An adaptive Kriging-assisted reliability-based design optimization framework with reliability assurance and high efficiency

While reliability-based design optimization (RBDO) significantly improves engineering safety, computational expenses and accuracy concerns restrict its use in complex, high-dimensional, nonlinear, and black-box scenarios. To address this challenge, a Kriging-AMV-MCS reliability optimization method (KAMRO) is proposed in this paper. The algorithm integrates the Kriging surrogate model, an improved advanced mean value (AMV) method, and a Monte-Carlo simulation (MCS) validation mechanism, aiming to achieve efficient and robust design optimization. First, through an adaptive sampling strategy based on the expected feasibility function and space filling criteria, actively constrained regions are intelligently identified and sample distribution is optimized. Second, a two-stage optimization framework is adopted. In the first stage, the penalty function is used to quickly approximate the feasible domain, and in the second stage, explicit constraints are combined for precise optimization. Finally, an MCS-guided post-optimization process is proposed to further optimize and improve the design scheme when the reliability is insufficient. Through validation with engineering cases, including a two-dimensional analytical example, a seven-dimensional gear reducer structural optimization example, and a three-dimensional pressure control head structure design, this RBDO framework significantly reduces computational costs while ensuring design reliability, offering both optimization accuracy and engineering practicality.