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Non-parametric adaptive importance sampling for the probability estimation of a launcher impact position

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  • Morio, Jérôme

Abstract

Importance sampling (IS) is a useful simulation technique to estimate critical probability with a better accuracy than Monte Carlo methods. It consists in generating random weighted samples from an auxiliary distribution rather than the distribution of interest. The crucial part of this algorithm is the choice of an efficient auxiliary PDF that has to be able to simulate more rare random events. The optimisation of this auxiliary distribution is often in practice very difficult. In this article, we propose to approach the IS optimal auxiliary density with non-parametric adaptive importance sampling (NAIS). We apply this technique for the probability estimation of spatial launcher impact position since it has currently become a more and more important issue in the field of aeronautics.

Suggested Citation

  • Morio, Jérôme, 2011. "Non-parametric adaptive importance sampling for the probability estimation of a launcher impact position," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 178-183.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:1:p:178-183
    DOI: 10.1016/j.ress.2010.08.006
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    References listed on IDEAS

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    1. Neddermeyer, Jan C., 2009. "Computationally Efficient Nonparametric Importance Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 788-802.
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    3. Reuven Rubinstein, 1999. "The Cross-Entropy Method for Combinatorial and Continuous Optimization," Methodology and Computing in Applied Probability, Springer, vol. 1(2), pages 127-190, September.
    4. Helton, J.C. & Johnson, J.D. & Sallaberry, C.J. & Storlie, C.B., 2006. "Survey of sampling-based methods for uncertainty and sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1175-1209.
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    6. Stuart Barber, 2005. "All of Statistics: a Concise Course in Statistical Inference," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 261-261, January.
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    Cited by:

    1. Mattrand, C. & Bourinet, J.-M., 2014. "The cross-entropy method for reliability assessment of cracked structures subjected to random Markovian loads," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 171-182.
    2. Chen, Jun-Yu & Feng, Yun-Wen & Teng, Da & Lu, Cheng & Fei, Cheng-Wei, 2022. "Support vector machine-based similarity selection method for structural transient reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    3. Mathieu Balesdent & Jérôme Morio & Loïc Brevault, 2016. "Rare Event Probability Estimation in the Presence of Epistemic Uncertainty on Input Probability Distribution Parameters," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 197-216, March.
    4. Villén-Altamirano, J., 2014. "Asymptotic optimality of RESTART estimators in highly dependable systems," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 115-124.
    5. Vergé, Christelle & Morio, Jérôme & Moral, Pierre Del, 2016. "An island particle algorithm for rare event analysis," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 63-75.
    6. Cao, Quoc Dung & Choe, Youngjun, 2019. "Cross-entropy based importance sampling for stochastic simulation models," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    7. J Morio & R Pastel, 2012. "Plug-in estimation of d-dimensional density minimum volume set of a rare event in a complex system," Journal of Risk and Reliability, , vol. 226(3), pages 337-345, June.
    8. Chabridon, Vincent & Balesdent, Mathieu & Bourinet, Jean-Marc & Morio, Jérôme & Gayton, Nicolas, 2018. "Reliability-based sensitivity estimators of rare event probability in the presence of distribution parameter uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 164-178.
    9. El Masri, Maxime & Morio, Jérôme & Simatos, Florian, 2021. "Improvement of the cross-entropy method in high dimension for failure probability estimation through a one-dimensional projection without gradient estimation," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    10. Balesdent, Mathieu & Morio, Jérôme & Marzat, Julien, 2015. "Recommendations for the tuning of rare event probability estimators," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 68-78.
    11. Dai, Hongzhe & Zhang, Hao & Wang, Wei, 2012. "A support vector density-based importance sampling for reliability assessment," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 86-93.

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