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

Mitard, J.

doi:10.1016/j.ress.2010.08.006

Cited by 29 publications

(4 citation statements)

References 13 publications

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“…23,24 AIS, in contrast, adaptively modifies the importance function using already generated samples to reduce the variance of the importance weights. 25,26 Despite their advantages, these MC-based methods require an initial assumption about the sample distribution. 27 This requirement poses challenges in practical engineering applications, especially in safety-critical systems such as nuclear power plants, aerospace systems, and medical devices.…”

Section: Pn Computation Algorithmmentioning

confidence: 99%

“…AMCMC, an advanced version of traditional MCMC, employs an adaptive mechanism to adjust the proposal distribution based on the chain's history, thereby enhancing the efficiency of the sampling process 23,24 . AIS, in contrast, adaptively modifies the importance function using already generated samples to reduce the variance of the importance weights 25,26 …”

Section: Introductionmentioning

confidence: 99%

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A reliability evaluation method for complex systems based on the editable GSPN and adaptive Monte Carlo simulation

Zeng,

Sun,

et al. 2023

Systems Engineering

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This paper presents an innovative EGSPN (Editable Generalized Stochastic Petri Net) model, optimizing the size of GSPN (Generalized Stochastic Petri Net) while preserving its core benefits. Specifically, the EGSPN introduces a transition termed “editable transition,” which allows for the establishment of any dynamic logic, thereby circumventing the intricacies associated with the EGSPN model structure. A Monte Carlo (MC) simulation technique is put forth for EGSPN analysis, enhanced by the integration of Sobol sequences with a Bayesian optimizer. This MC simulation approach, unbounded by any specific distribution constraints, exhibits accelerated convergence rates. To address the issue of preset sampling size, an adaptive sampling strategy rooted in confidence intervals has been proposed. By real‐time computation of margin of errors under varying confidence levels, simulations can be halted prior to reaching the preset sampling size. This method strikes a balance between reduced simulation time and maintained accuracy. The applicability and efficacy of the proposed method are further elucidated through a numerical example of a flight control system.

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Section: Pn Computation Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A reliability evaluation method for complex systems based on the editable GSPN and adaptive Monte Carlo simulation

Zeng,

Sun,

et al. 2023

Systems Engineering

View full text Add to dashboard Cite

show abstract

“…At the end of its mission, the rocket booster falls into the sea at some distance of a predicted position. Similar models have already been analyzed in [47]. The launch vehicle stage fall-back is thus modeled as an inputoutput function ϕ with 12 Gaussian inputs X and one output Y ¼ ϕðXÞ, representing the distance between the estimated launch stage fall-back position and the predicted one.…”

Section: Spatial Launch Vehicle Fall-back Safety Zone Estimationmentioning

confidence: 99%

Recommendations for the tuning of rare event probability estimators

Balesdent

Mitard

Marzat

2015

Reliability Engineering & System Safety

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a b s t r a c tBeing able to accurately estimate rare event probabilities is a challenging issue in order to improve the reliability of complex systems. Several powerful methods such as importance sampling, importance splitting or extreme value theory have been proposed in order to reduce the computational cost and to improve the accuracy of extreme probability estimation. However, the performance of these methods is highly correlated with the choice of tuning parameters, which are very difficult to determine. In order to highlight recommended tunings for such methods, an empirical campaign of automatic tuning on a set of representative test cases is conducted for splitting methods. It allows to provide a reduced set of tuning parameters that may lead to the reliable estimation of rare event probability for various problems. The relevance of the obtained result is assessed on a series of real-world aerospace problems.

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“…The principle of this method is to generate samples from an auxiliary density rather than the density of interest. To determine an efficient auxiliary density for minimum density volume set estimation, a nonparametric adaptive importance sampling (NAIS) algorithm that has been presented for probability estimation and recently extended to quantile estimation [17][18][19][20][21] is defined. This paper first reviews the principle of multidimensional density minimum volume set estimations of a given probability with Monte Carlo methods and shows their limitations when considering rare events.…”

Section: Introductionmentioning

confidence: 99%

Plug-in estimation of d-dimensional density minimum volume set of a rare event in a complex system

Mitard

Pastel

2011

Proceedings of the Institution of Mechanical Engineers, Part O:

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International audienceVarious reliability or hedging problems boil down to quantile estimation. However, real-life systems are usually multidimensional and thus often imply multidimensional density minimum volume set estimation which is usually done with Monte Carlo simulations. Increasing safety standards create a need for density minimum volume set estimation with low probability that crude Monte Carlo cannot fulfil. This paper proposes a new importance sampling algorithm that estimates efficiently multidimensional density minimum volume sets for extreme probability. It also presents some numerical results on a simple bidimensional Gaussian case and on a realistic launcher impact safety zone estimation

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

Cited by 29 publications

References 13 publications

A reliability evaluation method for complex systems based on the editable GSPN and adaptive Monte Carlo simulation

A reliability evaluation method for complex systems based on the editable GSPN and adaptive Monte Carlo simulation

Recommendations for the tuning of rare event probability estimators

Plug-in estimation of d-dimensional density minimum volume set of a rare event in a complex system

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