Kriging-Aided Cross-Entropy-Based Adaptive Importance Sampling Using Gaussian Mixture

Abstract

In the reliability analysis, rare-event probability estimation imposes serious difficulties on conventional simulation methods like crude Monte Carlo. Several advanced variance reduction techniques such as importance sampling and importance splitting are presented to address this issue. Even though these methods require a low number of samples compared with crude Monte Carlo of the same accuracy, their implementation on time-consuming simulation codes is still very demanding. A joint employment of sampling methods and surrogate models is a proper solution. In this study, we integrate the Kriging surrogate model with a cross-entropy-based adaptive importance sampling, which uses the Gaussian mixture as the auxiliary sampling function. The novelty resides in efficient integration of the importance sampling and Kriging model. Results of various presented tests show a remarkable improvement with respect to importance sampling without surrogate. The statistical analysis results reveal that this advantage is achievable without any significant loss of accuracy.