Kriging-based adaptive Importance Sampling algorithms for rare event estimation

Balesdent, Mathieu; Mitard, J.; Marzat, Julien

doi:10.1016/j.strusafe.2013.04.001

Cited by 128 publications

(56 citation statements)

References 37 publications

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“…Some available works have investigated the Kriging‐based IS methods . Here, we will discuss the differences between the proposed method and the published studies.…”

Section: The Proposed Iterative Is Methodsmentioning

confidence: 99%

A surrogate‐based iterative importance sampling method for structural reliability analysis

Tang

Xia

2018

Quality & Reliability Eng

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In this paper, a surrogate‐based iterative importance sampling (IS) method is proposed to efficiently evaluate failure probability (FP) of engineering structures. The surrogate is constructed by the training points centered at the most probable failure point (MPP), which is estimated by an approximate algorithm without any additional evaluations of the real limit state function (LSF), and the IS method using the estimated MPP is further obtained; and an iterative procedure combined with the surrogate and the IS method is finally proposed to improve the accuracy of the estimated result for the FP. Three numerical examples are employed to demonstrate the accuracy of the proposed method, and further, an inside flap of an aircraft is employed to demonstrate the practical application of the proposed method in engineering problems. The results show that the reasonable estimated result of the FP within the range of 10−3‐10−5 can be evaluated by the proposed method with only hundreds of the evaluations of the real LSF.

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“…Some available works have investigated the Kriging‐based IS methods . Here, we will discuss the differences between the proposed method and the published studies.…”

Section: The Proposed Iterative Is Methodsmentioning

confidence: 99%

A surrogate‐based iterative importance sampling method for structural reliability analysis

Tang

Xia

2018

Quality & Reliability Eng

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“…This indicator can be directly used to refine the model, i.e., to choose new points to evaluate the real function that allow to improve the accuracy of the model. Kriging has been extensively used with classical Monte Carlo estimator [152], Importance sampling method [145,[153][154][155], importance sampling with control variates [156] or subset simulation [157][158][159]. The way to refine the Kriging model is a key point and different strategies have been proposed [155,160,161] to exploit the complete probabilistic description given by the Kriging to evaluate the minimal number of points on the real expensive input-output function.…”

Section: Use Of Metamodels In Rare Event Probability Estimationmentioning

confidence: 99%

A survey of rare event simulation methods for static input–output models

Mitard

Balesdent

Jacquemart

et al. 2014

Simulation Modelling Practice and Theory

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International audienceCrude Monte-Carlo or quasi Monte-Carlo methods are well suited to characterize events of which associated probabilities are not too low with respect to the simulation budget. For very seldom observed events, such as the collision probability between two aircraft in airspace, these approaches do not lead to accurate results. Indeed, the number of available samples is often insufficient to estimate such low probabilities (at least 10^6 samples are needed to estimate a probability of order 10^-4with 10% relative error with Monte-Carlo simulations). In this article, one reviewed different appropriate techniques to estimate rare event probabilities that require a fewer number of samples. These methods can be divided into four main categories: parameterization techniques of probability density function tails, simulation techniques such as importance sampling or importance splitting, geometric methods to approximate input failure space and finally, surrogate modeling. Each technique is detailed, its advantages and drawbacks are described and a synthesis that aims at giving some clues to the following question is given: “which technique to use for which problem?”

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“…Finally, the decoupled approaches transform the double-loop into a sequence of deterministic problems. A well-known example is sequential optimization and reliability analysis (SORA) proposed in Du and Chen (2004 Balesdent et al (2013). For the specific task of RBDO, conservative surrogate models which rely on Kriging or polynomial response surfaces were considered in Viana et al (2010); Picheny et al (2008).…”

Section: Introductionmentioning

confidence: 99%

Quantile-based optimization under uncertainties using adaptive Kriging surrogate models

Moustapha

Sudret

Bourinet

et al. 2016

Struct Multidisc Optim

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Uncertainties are inherent to real-world systems. Taking them into account is crucial in industrial design problems and this might be achieved through reliability-based design optimization (RBDO) techniques. In this paper, we propose a quantile-based approach to solve RBDO problems. We first transform the safety constraints usually formulated as admissible probabilities of failure into constraints on quantiles of the performance criteria. In this formulation, the quantile level controls the degree of conservatism of the design. Starting with the premise that industrial applications often involve high-fidelity and time-consuming computational models, the proposed approach makes use of Kriging surrogate models (a.k.a. Gaussian process modeling).Thanks to the Kriging variance (a measure of the local accuracy of the surrogate), we derive a procedure with two stages of enrichment of the design of computer experiments (DoE) used to construct the surrogate model. The first stage globally reduces the Kriging epistemic uncertainty and adds points in the vicinity of the limit-state surfaces describing the system performance to be attained. The second stage locally checks, and if necessary, improves the accuracy of the quantiles estimated along the optimization iterations. Applications to three analytical examples and to the optimal design of a car body subsystem (minimal mass under mechanical safety constraints) show the accuracy and the remarkable efficiency brought by the proposed procedure.

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Kriging-based adaptive Importance Sampling algorithms for rare event estimation

Cited by 128 publications

References 37 publications

A surrogate‐based iterative importance sampling method for structural reliability analysis

A surrogate‐based iterative importance sampling method for structural reliability analysis

A survey of rare event simulation methods for static input–output models

Quantile-based optimization under uncertainties using adaptive Kriging surrogate models

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