Consideration of Confidence Intervals for Estimated Limit State Probability in Surrogate Model Active Learning

Echard et al. (2011) introduced an active learning reliability method combining Kriging and Monte Carlo Simulation (AK-MCS) to efficiently estimate the probability of exceeding limit states. This method adaptively constructs and updates a surrogate model by strategically adding calculation points. Since its inception, numerous studies have enhanced AK-MCS, including improvements to its learning functions (LFs), which determine the additional points for improved surrogate accuracy. Moustapha et al. (2022) reviewed these advancements and emphasized the importance of considering the input Probability Density Function (PDF) when designing LFs. In this study, we propose a novel LF that incorporates probability density, prioritizing sampling near critical design points. We evaluate its performance against the traditional LF, renowned for its accuracy, using a simplified benchmark problem. The analysis focuses on two key criteria: learning speed and the confidence interval of the estimated probability of limit state exceedance. The latter is crucial for establishing effective stopping rules in active learning. By comparing these LFs, we aim to provide insights that support the development of active learning and surrogate modeling techniques, particularly for geotechnical engineering applications.

Keywords: Adaptive surrogate model, Reliability analysis, Learning function, Gaussian progress regression.