Kriging-based adaptive Importance Sampling algorithms for rare event estimation

• Adaptation of Kriging surrogate model to adaptive rare event estimation.
• Definition of confidence interval for the probability estimation.
• The novelty resides in the use of adaptive Importance Sampling and the ability to estimate very rare event probabilities.
• Kriging-based Importance Sampling approach has been illustrated and compared on analytical test-cases from the literature.
• Proposed method is suitable for time-consuming simulation codes.

Very efficient sampling algorithms have been proposed to estimate rare event probabilities, such as Importance Sampling or Importance Splitting. Even if the number of samples required to apply these techniques is relatively low compared to Monte-Carlo simulations of same efficiency, it is often difficult to implement them on time-consuming simulation codes. A joint use of sampling techniques and surrogate models may thus be of use. In this article, we develop a Kriging-based adaptive Importance Sampling approach for rare event probability estimation. The novelty resides in the use of adaptive Importance Sampling and consequently the ability to estimate very rare event probabilities (lower than 10−3) that have not been considered in previous work on similar subjects. The statistical properties of Kriging also make it possible to compute a confidence measure for the resulting estimation. Results on both analytical and engineering test cases show the efficiency of the approach in terms of accuracy and low number of samples.