For modeling correlation of input variables, copula is used instead of true joint cumulative density function (CDF). A flexible Johnson family of distributions is used to handle the stochastic but poorly known epistemic uncertainty. In order to handle the uncertainty in correlation measures, arisen due to interval data, expert suggested bounds of correlation measures have been recommended. For the overall RBDO problem, a decoupled approach to optimization is explored. Two numerical examples — one mathematical problem and one engineering problem — have been solved to properly explicate the proposed RBDO process. It is demonstrated that correlations in input variables have significant impact on the optimal design solutions.

中文翻译：

---

因区间变量的基于降维方法的 RBDO

在认知不确定性（即不精确的概率信息）下，尤其是在输入变量存在相关性的情况下，基于可靠性的设计优化 (RBDO) 是一个具有挑战性的问题。在本文中，我们提出了一种考虑因区间变量的基于降维的 RBDO 框架，该框架以纯概率方式进行。基于最大概率点（MPP）的降维方法（DRM）由于能够规避一阶可靠性方法（FORM）近似性差和二阶可靠性方法（SORM）计算复杂度显着的缺点，被用于可靠性评估。对于输入变量的相关性建模，使用 copula 代替真正的联合累积密度函数 (CDF)。一个灵活的约翰逊分布族用于处理随机但鲜为人知的认知不确定性。为了处理由区间数据引起的相关度量的不确定性，专家建议的相关度量范围已被推荐。对于整个 RBDO 问题，探索了一种解耦的优化方法。已经解决了两个数值示例——一个数学问题和一个工程问题——以正确解释所提出的 RBDO 过程。研究表明，输入变量的相关性对最优设计解决方案有显着影响。探索了一种解耦的优化方法。已经解决了两个数值示例——一个数学问题和一个工程问题——以正确解释所提出的 RBDO 过程。研究表明，输入变量的相关性对最优设计解决方案有显着影响。探索了一种解耦的优化方法。已经解决了两个数值示例——一个数学问题和一个工程问题——以正确解释所提出的 RBDO 过程。研究表明，输入变量的相关性对最优设计解决方案有显着影响。