This paper proposes an effective active learning strategy for reliability-based design optimization (RBDO) problems in which the constraint functions are acquired from multiple simulation models. To achieve this goal, a new active learning function (ALF) is derived by estimating the increased reliability of active constraint functions after adding one point to the train points of constraint functions in each simulation model. The proposed ALF distinguishes possibly active constraint functions that seem active near the current optimum and considers how the constraint functions are active. In the proposed RBDO method, a Kriging model is iteratively updated by adding the best point to the train points of constraint functions included in the crucial simulation model until the optimum converges and the Kriging model is sufficiently accurate. The best point and the crucial simulation model are obtained by comparing the proposed ALF. The ALF is further modified to apply to problems where the cost of each simulation model is different. To verify the effectiveness of the proposed method, two numerical and one engineering examples are analyzed. The results show that the proposed method efficiently and accurately obtains the RBDO optimum involving multiple simulation models, regardless of simulation cost.

本文针对基于可靠性的设计优化（RBDO）问题提出了一种有效的主动学习策略，其中约束函数是从多个仿真模型中获取的。为了实现这一目标，在每个仿真模型中的约束函数的训练点上添加一个点后，通过估计主动约束函数的可靠性增加，导出了一种新的主​​动学习函数（ALF）。所提出的 ALF 区分了在当前最优值附近似乎活跃的可能活跃约束函数，并考虑了约束函数如何活跃。在所提出的RBDO方法中，通过将最佳点添加到关键仿真模型中包含的约束函数的训练点来迭代更新克里金模型，直到最优收敛并且克里金模型足够准确。通过比较所提出的 ALF，获得了最佳点和关键仿真模型。ALF 被进一步修改以适用于每个仿真模型的成本不同的问题。为了验证所提方法的有效性，对两个数值算例和一个工程算例进行了分析。结果表明，该方法能够高效、准确地获得涉及多个仿真模型的 RBDO 最优值，且不考虑仿真成本。