Reliability Estimation Method by Adaptive Surrogate Models Using Gaussian Process Regression and Importance Sampling

Abstract

Echard et al. (2011) proposed AK-MCS, which combines a surrogate model and Monte Carlo Simulation, as an efficient method for calculating the probability of exceeding a limit state. Many papers have been published on the application and improvement of this method. Since a large number of particles (samples) are required to calculate small probabilities in MCS, importance sampling method is introduced. Since importance sampling with design points needs a complicated procedure especially when several design points exist, we introduced a simple method without design points. By introducing the importance method, however, the surrogate model of a two-dimensional simple example became unstable. Gaussian process regression with multiple random fields could stabilize the surrogate model. Application of the method is also shown for an eight-dimensional consolidation settlement problem.