The estimation of the failure probability for complex systems is a crucial issue for sustainability. Reliability analysis methods are needed to be developed to provide accurate estimations of the safety levels for the complex systems and structures of today. In this paper, a novel hybrid framework for the reliability analysis of engineering systems and structures is extended to reduce the computational burden. The proposed hybrid framework is named as SVR–CFORM and consists of coupling two parts: the first is an enhanced first-order reliability method (FORM) using nonlinear conjugate map (CFORM); the second is an artificial intelligence technique called support vector regression (SVR). The conjugate FORM (CFORM) is adaptively formulated to improve the robustness of the original iterative FORM algorithm, whereas the SVR technique is used to enhance the efficiency of the reliability analysis by reducing the computational burden. The performance of the proposed SVR–CFORM formulation is compared in terms of efficiency and robustness with several FORM formulas (i.e. HL–RF, directional stability transformation method, conjugate HL–RF and finite step length) through different numerical/structural reliability examples. Results indicate that the proposed SVR–CFORM formulation is more accurate and efficient than other reliability methods. Based on the comparative analysis results, the SVR technique can highly reduce the computational costs and accurately model the response of complex performance functions, while the iterative CFORM formulation found to provide stable and robust reliability index results compared to the others reliability methods.

复杂系统故障概率的估计是可持续性的关键问题。需要开发可靠性分析方法，以提供当今复杂系统和结构的安全级别的准确估计。在本文中，扩展了一种用于工程系统和结构可靠性分析的新型混合框架，以减少计算负担。提出的混合框架称为SVR-CFORM，它包括两部分：第一部分是使用非线性共轭映射（CFORM）的增强的一阶可靠性方法（FORM）。第二种是称为支持向量回归（SVR）的人工智能技术。共轭形式（CFORM）被自适应地制定以提高原始迭代形式算法的鲁棒性，而SVR技术通过减少计算负担来使用“可靠性”来提高可靠性分析的效率。通过不同的数值/结构可靠性示例，通过几种FORM公式（即HL-RF，方向稳定性转换方法，共轭HL-RF和有限步长），在效率和鲁棒性方面比较了建议的SVR-CFORM公式的性能。结果表明，提出的SVR–CFORM公式比其他可靠性方法更准确，更有效。根据比较分析结果，SVR技术可以大大降低计算成本，并可以准确地建模复杂性能函数的响应，而迭代CFORM公式与其他可靠性方法相比可以提供稳定而可靠的可靠性指标结果。