This paper presents the development of an algorithm, termed the Global-Local Hybrid Surrogate (GLHS), designed to efficiently compute the probability of rare failure events in complex systems. The primary goal is to enhance the accuracy of reliability analysis while minimizing computational cost, particularly for high-dimensional problems where traditional methods, such as Monte Carlo simulations, become prohibitively expensive. The proposed GLHS builds upon the foundational work of Li et al., by integrating an adaptive strategy based on the General Domain Adaptive Strategy (Adcock et al.). The algorithm aims to approximate the failure domain of a given system, defined as the region in the input domain where the system transitions from safe to failure modes, described by a limit state surface. This failure domain is not explicitly known and must be learned iteratively during the analysis. The method employs a buffer zone, defined as the region surrounding the limit state surface. Within this buffer zone, Christoffel Adaptive Sampling is utilized to select new samples for constructing localized surrogate models, which are designed to refine the approximation in regions critical to failure probability estimation. The iterative process proceeds until convergence is reached. This results in a hybrid methodology that integrates a global surrogate to capture the overall trend with local surrogates that concentrate on critical regions near the limit state function. By adopting this strategy, the GLHS method balances computational efficiency with accuracy in estimating the failure probability.

翻译：本文提出了一种称为全局-局部混合代理模型（GLHS）的算法，旨在高效计算复杂系统中罕见失效事件的概率。其主要目标是在最小化计算成本的同时提高可靠性分析的准确性，尤其针对高维问题，其中传统方法（如蒙特卡洛模拟）的计算代价过高。所提出的GLHS算法基于Li等人的基础工作，并整合了基于通用域自适应策略（Adcock等人）的自适应策略。该算法旨在近似给定系统的失效域，即输入域中系统从安全模式过渡到失效模式的区域，由极限状态曲面描述。该失效域并非显式已知，必须在分析过程中迭代学习。该方法采用缓冲区，即极限状态曲面周围的区域。在此缓冲区内，利用Christoffel自适应采样选择新样本以构建局部代理模型，这些模型旨在细化对失效概率估计关键区域的近似。迭代过程持续进行直至收敛。由此形成一种混合方法，整合了捕捉整体趋势的全局代理模型与专注于极限状态函数附近关键区域的局部代理模型。通过采用此策略，GLHS方法在计算效率与失效概率估计准确性之间取得了平衡。