Practical enhancement of failure-probability estimation using probability density-driven active learning

Abstract

This study proposes a novel learning function, referred to as the T-learning function (TLF), that incorporates prior probability density into active learning for failure probability estimation. The method is developed within the framework of Adaptive Kriging-based Monte Carlo Simulation (AK-MCS), with the goal of improving estimation efficiency and robustness. The TLF prioritizes sampling in high-probability regions near the limit state by combining three components: prior density weighting, prediction uncertainty, and a redundancy suppression term. Comparative evaluations were conducted with two established learning functions, the U-function (ULF) and the Expected Feasibility function (EFF), using three benchmark problems and a practical application to port structure design. Numerical results show that the TLF achieves more accurate and stable failure probability estimates under limited computational resources and outperforms ULF in robustness to random initial conditions. Additionally, the EFF exhibited high compatibility with the stopping criterion and strong reliability in estimation. The proposed TLF enables an efficient and stable single reliability analysis, which is commonly required in engineering practice. This approach significantly reduces computational cost while maintaining estimation accuracy, and it offers practical applicability to real-world structural design problems.