Adaptive learning function selection for Kriging-assisted structural reliability analysis

Active learning Kriging is widely used for structural reliability because it can concentrate samples near the limit-state surface while keeping model evaluations modest. However, no single learning function is uniformly optimal across problem classes or along the sequential design, therefore in this work an adaptive learning function selection mechanism that updates their sampling probabilities through a reward-driven dynamically exponential weighting scheme is proposed. The reward is a scale-balanced composite that couples the normalized distance to the estimated limit-state surface with the predictive uncertainty, aligning exploitation and exploration without introducing additional algorithmic complexity. Across numerical benchmarks and engineering structures, including time-varying settings, high-dimensional truss problems, and multimodal discontinuous limit-state cases, the proposed method consistently achieves faster convergence and lower tail variance than single-function active learning Kriging. Notably, it addresses the failure modes often seen with a fixed learning function on multimodal, discontinuous examples, namely non-convergence or the need for an excessive number of iterations to reach convergence while preserving the accuracy required for engineering practice. A runtime analysis further separates per-iteration overhead from end-to-end time and shows that a modest per-iteration cost is converted into fewer iterations, competitive total wall clock time, and improved timing stability, hence, overall computational complexity and total cost do not increase. These results indicate that adaptive selection of learning functions is a practical and robust route to improve the efficiency and reliability of Kriging-assisted structural reliability analysis without additional algorithmic complexity.