To reduce the computational burden for structural reliability analysis involving complex numerical models, many adaptive algorithms based on surrogate models have been developed. Among the various surrogate models, the support vector machine for regression (SVR) which is derived from statistical learning theory has demonstrated superior performance to handle nonlinear problems and to avoid overfitting with excellent generalization. Therefore, to take the advantage of the desirable features of SVR, an Adaptive algorithm based on the Bayesian SVR model (ABSVR) is proposed in this study. In ABSVR, a new learning function is devised for the effective selection of informative sample points following the concept of the penalty function method in optimization. To improve the uniformity of sample points in the design of experiments (DoE), a distance constraint term is added to the learning function. Besides, an adaptive sampling region scheme is employed to filter out samples with weak probability density to further enhance the efficiency of the proposed algorithm. Moreover, a hybrid stopping criterion based on the error-based stopping criterion using the bootstrap confidence estimation is developed to terminate the active learning process to ensure that the learning algorithm stops at an appropriate stage. The proposed ABSVR is easy to implement since no embedded optimization algorithm nor iso-probabilistic transformation is required. The performance of ABSVR is evaluated using six numerical examples featuring different complexity, and the results demonstrate the superior performance of ABSVR for structural reliability analysis in terms of accuracy and efficiency.

为了减少涉及复杂数值模型的结构可靠性分析的计算负担，已经开发了许多基于代理模型的自适应算法。在各种代理模型中，源自统计学习理论的回归支持向量机（SVR）在处理非线性问题和避免过度拟合方面表现出优异的性能，并具有出色的泛化能力。因此，为了利用 SVR 的理想特性，本研究提出了一种基于贝叶斯SVR 模型 (ABSVR)的自适应算法。在 ABSVR 中，遵循惩罚函数方法的概念，设计了一种新的学习函数，用于有效选择信息样本点在优化。为了提高实验设计 (DoE) 中样本点的均匀性，在学习函数中添加了距离约束项。此外，采用自适应采样区域方案滤除具有弱的样本。概率密度进一步提高了算法的效率。此外，开发了一种基于误差停止标准的混合停止标准，使用自举置信度估计来终止主动学习过程，以确保学习算法在适当的阶段停止。所提出的 ABSVR 易于实现，因为不需要嵌入式优化算法或等概率变换。ABSVR 的性能通过六个不同复杂度的数值算例进行评估，结果表明 ABSVR 在结构可靠性分析中在准确性和效率方面的优越性能。