A hybrid single-loop approach combining the target beta-hypersphere sampling and active learning Kriging for reliability-based design optimization

In engineering design, system-level requirements typically provide each subsystem with specific target reliability indexes. This makes reliability-based design optimization (RBDO) under the prescribed target reliability index particularly relevant for practical applications. However, solving complex nonlinear RBDO problems often involves nested double-loop optimization, leading to prohibitive computational costs and potential convergence issues. To address these challenges, this study proposes a minimum performance measure-based hybrid single-loop approach (TSPM-AK-HSLA) that integrates target beta-hypersphere sampling and active learning Kriging. First, a novel sampling strategy combining target beta-hypersphere and local enhancement is introduced to accurately identify the minimum performance target point (MPTP) without requiring gradient calculations or iterative search direction adjustments. Second, an identification criterion for the active constraint is incorporated to determine whether the Kriging model needs updating within the local region around the approximate MPTP, thereby focusing sampling efforts for improved efficiency. Finally, an adaptive strategy is employed to implement the hybrid single-loop approach, accelerating convergence while maintaining robustness for nonlinear problems. Comparative analyses with existing methods, along with two numerical MPTP search examples and two nonlinear RBDO examples demonstrate the superior efficiency and accuracy of the proposed approach. The RBDO application for an engineering clamping mechanism of the aircraft engine guides the design.