Structural reliability assessment using Kriging metamodel and Monte Carlo simulation: AK-MCS method

Summary This article presents an approach to build a multifidelity kriging metamodel from finite element computations on different meshes for stuctural reliability assessment. The proposed method takes advantage of the computation of bounds on the discretization error, which enables to guarantee the state (safe or failure) of each computation of the performance function. An algorithm to build the metamodel from the different levels of fidelity and estimate the failure probability is provided. Illustrations are presented on a two dimensional mechanical crack opening problem. Bounds on the failure probability are also post‐processed.

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“…Therefore, the metamodel can be improved by adding observations on points corresponding to large uncertainty on

ĝ

. This strategy is developed for reliability analysis in Reference 44 where the learning function chosen for enrichment is:

\underline{x} \to U (\underline{x}) = \frac{| ĝ (\underline{x}) |}{s_{ĝ}^{2} (\underline{x})} .

…”

Section: Multifidelity Kriging For Reliability Analysismentioning

confidence: 99%

Multifidelity adaptive kriging metamodel based on discretization error bounds

Mell

Rey

Schoefs

2020

Numerical Meth Engineering

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“…Echard et al [26] combined the kriging model and the MCS method and proposed an AK-MCS method; the high accuracy of the proposed method is demonstrated by several examples. Other studies on the kriging model can be found in [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Reliability Analysis Method Combining Improved EIF Active Learning Mechanism and Kriging Metamodel

Zhang

et al. 2018

Mathematical Problems in Engineering

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Complex implicit performance functions widely exist in many engineering problems. The reliability analysis of these problems has always been a challenge. Using surrogate model instead of real performance function is one of the methods to solve this kind of problem. Kriging is one of the surrogate models with precise interpolation technique. In order to make the kriging model achieve higher accuracy using a small number of samples, i.e., improve its practicability and feasibility in practical engineering problems, some active learning equations are wildly studied. Expected improvement function (EIF) is one of them. However, the EIF has a great disadvantage in selecting the added sample point. Therefore, a joint active learning mechanism, J-EIF, is proposed to obtain the ideal added point. The J-EIF active learning mechanism combines the two active learning mechanisms and makes full use of the characters of kriging model. It overcomes the shortcoming of EIF active learning mechanism in the selection of added sample points. Then, using Monte Carlo Simulation (MCS) results as a reference, the reliability of two examples is estimated. The results are discussed showing that the learning efficiency and accuracy of the improved EIF are both higher than those of the traditional EIF.

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“…Several kinds of surrogate meta-models have been developed, including polynomial response surface (Rajashekhar et al, 1993;Zheng et al, 2000), Kriging meta-modeling (Kaymaz, 2005;Echard et al, 2009;Echard et al, 2010), Gaussian meta-models (Marrel et al, 2009), artificial neural networks (Papadrakakis et al, 1996;Elhewy et al, 2006;Cheng et al, 2008), radial basis functions and support vector machines (Hurtado, 2007;Li et al, 2010). Even if Monte Carlo methods are universal, they are time computing expansive and sometimes impossible to use.…”

Section: Introductionmentioning

confidence: 99%

“…Besides, the model function is typically chosen to be firstor second-order polynomials which is likely awkward when it is used for representing multi-modalities and non-linearity commonly appearing in complex engineering problem (Giunta et al, 1998). Following this classification approach, (Echard et al, 2009;Echard et al, 2010) proposed to used Kriging in reliability analysis (based on the work by (Kaymaz, 2005)). To interpolate the limit-state, an-Downloaded by [UQ Library] at 12:21 04 November 2014 798 European Journal of Computational Mechanics.…”

Section: Introductionmentioning

confidence: 99%

RPCM: a strategy to perform reliability analysis using polynomial chaos and resampling

Notin

Gayton

Dulong

et al. 2010

European Journal of Computational Mechanics

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Using stochastic finite elements, the response quantity can be written as a series expansion which allows an approximation of the limit state function. For computational purpose, the series must be truncated in order to retain only a finite number of terms. In the context of reliability analysis, we propose a new approach coupling polynomial chaos expansions and confidence intervals on the generalized reliability index as truncating criterion.RÉSUMÉ. La méthode des éléments finis stochastiques permet d'exprimer la réponse d'un système sous forme d'une série polynomiale appelée chaos polynomial. Numériquement, cette série doit être tronquée pour ne retenir qu'un nombre fini de termes. Dans le cadre de l'analyse de fiabilité, nous proposons une méthode adaptative utilisant les intervalles de confiance sur l'indice de fiabilité généralisé comme critère de troncature du chaos.

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Structural reliability assessment using Kriging metamodel and Monte Carlo simulation: AK-MCS method

Cited by 3 publications

References 1 publication

Multifidelity adaptive kriging metamodel based on discretization error bounds

Multifidelity adaptive kriging metamodel based on discretization error bounds

An Efficient Reliability Analysis Method Combining Improved EIF Active Learning Mechanism and Kriging Metamodel

RPCM: a strategy to perform reliability analysis using polynomial chaos and resampling

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