Estimation of Limit State Probabilities of Consolidation Settlement by Adaptive Gaussian Process Regression and Importance Sampling

Many methods based on Monte Carlo simulation (MCS) have been studied and developed for calculating small limit state probabilities efficiently. Recently reliability estimation methods with surrogate model have attracted attention due to their low calculation cost. Since Echard et al. proposed active learning method combining kriging and MCS (AK-MCS) in 2011, many papers have been published on the improvement of this method. AK-MCS uses surrogate models by kriging to evaluate not only the estimated values but also their uncertainties. In this study, we use the Gaussian process regression with multiple random as a surrogate model and importance sampling without design points to calculate the limit state probability as the reliability estimation method. Finally, as an example of the application, we show the results of estimating the limit state probability using the proposed method for an eight-dimensional consolidation settlement problem.