This article proposes a new method for hybrid reliability‐based design optimization under random and interval uncertainties (HRBDO‐RI). In this method, Monte Carlo simulation (MCS) is employed to estimate the upper bound of failure probability, and stochastic sensitivity analysis (SSA) is extended to calculate the sensitivity information of failure probability in HRBDO‐RI. Due to a large number of samples involved in MCS and SSA, Kriging metamodels are constructed to substitute true constraints. To avoid unnecessary computational cost on Kriging metamodel construction, a new screening criterion based on the coefficient of variation of failure probability is developed to judge active constraints in HRBDO‐RI. Then a projection‐outline‐based active learning Kriging is achieved by sequentially select update points around the projection outlines on the limit‐state surfaces of active constraints. Furthermore, the prediction uncertainty of Kriging metamodel is quantified and considered in the termination of Kriging update. Several examples, including a piezoelectric energy harvester design, are presented to test the accuracy and efficiency of the proposed method for HRBDO‐RI.

中文翻译：

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随机和区间不确定性下基于混合可靠性的设计优化新方法

本文提出了一种在随机和区间不确定性（HRBDO-RI）下基于混合可靠性的设计优化的新方法。在这种方法中，采用蒙特卡罗模拟（MCS）估计失败概率的上限，并扩展了随机敏感性分析（SSA）以计算HRBDO-RI中失败概率的敏感性信息。由于MCS和SSA中涉及大量样本，因此构造了Kriging元模型来替代真实约束。为避免在Kriging元模型构建过程中产生不必要的计算成本，开发了一种基于失效概率变异系数的新筛选标准来判断HRBDO-RI中的活动约束。然后，通过在活动约束的极限状态曲面上的投影轮廓周围顺序选择更新点，从而实现基于投影轮廓的主动学习Kriging。此外，在克里格更新的终止中，对克里格元模型的预测不确定性进行了量化和考虑。给出了几个示例，包括压电能量收集器设计，以测试所提出的HRBDO-RI方法的准确性和效率。