Unified reliability analysis by active learning Kriging model combining with random‐set based Monte Carlo simulation method

Yuan, Xufeng; Liu, Yongshou; Gao, Yi

doi:10.1002/nme.5255

Cited by 48 publications

(23 citation statements)

References 40 publications

(111 reference statements)

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“…Based on Karush-Kuhn-Tucher (KKT) [35], Yang et al [28] proposed a KKTO optimization method to make the calculation of random-evidence hybrid failure probability more convenient. The KKTO method is briefly introduced in this subsection and used to reduce the optimization costs caused by a large number of simulations.…”

Section: Kkto Optimization Methodsmentioning

confidence: 99%

“…Simultaneously, the surrogate model established in this paper is directly constructed based on the relationship of inputs and the output responses of the performance function rather than based on the non-probabilistic index, which greatly decreases the difficulty of modeling. Yang et al [28] proved that only a surrogate model that correctly predicts the sign of limit state function can meet the requirements of random-evidence hybrid reliability analysis. Based on this viewpoint, an extreme value symbol theorem and an expected risk function (ERF) [29,30] are introduced to construct an efficient active learning kriging (ALK) model under the framework of random-evidence hybrid reliability analysis.…”

Section: Introductionmentioning

confidence: 99%

“…Based on this viewpoint, an extreme value symbol theorem and an expected risk function (ERF) [29,30] are introduced to construct an efficient active learning kriging (ALK) model under the framework of random-evidence hybrid reliability analysis. In order to screen out those JFEs on which the limit state function is monotone, a Karush-Kuhn-Tucker-based optimization (KKTO) method [28] is used in the proposed method to decrease the optimization burden. Through the above improvements, the computational efficiency and the practicality of CFP will dramatically increase.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Efficient Regional Sensitivity Analysis Method Based on Failure Probability with Hybrid Uncertainty

Zhang

et al. 2018

Energies

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Abstract:The application of reliability sensitivity analysis (RSA) to the high voltage direct current (HVDC) transmission systems is one of the hot topics in the future. A regional RSA method, the contribution to failure probability (CFP) plot, is investigated in this paper. This CFP plot contains both aleatory and epistemic uncertain variables modeled as random variables by probability theory and interval variables by evidence theory, respectively. A surrogate model of second-level limit state function needs to be established for each joint focal element (JFE), which is a time-consuming process. Additionally, an excessive number of Monte Carlo simulations (MCS) and optimizations may exceed the computing power of modern computers. In order to deal with the above problems and further decrease the computational cost, a more effective CFP calculation method under the framework of random-evidence hybrid reliability analysis is proposed. Three important improvements in the proposed method make the calculation of CFP more efficient and easy to implement. Firstly, an active learning kriging (ALK) based on the symbol prediction idea is employed to directly establish a surrogate model rather than a second-level limit state function with fewer function calls, which greatly simplifies construction of the model. Secondly, a random set-based Monte Carlo simulation (RS-MCS) is used to handle the issue of oversized optimization caused by too many JFEs. Thirdly, for further reducing the size of optimizations and improving the efficiency of the CFP calculation, a Karush-Kuhn-Tucker-based optimization (KKTO) method is recommended in the proposed method to solve the extreme value of performance function. A numerical example and an engineering example were studied to verify the accuracy, effectiveness and practicality of the proposed method. It can be seen from the results that regardless of whether it is modeling or computational efficiency, the proposed method is better than the original method.

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Section: Kkto Optimization Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An Efficient Regional Sensitivity Analysis Method Based on Failure Probability with Hybrid Uncertainty

Zhang

et al. 2018

Energies

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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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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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Unified reliability analysis by active learning Kriging model combining with random‐set based Monte Carlo simulation method

Cited by 48 publications

References 40 publications

An Efficient Regional Sensitivity Analysis Method Based on Failure Probability with Hybrid Uncertainty

An Efficient Regional Sensitivity Analysis Method Based on Failure Probability with Hybrid Uncertainty

Adaptive Emulation-Based Reliability Analysis

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

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