Some Recent Results in Rare Event Estimation

Caron, Virgile; Guyader, Arnaud; Zuniga, Miguel Munoz; Tuffin, Bruno

doi:10.1051/proc/201444015

Cited by 11 publications

(7 citation statements)

References 45 publications

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“…To reduce this computational burden, one option is to reduce the number of simulations needed by using a variance reduction method. Among variance reduction techniques [3,24], we may think of multilevel splitting techniques [5,14] and of importance sampling techniques [2,13,15,30]. A variance reduction method, inspired from particle filtering can be used on a particular case of PDMP that is a PDMP whithout boundary [28].…”

Section: Accelerate Reliability Assessment By Using Importance Samplingmentioning

confidence: 99%

On the optimal importance process for piecewise deterministic Markov process

Chraibi¹,

Dutfoy²,

Galtier

et al. 2019

ESAIM: PS

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In order to assess the reliability of a complex industrial system by simulation, and in reasonable time, variance reduction methods such as importance sampling can be used. We propose an adaptation of this method for a class of multi-component dynamical systems which are modeled by piecewise deterministic Markovian processes (PDMP). We show how to adapt the importance sampling method to PDMP, by introducing a reference measure on the trajectory space. This reference measure makes it possible to identify the admissible importance processes. Then we derive the characteristics of an optimal importance process, and present a convenient and explicit way to build an importance process based on theses characteristics. A simulation study compares our importance sampling method to the crude Monte-Carlo method on a three-component systems. The variance reduction obtained in the simulation study is quite spectacular.1991 Mathematics Subject Classification. 60K10;90B25;62N05.The dates will be set by the publisher. A model based on a PDMPDue to the complexity of the systems the reliability analysis is often done through an event tree analysis [4] which requires static approximations of the system, and relies on conservative approximations. With the development of computational capacities, it is now possible to consider more accurate tools for reliability

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Section: Accelerate Reliability Assessment By Using Importance Samplingmentioning

confidence: 99%

On the optimal importance process for piecewise deterministic Markov process

Chraibi¹,

Dutfoy²,

Galtier

et al. 2019

ESAIM: PS

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“…Most other studied methods, such as BMC acceleration by statistically ‘learned’ indicator functions, e.g. by Kriging (20) or Support Vector Machines (18) , or recent Particle Algorithms (21) were also considered unappealing for the particular problem at hand, mainly due to their complexity and difficulties due to the high dimensionality and the complexity of Ω that the model in Section 4.2 dictates.…”

Section: Simulation-based Substantiationmentioning

confidence: 99%

Reliability modelling for rotorcraft component fatigue life prediction with assumed usage

2016

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Fatigue life is a random variable. The reliability of a conservative fatigue life prediction for a component in the helicopter dynamic system thus needs to be substantiated. A standard analytical substantiation method uses averaged manoeuvre loads instead of seeing manoeuvre loads as a random variable whose distribution is estimated with limited precision. This simplification may lead to inaccuracies. A new simulation-based method is developed to conservatively predict fatigue life while also accounting for the full random distribution and uncertainty of manoeuvre loads. Both methods fully account for uncertain fatigue strength but assume that the mission profile is known or can at least be conservatively estimated. Simulations under synthetic but realistic engineering conditions demonstrate that both methods may be used for accurate substantiation of conservative fatigue life predictions. The simulations also demonstrate that, under the tested conditions, uncertainties from manoeuvre loads may be neglected in fatigue life substantiations as the resulting error is not significant with respect to uncertainties in component fatigue strength.

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“…with an arbitrary y 0 and π v u defined in (8). For 1 ≤ i ≤ k − 1, we recursively define g(y i+1 |y i 1 ).…”

Section: Notations and Hypothesesmentioning

confidence: 99%

“…Remark 5 In the real case and for A = (a, ∞), the authors of [3] shows that under regularity conditions the resulting relative error of the estimator is proportional to √ n − k n and drops by a factor √ n − k n / √ n with respect to the state independent IS scheme. Slight modification in the extension of g nA allows to prove the strong efficiency of the estimator (18) using arguments from both [2] and [3]; see [8].…”

Section: Adaptive Is Estimator For Rare Event Probabilitymentioning

confidence: 99%

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Importance Sampling for Multi-Constraints Rare Event Probability

Caron

2014

Springer Proceedings in Mathematics &Amp; Statistics

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Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of the optimal density leading to a nearly zero-variance estimator. This paper presents a new way to handle the estimation of the probability of a rare event defined as a finite intersection of subset. We provide a sharp approximation of the density of long runs of a random walk conditioned by multiples constraints, each of them defined by an average of a function of its summands as their number tends to infinity.

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Some Recent Results in Rare Event Estimation

Cited by 11 publications

References 45 publications

On the optimal importance process for piecewise deterministic Markov process

On the optimal importance process for piecewise deterministic Markov process

Reliability modelling for rotorcraft component fatigue life prediction with assumed usage

Importance Sampling for Multi-Constraints Rare Event Probability

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