Rare Event Analysis by Monte Carlo Techniques in Static Models

Cancela, Héctor; Khadiri, Mohamed El; Rubino, Gerardo

doi:10.1002/9780470745403.ch7

Cited by 31 publications

(19 citation statements)

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“…This problem is encountered in a wide range of applications such as telecommunications, transportation, energy supply systems, and social networking, among others (Cancela et al, 2009a;Gertsbakh and Shpungin, 2010).…”

Section: Introductionmentioning

confidence: 99%

“…There are many more. Cancela et al (2009a) survey and compare the best available methods so far for large highly-reliable networks. They conclude that one of the best performing methods is that of Hui et al (2005), which combines a cross-entropy technique with the merge process (also called turnip method) described in Gertsbakh and Shpungin (2010).…”

Section: Introductionmentioning

confidence: 99%

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Static Network Reliability Estimation via Generalized Splitting

Botev

L’Ecuyer

Rubino

et al. 2013

INFORMS Journal on Computing

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We propose a novel simulation-based method that exploits a generalized splitting (GS) algorithm to estimate the reliability of a graph (or network), defined here as the probability that a given set of nodes are connected, when each link of the graph is failed with a given (small) probability. For large graphs, in general, computing the exact reliability is an intractable problem and estimating it by standard Monte Carlo methods poses serious difficulties, because the unreliability (one minus the reliability) is often a rare-event probability. We show that the proposed GS algorithm can accurately estimate extremely small unreliabilities and we exhibit large examples where it performs much better than existing approaches. It is also flexible enough to dispense with the frequently made assumption of independent edge failures.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Static Network Reliability Estimation via Generalized Splitting

Botev

L’Ecuyer

Rubino

et al. 2013

INFORMS Journal on Computing

Self Cite

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show abstract

“…Ditlevsen and Madsen [1], also known as static simulation problems or models by some other authors, see e.g. Homem-de-Mello and Rubinstein [2] and Cancela et al [3] and in which time is not an explicit variable. The probability w.r.t.…”

Section: Introductionmentioning

confidence: 99%

Reliability Assessment With Adaptive Surrogates Based on Support Vector Machine Regression

Bourinet¹

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. Reliability assessment in the context of rare failure events still suffers from its computational cost despite some available methods widely accepted by researchers and engineers. Monte Carlo simulation methods even in their most efficient version such as subset simulation often require a large number of samples for an acceptable accuracy on the failure probability of interest. For low to moderately high dimensional problems and under the assumption of a rather smooth limit-state function, surrogate models a.k.a. metamodels or response surfaces represent interesting alternative solutions. This paper presents an adaptive method based on SVM surrogates used in regression. The SVM formulation hinges on the -insensitive loss function and a Gaussian RBF kernel. The key idea of the proposed method is to iteratively construct SVM surrogates which become more accurate as they get closer to the limit-state surface. Subset simulation is applied to the constructed SVM surrogates for assessing probabilities with respect to intermediate threshold values of the LSF and more importantly for generating new training points. The efficiency of the method is tested on several examples featuring various challenges: a parallel system, a highly curved limit-state surface at a single most probable failure point and a smooth high-dimensional limit-state surface with equal curvatures. The paper puts an emphasis on the key role of an optimal selection of SVM surrogate hyperparameters. This is achieved in the present work by minimizing an estimate of the leave-one-out error using the cross-entropy method.652

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“…Among the most prominent ones are conditional Monte Carlo approaches (Cancela and El Khadiri 2003), , Elperin et al 1991, Shpungin 2010, Lomonosov andShpungin 1999), approximate zero-variance importance sampling , and combinations of these, see (Cancela et al 2010). For a survey of some of these methods see (Cancela, El Khadiri, and Rubino 2009).…”

Section: Introductionmentioning

confidence: 99%

Dependent failures in highly reliable static networks

Botev

L’Ecuyer²,

Tuffin³

2012

Proceedings Title: Proceedings of the 2012 Winter Simulation Conference (WSC)

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Static network reliability models typically assume that the failures of their components are independent. This assumption allows for the design of efficient Monte Carlo algorithms that can estimate the network reliability in settings where it is a rare-event probability. Despite this computational benefit, independent component failures is frequently not a realistic modeling assumption for real-life networks. In this article we show how the splitting methods for rare-event simulation can be used to estimate the reliability of a network model that incorporates a realistic dependence structure via the Marshal-Olkin copula.

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Rare Event Analysis by Monte Carlo Techniques in Static Models

Cited by 31 publications

References 0 publications

Static Network Reliability Estimation via Generalized Splitting

Static Network Reliability Estimation via Generalized Splitting

Reliability Assessment With Adaptive Surrogates Based on Support Vector Machine Regression

Dependent failures in highly reliable static networks

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