Existing active strategies for training surrogate models yield accurate structural reliability estimates by aiming at design space regions in the vicinity of a specified limit state function. In many practical engineering applications, various damage conditions, e.g. repair, failure, should be probabilistically characterized, thus demanding the estimation of multiple performance functions. In this work, we investigate the capability of active learning approaches for efficiently selecting training samples under a limited computational budget while still preserving the accuracy associated with multiple surrogated limit states. Specifically, PC-Kriging-based surrogate models are actively trained considering a variance correction derived from leave-one-out cross-validation error information, whereas the sequential learning scheme relies on U-function-derived metrics. The proposed active learning approaches are tested in a highly nonlinear structural reliability setting, whereas in a more practical application, failure and repair events are stochastically predicted in the aftermath of a ship collision against an offshore wind substructure. The results show that a balanced computational budget administration can be effectively achieved by successively targeting the specified multiple limit state functions within a unified active learning scheme.

翻译：现有的代理模型主动学习策略通过逼近特定极限状态函数附近的设计空间区域，能够获得准确的结构可靠性估计。在许多实际工程应用中，需对多种损伤工况（如维修、失效）进行概率表征，因此需要评估多个性能函数。本文研究了在有限计算预算下，主动学习方法高效选择训练样本的能力，同时保持多个代理极限状态函数的精度。具体而言，基于PC-Kriging的代理模型通过引入留一交叉验证误差信息导出的方差修正进行主动训练，而序贯学习方案则依赖于U函数衍生度量。所提出的主动学习方法在高度非线性的结构可靠性场景中进行了测试，并在更实际的工程应用中，随机预测了船舶撞击海上风电下部结构后发生的失效与维修事件。结果表明，通过在统一主动学习框架内连续针对指定多个极限状态函数，能够有效实现平衡的计算预算管理。