Kriging-based adaptive Importance Sampling algorithms for rare event estimation

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 diff...

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Vydáno v:	Structural safety Ročník 44; s. 1 - 10
Hlavní autoři:	Balesdent, Mathieu, Morio, Jérôme, Marzat, Julien
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier Ltd 01.09.2013 Elsevier
Témata:	Algorithms Applied sciences Computer simulation Estimates Exact sciences and technology Ground, air and sea transportation, marine construction Importance Sampling Input–output function Kriging Marine construction Rare event estimation Samples Sampling Statistical analysis Statistical methods Surrogate model Surrogate model Importance Sampling Input–output function Kriging Rare event estimation Estimation Aeronautics Spacecraft Probability Input-output function Rare event Modeling Adaptive method Statistics Case study Input output analysis Launching Safety Sampling
ISSN:	0167-4730, 1879-3355
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Abstract	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. •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.
AbstractList	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 10a3) 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. 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. •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.
Author	Morio, Jérôme Balesdent, Mathieu Marzat, Julien
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Keywords	Surrogate model Importance Sampling Input–output function Kriging Rare event estimation Estimation Aeronautics Spacecraft Probability Input-output function Rare event Modeling Adaptive method Statistics Case study Input output analysis Launching Safety Sampling
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Snippet	Very efficient sampling algorithms have been proposed to estimate rare event probabilities, such as Importance Sampling or Importance Splitting. Even if the...
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SubjectTerms	Algorithms Applied sciences Computer simulation Estimates Exact sciences and technology Ground, air and sea transportation, marine construction Importance Sampling Input–output function Kriging Marine construction Rare event estimation Samples Sampling Statistical analysis Statistical methods Surrogate model
Title	Kriging-based adaptive Importance Sampling algorithms for rare event estimation
URI	https://dx.doi.org/10.1016/j.strusafe.2013.04.001 https://www.proquest.com/docview/1500783343 https://www.proquest.com/docview/1753553148
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