Single-loop approach (SLA) is an efficient reliability-based design optimization (RBDO) method, where the current most probable point (MPP) is located through the gradient information of previous MPP. However, the MPP obtained by SLA may not be accurate for complex nonlinear RBDO problems, which probably causes SLA to be inefficient, converge to the wrong optimal solution or even difficulty in convergence. In this study, an enriched single-loop approach based on enhanced advanced mean value (ESLA-EAMV) is proposed to improve convergence performance of the original SLA for complex nonlinear RBDO problems. First, an enhanced advanced mean value (EAMV) method is developed to find the MPP, where the negative gradient vector of the previous MPP in AMV is replaced by a vector with adaptive step size in EAMV. Then, the proposed EAMV method is integrated into the original SLA to improve the convergence ability of the original SLA. Finally, seven benchmark nonlinear problems are presented to verify the accuracy, efficiency and robustness of the proposed ESLA-MAMV compared with other existing RBDO methods. Comparison results show that the proposed ESLA-MAMV can improve the convergence performance of the original SLA.

中文翻译：

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用于复杂非线性问题的基于可靠性的设计优化的丰富单回路方法

单环方法 (SLA) 是一种高效的基于可靠性的设计优化 (RBDO) 方法，其中当前最可能点 (MPP) 通过先前 MPP 的梯度信息定位。然而，SLA 获得的 MPP 对于复杂的非线性 RBDO 问题可能并不准确，这可能会导致 SLA 效率低下、收敛到错误的最优解甚至难以收敛。在这项研究中，提出了一种基于增强高级平均值（ESLA-EAMV）的丰富单环方法，以提高原始 SLA 对复杂非线性 RBDO 问题的收敛性能。首先，开发了一种增强高级平均值 (EAMV) 方法来找到 MPP，其中 AMV 中先前 MPP 的负梯度向量被 EAMV 中具有自适应步长的向量替换。然后，提出的 EAMV 方法被集成到原始 SLA 中，以提高原始 SLA 的收敛能力。最后，提出了七个基准非线性问题，以验证所提出的 ESLA-MAMV 与其他现有 RBDO 方法相比的准确性、效率和鲁棒性。比较结果表明，所提出的 ESLA-MAMV 可以提高原始 SLA 的收敛性能。