A Sequential Kriging reliability analysis method with characteristics of adaptive sampling regions and parallelizability

Pei, Haiqing; Liu, Hai; Yue, Zhufeng

doi:10.1016/j.ress.2016.05.002

Cited by 140 publications

(70 citation statements)

References 21 publications

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“…It is a synthetic function with a random part and an interval part. The random part is very complicated which has four failure regions and has been repeatedly tested in the field of PRA . The interval part is a linear function and the optima occur at the endpoints.…”

Section: Test Examplesmentioning

confidence: 99%

“…This method has also been applied into other kinds of HRA problems, such as the HRA problem with both random variables and hyperellipsoid‐modeled variables, and the HRA problem combining PRA and evidence theory . Actually, in the field of PRA, a variety of approaches based on ALK model have been proposed . ALK‐HRA was proposed based on the works of References .…”

Section: Introductionmentioning

confidence: 99%

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Bounds approximation of limit‐state surface based on active learning Kriging model with truncated candidate region for random‐interval hybrid reliability analysis

Yuan

Wang

et al. 2019

Numerical Meth Engineering

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Summary This article reports a brand‐new methodology based on active learning Kriging model for hybrid reliability analysis (HRA) with both random and interval variables. Unlike probabilistic reliability analysis, the limit state surface (LSS) of HRA is projected into a banded region in the domain of random variables. Only approximating the bounds of the banded region is able to meet the accuracy requirement of HRA. In the proposed methodology, the HRA problem is innovatively transformed into a traditional system reliability analysis (SRA) problem with numerous failure modes. And then a basic idea from the field of SRA is borrowed into HRA, and the so‐called truncated candidate region (TCR) for HRA is proposed. In each iteration, the negligible region which probably does not influence the bounds estimation of failure probability is truncated from the original candidate region, and the optimal training point is chosen from the TCR. After several iterations, the TCR will converge to the true ideal candidate region, that is, the candidate region without the inner part of LSS, and the added training points will be driven to the region around the bounds of LSS. The performance of the proposed method is compared with relevant methods by five case studies.

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Section: Test Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bounds approximation of limit‐state surface based on active learning Kriging model with truncated candidate region for random‐interval hybrid reliability analysis

Yuan

Wang

et al. 2019

Numerical Meth Engineering

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“…They use SUR to select new design points to improve the surrogate. Other methods that use EI or EI-based strategies are [12,13,14]. Other previously used utility functions include, the U-function [13,15], and the improved U-function [16], least improvement function [17] and an unnamed expression in [18].…”

Section: Introductionmentioning

confidence: 99%

“…Other previously used utility functions include, the U-function [13,15], and the improved U-function [16], least improvement function [17] and an unnamed expression in [18]. All approaches based on a utility function, except [14] search the entire input space for a candidate point that maximizes that function and add it to the training plan for the next iteration of the algorithm. Furthermore, many of the aforementioned strategies rely on a pre-generated population of samples (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…These issue are addressed in the present article.The other major part of all adaptive algorithms is the stopping condition. This ranges from the use of reliability indices [7,8] through error in the estimation of the failure probability [5,13,15,16,17] and forms of measure of the discrepancy between the GPE predictions and code observations [4,6,9,18] to thresholds on the learning function [3,12,14]. Most frameworks use some form of statistic related to the surrogate, which, depending on the use and complexity of the problem, could prove insufficiently robust.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Emulation-Based Reliability Analysis

Hristov¹,

DiazDelaO²,

Kubiak³

et al. 2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. This paper presents an approximation method for performing reliability analysis with high fidelity computer codes at a reasonable computational cost. Complex models are common in science and engineering due to their ability to substitute costly and some times infeasible practical experiments. These models, however, suffer from high computational cost. This causes problems when performing sampling -based reliability analysis, since the failure modes of the system typically occupy a small region of the input space and thus relatively large sample sizes are required for the accurate estimation of their characteristics. The sequential sampling method proposed in this article, combines Gaussian process-based optimisation and Subset Simulation. Gaussian process emulators construct a statistical approximation to the output of the original code, which is both affordable to use and has its own measure of predictive uncertainty. Subset Simulation is used to efficiently populate those regions of the initial approximation which are likely to lead to the performance function exceeding a predefined critical threshold. Among all samples, the ones that are likely to contribute most to increasing the quality of the surrogate in the vicinity of the failure regions are selected, using Bayesian optimisation methods. The iterative nature of the method ensures that an arbitrarily accurate approximation of the failure region in performance space is developed at a reasonable computational cost. The presented method is applied to a number of benchmark problems.

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Adaptive Kriging‐based Methods for Failure Probability Evaluation: Focus on AK Methods

Mattrand

Beaurepaire

Gayton

2021

Mechanical Engineering Under Uncertainties

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A Sequential Kriging reliability analysis method with characteristics of adaptive sampling regions and parallelizability

Cited by 140 publications

References 21 publications

Bounds approximation of limit‐state surface based on active learning Kriging model with truncated candidate region for random‐interval hybrid reliability analysis

Bounds approximation of limit‐state surface based on active learning Kriging model with truncated candidate region for random‐interval hybrid reliability analysis

Adaptive Emulation-Based Reliability Analysis

Adaptive Kriging‐based Methods for Failure Probability Evaluation: Focus on AK Methods

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