Scale-free and coverage-aware active learning for Kriging-based surrogate assisted structural reliability analysis

Structural reliability analysis quantifies failure probabilities under multiple sources of uncertainty, yet the computational expense of high-fidelity models renders direct Monte Carlo simulation impractical for most engineering systems. Existing active-learning strategies frequently switch unstably between global exploration and boundary refinement, leading to redundant sampling and limited efficiency. This study develops an active-learning Kriging framework that integrates a scale-free, coverage-aware acquisition rule with an iterative reliability estimator. The acquisition combines three jointly normalized indicators—the distance to the estimated limit-state surface, the predictive uncertainty, and the local sample spacing, to balance exploration and refinement while maintaining scale invariance. Joint normalization prevents dominance by any single indicator and suppresses clustering, while an annealed scheduling mechanism progressively shifts the search from global coverage to local boundary sharpening. Numerical benchmarks and engineering case studies show that the method produces accurate and smoothly convergent failure-probability estimates with substantially fewer true-model evaluations than representative active-learning criteria. The sampling trajectory preserves broad domain coverage, reduces run-to-run variability, and avoids premature focus on isolated failure regions. Run-time analysis further shows that the modest increase in per-iteration cost is outweighed in practice by the significantly reduced number of iterations and leads to competitive wall-clock performance. These findings confirm that the proposed approach is both practical and robust for surrogate-assisted reliability assessment of complex engineering structures.