A hybrid algorithm for reliability analysis combining Kriging and subset simulation importance sampling

Tong, Cao; Sun, ZhengMing; Zhao, Qianli; Wang, Qibin; Wang, Shuang

doi:10.1007/s12206-015-0717-6

Cited by 82 publications

(29 citation statements)

References 26 publications

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“…Furthermore, the majority of methods select one point at a time, which, given the dynamical nature of sequential sampling could either miss important regions of the domain, or slow down convergence. Different strategies to selecting improvement points are presented in [10,[18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Literature Reviewmentioning

confidence: 99%

“…The last major part of all adaptive algorithms is the stopping condition. This ranges from the use of reliability indices [20,22] through error in the estimation of the failure probability [11,18,27,28,30] and forms of measure of the discrepancy between the emulator predictions and code observations [10,19,23,29] to thresholds on the learning function [9,26,31]. Problems with some of these stopping conditions include the fact that they are based on relative error between iterations of the same algorithm, or that they depend on the form of the learning function.…”

Section: Literature Reviewmentioning

confidence: 99%

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Adaptive Gaussian process emulators for efficient reliability analysis

Hristov¹,

DiazDelaO²,

Farooq³

et al. 2019

Applied Mathematical Modelling

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ReuseThis article is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs (CC BY-NC-ND) licence. This licence only allows you to download this work and share it with others as long as you credit the authors, but you can't change the article in any way or use it commercially. More information and the full terms of the licence here: https://creativecommons.org/licenses/ TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. AbstractThis paper presents an approximation method for performing efficient reliability analysis with complex computer models. The computational cost of industrial-scale models causes problems when performing sampling-based reliability analysis. This is due to the fact that the failure modes of the system typically occupy a small region of the performance space and thus require relatively large sample sizes to accurately estimate 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 as an integral part of the algorithm to efficiently populate those regions of the surrogate which are likely to lead to the performance function exceeding a predefined critical threshold. The emulator itself is used to inform decisions about efficiently using the original code to augment its predictions. The iterative nature of the method ensures that an arbitrarily accurate approximation of the failure region is developed at a reasonable computational cost. The presented method is applied to an industrial model of a biodiesel filter.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Adaptive Gaussian process emulators for efficient reliability analysis

Hristov¹,

DiazDelaO²,

Farooq³

et al. 2019

Applied Mathematical Modelling

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“…Balesdent [11] developed an adaptive importance sampling method based on Kriging when event probability estimation is rare. Tong [12] proposed a hybrid adaptive method by combining subset simulation and Kriging. In recent years, most studies concentrate more on how to apply Kriging model develped by Lophaven [13] In this paper, to reduce the number of calls to the expensive performance function, a hybrid algorithm for the calculation of reliability is presented.…”

Section: Introductionmentioning

confidence: 99%

A hybrid reliability algorithm using PSO-optimized Kriging model and adaptive importance sampling

Tong

Gong

2018

IOP Conf. Ser.: Earth Environ. Sci.

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Abstract. This paper aims to reduce the computational cost of reliability analysis. A new hybrid algorithm is proposed based on PSO-optimized Kriging model and adaptive importance sampling method. Firstly, the particle swarm optimization algorithm (PSO) is used to optimize the parameters of Kriging model. A typical function is fitted to validate improvement by comparing results of PSO-optimized Kriging model with those of the original Kriging model. Secondly, a hybrid algorithm for reliability analysis combined optimized Kriging model and adaptive importance sampling is proposed. Two cases from literatures are given to validate the efficiency and correctness. The proposed method is proved to be more efficient due to its application of small number of sample points according to comparison results. IntroductionIn recent years, the first-order reliability method (FORM) or the second-order reliability method (SORM) 5-6 is often applied to calculating the reliability, but the accuracy of the estimated reliability is very low because FORM and SORM are based on Taylor expansion, which ignores higher order terms. It is well known that the Monte Carlo simulation (MCS) is a widely accepted and robust method, but it is impossible to calculate the reliability with a great many samples in a short time. Especially, in case that the performance function is a complicated and time-consuming process.To reduce computations of the expensive performance function, the Kriging surrogate model been used to deal with this issue for many years. Romero [4], the first researcher applied Kriging on structural reliability problems, compared Kriging with polynomial regression and finite-element interpolation by the Latin hypercube sampling method. Kaymaz [5] calculate structural reliability based on Bucher's design and central composite design, and compared Kriging model method with classic response surface method. Choi [6] proposed an Bayesian reliability algorithm based on the Kriging dimension reduction method. Echard [7] proposed an active learning function for updating the design of experiment (DoE) base on Kriging, and compared it with other metamodels [8]. Dubourg [9] developed a hybrid algorithm based on Kriging model to solve reliability-based design optimization (RBDO). Zhang [10] used Kriging model for geotechnical reliability ansys. Balesdent [11] developed an adaptive importance sampling method based on Kriging when event probability estimation is rare. Tong [12] proposed a hybrid adaptive method by combining subset simulation and Kriging. In recent years, most studies concentrate more on how to apply Kriging model develped by Lophaven [13] to the structural reliability. However, study finds the solution of Kriging model developed by Lophaven is greatly affected by the given initial value  , and the pattern search method by Lophaven may lead

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“…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]. 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.…”

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%

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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A hybrid algorithm for reliability analysis combining Kriging and subset simulation importance sampling

Cited by 82 publications

References 26 publications

Adaptive Gaussian process emulators for efficient reliability analysis

Adaptive Gaussian process emulators for efficient reliability analysis

A hybrid reliability algorithm using PSO-optimized Kriging model and adaptive importance sampling

Adaptive Emulation-Based Reliability Analysis

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