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.

本文研究了主动学习方法用于在有限计算预算下高效选择训练样本的能力，同时保留与多个代理极限状态相关联的准确性。研究结果表明，可以通过在统一的主动学习方案中依次针对指定的多个限制状态函数来实现有效的均衡的计算预算管理。

基于方差增强PC-Kriging代理模型的多限状态结构可靠性分析主动学习