scholarly journals Importance Sampling Simulations of Markovian Reliability Systems Using Cross-Entropy

2005 ◽  
Vol 134 (1) ◽  
pp. 119-136 ◽  
Author(s):  
Ad Ridder
Keyword(s):  
Importance Sampling ◽  
Cross Entropy ◽  
Reliability Systems

Structural Reliability Analysis With Cross Entropy and Low Discrepancy Sampling Methods

2011 ◽  
Author(s):  
K. Pugazhendhi ◽  
A. K. Dhingra
Keyword(s):  
Monte Carlo ◽  
Importance Sampling ◽  
Structural Reliability ◽  
Sampling Methods ◽  
Reliability Evaluation ◽  
Cross Entropy ◽  
Sampling Density ◽  
Quasi Monte Carlo ◽  
Importance Sampling Techniques ◽  
Optimum Sampling

In recent years quasi Monte-Carlo (QMC) techniques are gaining more popularity for reliability evaluation because of their increased accuracy over traditional Monte-Carlo simulation. A QMC technique like Low Discrepancy Sequence (LDS) combined with importance sampling is shown to be more accurate and robust in the past for the evaluation of structural reliability. However, one of the challenges in using importance sampling techniques to evaluate the structural reliability is to identify the optimum sampling density. In this article, a novel technique based on a combination of cross entropy and low discrepancy sampling methods is used for the evaluation of structural reliability. The proposed technique does not require an apriori knowledge of Most Probable Point of failure (MPP), and succeeds in adaptively identifying the optimum sampling density for the structural reliability evaluation. Several benchmark examples verify that the proposed method is as accurate as the quasi Monte-Carlo technique using low discrepancy sequence with the added advantage of being able to accomplish this without a knowledge of the MPP.

scholarly journals Cross entropy-based importance sampling using Gaussian densities revisited

2019 ◽  
Vol 76 ◽  
pp. 15-27 ◽  
Author(s):  
Sebastian Geyer ◽  
Iason Papaioannou ◽  
Daniel Straub
Keyword(s):  
Importance Sampling ◽  
Cross Entropy

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

2018 ◽  
Vol 43 (S1) ◽  
pp. 81-88
Author(s):  
Moien Barkhori ◽  
Mohsen Ali Shayanfar ◽  
Mohammad Ali Barkhordari ◽  
Taha Bakhshpoori
Keyword(s):  
Importance Sampling ◽  
Gaussian Mixture ◽  
Cross Entropy ◽  
Adaptive Importance Sampling

Improved cross entropy-based importance sampling with a flexible mixture model

2019 ◽  
Vol 191 ◽  
pp. 106564 ◽  
Author(s):  
Iason Papaioannou ◽  
Sebastian Geyer ◽  
Daniel Straub
Keyword(s):  
Mixture Model ◽  
Importance Sampling ◽  
Cross Entropy

scholarly journals A comparison of cross-entropy and variance minimization strategies

2011 ◽  
Vol 48 (A) ◽  
pp. 183-194 ◽  
Author(s):  
Joshua C. C. Chan ◽  
Peter W. Glynn ◽  
Dirk P. Kroese
Keyword(s):  
Importance Sampling ◽  
Rare Event ◽  
Cross Entropy ◽  
Variance Minimization ◽  
Adaptive Importance Sampling ◽  
Estimation Problems ◽  
Sampling Procedures

The variance minimization (VM) and cross-entropy (CE) methods are two versatile adaptive importance sampling procedures that have been successfully applied to a wide variety of difficult rare-event estimation problems. We compare these two methods via various examples where the optimal VM and CE importance densities can be obtained analytically. We find that in the cases studied both VM and CE methods prescribe the same importance sampling parameters, suggesting that the criterion of minimizing the CE distance is very close, if not asymptotically identical, to minimizing the variance of the associated importance sampling estimator.

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