A new paradigm for hybrid reliability-based design optimization (HRBDO) is proposed. The key innovation lies in expanding the traditional β-circle into a β-cylinder along the interval dimensions, integrating both random and interval dimensional information. Building upon this theoretical foundation, a novel interval-based dimensional expansion β-cylinder active learning (IBAL) method is proposed, transforming the complex double-loop reliability calculation into an efficient single-loop process. The method employs Kriging models to replace expensive physical responses. Unlike traditional sampling techniques, the IBAL method focuses exclusively on predicted means and deviations on the β-cylinder to guide the Kriging models of performance functions, efficiently identifying the Most Probable Point (MPP). This approach effectively addresses challenges including interval dimensions nonlinearity, multiple extreme points, and multiple MPPs. In HRBDO, the method incorporates an active constraint screening (ACS) mechanism and an MPP objective function isosurface active learning (MIAL) method to enhance computational efficiency and avoid convergence to local optima. The effectiveness of the proposed method is validated through four mathematical examples and one engineering case study.

中文翻译：

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基于混合可靠性的设计优化的新范式：从 β 圆到 β 圆柱


提出了一种基于混合可靠性的设计优化 （HRBDO） 的新范式。关键创新在于将传统的β圆沿区间维度扩展为β圆柱体，同时整合随机和区间维度信息。在此理论基础上，提出了一种新的基于区间的维度扩展β圆柱主动学习 （IBAL） 方法，将复杂的双环可靠性计算转化为高效的单环过程。该方法采用克里金模型来替换昂贵的物理响应。与传统的抽样技术不同，IBAL 方法只关注 β 圆柱体上的预测均值和偏差，以指导性能函数的克里金模型，从而有效地识别最大可能点 （MPP）。这种方法有效地解决了包括区间维度非线性、多个极值点和多个 MPP 在内的挑战。在 HRBDO 中，该方法结合了主动约束筛选 （ACS） 机制和 MPP 目标函数等值面主动学习 （MIAL） 方法，以提高计算效率并避免收敛到局部最优值。通过四个数学实例和一个工程案例研究验证了所提方法的有效性。