AK-MCSi: A Kriging-based method to deal with small failure probabilities and time-consuming models

Lelièvre, Nicolas; Beaurepaire, Pierre; Mattrand, Cécile; Gayton, Nicolas

doi:10.1016/j.strusafe.2018.01.002

Cited by 170 publications

(62 citation statements)

References 33 publications

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“…e second example is a multidimensional performance function, which is a classic illustration in [13,25]. e explicit expression of the performance function is given as…”

Section: Case 2 (Multidimensional Performance Function)mentioning

confidence: 99%

“…When |y| ≤ Δy, g(x) ≤ 0, and then the gear is in the failure state. It is known from Section 5.1 that y(t) is an implicit response and needs to be obtained by solving equation (25) with the fourth-order Runge-Kutta numerical integration method, so the performance function g(x) is also an implicit response as well, and each calculation of the gear performance function requires about 7.260 seconds (i3 cpu). Furthermore, the response of the gear performance function is highly nonlinear.…”

Section: Limit State Function Of Gear Vibrationmentioning

confidence: 99%

“…is stopping criterion is too rough and not rigorous. In order to more accurately predict the sign of all sampling points, a stopping criterion considering global samples is presented in the literature [25], namely,…”

mentioning

confidence: 99%

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A Kriging‐Based Active Learning Algorithm for Mechanical Reliability Analysis with Time‐Consuming and Nonlinear Response

Tong

Wang

Liu

2019

Mathematical Problems in Engineering

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When the reliability analysis of the mechanical products with high nonlinearity and time-consuming response is carried out, there will be the problems of low precision and huge computation using the traditional reliability methods. To solve these issues, the active learning reliability methods have been paid much attention in recent years. It is the key to choose an efficient learning function (such as U, EFF, and ERF). The aim of this study is to further decrease the computation and improve the accuracy of the reliability analysis. Inspired from these learning functions, a new point-selected learning function (called HPF) is proposed to update DOE, and a new point is sequentially added step by step to the DOE. The proposed learning function can consider the features like the sampling density, the probability to be wrongly predicted, and the local and global uncertainty close to the limit state. Based on the stochastic property of the Kriging model, the analytic expression of HPF is deduced by averaging a hybrid indicator throughout the real space. The efficiency of the proposed method is validated by two explicit examples. Finally, the proposed method is applied to the mechanical reliability analysis (involving time-consuming and nonlinear response). By comparing with traditional mechanical reliability methods, the results show that the proposed method can solve the problems of large computation and low precision.

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“…e second example is a multidimensional performance function, which is a classic illustration in [13,25]. e explicit expression of the performance function is given as…”

Section: Case 2 (Multidimensional Performance Function)mentioning

confidence: 99%

Section: Limit State Function Of Gear Vibrationmentioning

confidence: 99%

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A Kriging‐Based Active Learning Algorithm for Mechanical Reliability Analysis with Time‐Consuming and Nonlinear Response

Tong

Wang

Liu

2019

Mathematical Problems in Engineering

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“…Several algorithms have been proposed to deal with very small failure probabilities (10 −5 −10 −9 ) and multiple failure regions: Meta‐IS, MetaAK‐IS 2 , BSS, ASVR, 2 SMART, AK‐MCSi, GPSS, AK‐MCS‐IS, S4IS, and SS‐KK . Some other methods such as SORM or AK‐IS are suitable for very small failure probabilities, but rely on the existence of an assumed unique so‐called most probable failure point.…”

Section: Introductionmentioning

confidence: 99%

Efficient estimation of extreme quantiles using adaptive kriging and importance sampling

Razaaly

Crommelin

Congedo

2020

Numerical Meth Engineering

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SUMMARY This study considers an efficient method for the estimation of quantiles associated to very small levels of probability (up to O(10−9)), where the scalar performance function J is complex (eg, output of an expensive‐to‐run finite element model), under a probability measure that can be recast as a multivariate standard Gaussian law using an isoprobabilistic transformation. A surrogate‐based approach (Gaussian Processes) combined with adaptive experimental designs allows to iteratively increase the accuracy of the surrogate while keeping the overall number of J evaluations low. Direct use of Monte‐Carlo simulation even on the surrogate model being too expensive, the key idea consists in using an importance sampling method based on an isotropic‐centered Gaussian with large standard deviation permitting a cheap estimation of small quantiles based on the surrogate model. Similar to AK‐MCS as presented in the work of Schöbi et al., (2016), the surrogate is adaptively refined using a parallel infill criterion of an algorithm suitable for very small failure probability estimation. Additionally, a multi‐quantile selection approach is developed, allowing to further exploit high‐performance computing architectures. We illustrate the performances of the proposed method on several two to eight‐dimensional cases. Accurate results are obtained with less than 100 evaluations of J on the considered benchmark cases.

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“…al [21]. Other methods have also been presented to address specific problems such as small failure probabilities (rare events) estimations [3,22,23,24,25,7,26] , multiple failure regions problems [27,28,29,30] or systems failure probabilities assessment [6,31,5,2,9,32].…”

Section: Introductionmentioning

confidence: 99%

Adaptive coupling of reduced basis modeling and Kriging based active learning methods for reliability analyses

Menz

Gogu

Dubreuil

et al. 2020

Reliability Engineering & System Safety

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Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive. Hence, advanced methods are required to reduce the number of calls to the expensive computer codes. Adaptive sampling based reliability analysis methods are one promising way to reduce computational costs. Reduced order modelling is another one. In order to further reduce the numerical costs of Kriging based adaptive sampling approaches, the idea developed in this paper consists in coupling both approaches by adaptively deciding whether to use reduced-basis solutions in place of full numerical solutions whenever the performance function needs to be assessed. Thus, a method combining such adaptive sampling based reliability analyses and reduced basis modeling is proposed using on an efficient coupling criterion. The proposed method enabled significant computational cost reductions, while ensuring accurate estimations of failure probabilities.

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AK-MCSi: A Kriging-based method to deal with small failure probabilities and time-consuming models

Cited by 170 publications

References 33 publications

A Kriging‐Based Active Learning Algorithm for Mechanical Reliability Analysis with Time‐Consuming and Nonlinear Response

A Kriging‐Based Active Learning Algorithm for Mechanical Reliability Analysis with Time‐Consuming and Nonlinear Response

Efficient estimation of extreme quantiles using adaptive kriging and importance sampling

Adaptive coupling of reduced basis modeling and Kriging based active learning methods for reliability analyses

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