AK-MCS-C2 : Active Kriging Monte Carlo Simulation method with conformal certification for failure probability estimation

2026-06-18

AI Summary

This study addresses the high uncertainty in failure probability estimation and unreliable classification in structural reliability analysis under small-sample and rare-event conditions. To this end, it introduces distribution-free conformal prediction into the active Kriging Monte Carlo simulation (AK-MCS) framework for the first time, proposing an adaptive cross-conformal strategy and a J+GP conformal estimator. The method enables reliable classification near the limit state surface and provides rigorous finite-sample error guarantees for failure probability estimates. Numerical experiments on classical benchmark problems demonstrate that the proposed approach significantly outperforms conventional AK-MCS, particularly in rare-event scenarios, achieving superior efficiency, robustness, and accuracy.

Abstract

We introduce a novel active-learning framework for failure probability estimation in structural reliability analysis that integrates Active Kriging Monte Carlo simulation with conformal prediction. The proposed approach employs an adaptive cross-conformal strategy specifically designed for small-sample settings and kriging surrogate models using the J+GP conformal estimator. Unlike standard AK-MCS methods, the proposed framework provides distribution-free guarantees on prediction errors, leading to more reliable classification of samples near the limit-state surface. This improved uncertainty quantification enhances both the accuracy and robustness of failure probability estimates, especially for rare-event regimes where such efficiency is crucial. Reproducible numerical results illustrate the effectiveness of the method and also compare it to classical approaches on well-established benchmarks.

Problem

• failure probability estimation
• structural reliability
• rare-event simulation
• uncertainty quantification
• limit-state surface

Innovation

• Active Kriging
• Conformal Prediction
• Failure Probability Estimation
• Surrogate Modeling
• Rare-Event Simulation