Enhanced active learning Gaussian process metamodel for estimating the one-sided tail probability of nonlinear structural response

The safety operation and maintenance of mega-structures in China are increasingly challenged by rare but high-impact structural failures. To address the difficulty in accurately estimating the low-probability tail of the response distribution, we propose a novel framework centered on the Tail-Sensitive Global Learning (TS-GL) algorithm. Unlike existing active learning-based Gaussian process (AL-GP) metamodels, TS-GL introduces a tail-focused search mechanism with a newly designed weight function, significantly improving the estimation of one-sided tail probabilities. To ensure computational practicality, the effect of different activation functions on iteration efficiency is also examined. The method is validated on a classical nonlinear system-the bond-slip relationship between steel and concrete-relevant to anchorage connections in subway tunnels. Insufficient anchorage length can cause excessive bolt slip and deformation, leading to gaps and leakage in underground structures. TS-GL outperforms AL-GP in both accuracy and efficiency when quantifying such rare events, providing a practical tool for uncertainty analysis in critical infrastructure.