A coupled subset simulation and active learning kriging reliability analysis method for rare failure events

Ling, Chunyan; Lü, Zhenzhou; Feng, Kaixuan; Zhang, Xiaobo

doi:10.1007/s00158-019-02326-3

Cited by 40 publications

(14 citation statements)

References 38 publications

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“…This approach can be used to derive unbiased estimates for conditional failure probabilities and improve the accuracy of the results. For example, the probability of failure estimated through the AK-SS and the method by Ling et al (Ling et al 2019) are 1.4 × 10 −4 and 1.639 × 10 −4 , which are not close to the one estimated through the pure MCS. This is in part due to the effect of using MCMC to generate samples in the subsets, which requires sophisticated definitions of the proposal (jumping) sampling function.…”

Section: Convergence History For Intermediate Failure Thresholdsmentioning

confidence: 78%

“…This very large number is not computationally feasible to analyze using most regular PCs. The results here are compared with two other subset simulation-based method including AK-SS (Huang et al 2016) and the method proposed by Ling et al (Ling et al 2019), which hereafter is referred to as AK-SS (Ling et al).…”

Section: Convergence History For Intermediate Failure Thresholdsmentioning

confidence: 99%

“…Compared to other Kriging-based subset simulation techniques, e.g., (Huang et al 2016;Ling et al 2019), three major advantages of RASA stand out. First, failure probability analysis using RASA is not hampered by the number of random inputs and the probability of the rare event.…”

Section: Convergence History For Intermediate Failure Thresholdsmentioning

confidence: 99%

“…This feature is unique to RASA and is not present in other methods in the literature. For example, the method proposed by Ling et (Ling et al 2019) neglects the check needed for COV b P ss f . Hence, it can easily lead to high computational demand or a large deviation of the estimated failure probability from the true value if N ss is set inappropriately.…”

Section: Convergence History For Intermediate Failure Thresholdsmentioning

confidence: 99%

See 3 more Smart Citations

Metamodel-based subset simulation adaptable to target computational capacities: the case for high-dimensional and rare event reliability analysis

Wang

Shafieezadeh

2021

Struct Multidisc Optim

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Metamodel-based approaches to reliability analysis, e.g., adaptive Kriging, are computationally challenged by the complexity of reliability problems, thus limiting the application of these methods to problems that are low-dimensional or not rare. Here, we propose a reliability analysis approach via a deep integration of subset simulation and adaptive kriging (RASA) for an unbiased estimation of failure probabilities of high-dimensional or rare event problems. Concepts of conditional failure probability curves and dynamic learning function are introduced to decompose the original problem to subreliability problems and adaptively identify intermediate failure thresholds of limit state functions corresponding to the subreliability problems. The reliability decomposition and the establishment of target intermediate failure thresholds are guided by the available computational capacity, thus, enabling RASA to control the computational cost associated with the estimation of the intermediate failure thresholds in each subset and consequently to analyze the reliability of medium to high-dimensional problems or rare events. Three numerical examples are investigated as benchmark to explore the performance of the proposed method. Results indicate that the proposed method has high accuracy and has the ability to adjust to available computational resources.

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Section: Convergence History For Intermediate Failure Thresholdsmentioning

confidence: 78%

Section: Convergence History For Intermediate Failure Thresholdsmentioning

confidence: 99%

Section: Convergence History For Intermediate Failure Thresholdsmentioning

confidence: 99%

Section: Convergence History For Intermediate Failure Thresholdsmentioning

confidence: 99%

See 2 more Smart Citations

Metamodel-based subset simulation adaptable to target computational capacities: the case for high-dimensional and rare event reliability analysis

Wang

Shafieezadeh

2021

Struct Multidisc Optim

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show abstract

“…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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Efficient adaptive Kriging-based reliability analysis combining new learning function and error-based stopping criterion

Zhou

Cheng

et al. 2020

Struct Multidisc Optim

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A coupled subset simulation and active learning kriging reliability analysis method for rare failure events

Cited by 40 publications

References 38 publications

Metamodel-based subset simulation adaptable to target computational capacities: the case for high-dimensional and rare event reliability analysis

Metamodel-based subset simulation adaptable to target computational capacities: the case for high-dimensional and rare event reliability analysis

Efficient estimation of extreme quantiles using adaptive kriging and importance sampling

Efficient adaptive Kriging-based reliability analysis combining new learning function and error-based stopping criterion

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