Copula-based methods for global sensitivity analysis with correlated random variables and stochastic processes under incomplete probability information

Song, Shiji; Bai, Zhiwei; Wei, Hongkui; Xiao, Yingying

doi:10.1016/j.ast.2022.107811

Cited by 5 publications

(4 citation statements)

References 28 publications

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“…The idea of generating correlated samples by Copula functions is that they can be used to approximate the true joint CDF. 52 To achieve this goal, Vine Copula is firstly used to decompose the joint PDF of input variables into a series of pair-Copula and a product of marginal PDFs. After the joint PDF are decomposed, it is necessary to infer the optimal bivariate Copula function.…”

Section: Gsa Based On Sp Considering Correlationmentioning

confidence: 99%

“…Then these random samples are in conjunction with two SPM to compute Sobol indices. The idea of generating correlated samples by Copula functions is that they can be used to approximate the true joint CDF 52 . To achieve this goal, Vine Copula is firstly used to decompose the joint PDF of input variables into a series of pair‐Copula and a product of marginal PDFs.…”

Section: Gsa Based On Space Partition Considering Correlationmentioning

confidence: 99%

“…51 A Sobol index was derived which can describe the correlation between binary input variables by Copula, but its analysis of the correlation among multidimensional variables still has limitations. 52 Furthermore, the aforementioned Copula based methods require that the correlations among different variables follow the same Copula function. Currently, deterministic analysis of aero-disk typically focuses on the entire structure rather than hazardous regions, leading to a decrease in the accuracy of deterministic analysis.…”

Section: Introductionmentioning

confidence: 99%

“…proposed a Copula‐based uncertainty growth method which enables accurate growth analysis of uncertainties through correlated parameter p ‐boxes 51 . A Sobol index was derived which can describe the correlation between binary input variables by Copula, but its analysis of the correlation among multidimensional variables still has limitations 52 . Furthermore, the aforementioned Copula based methods require that the correlations among different variables follow the same Copula function.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fatigue reliability and sensitivity analysis of aero‐disk considering correlation

Di,

Li,

Nan

et al. 2024

Quality & Reliability Eng

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Aero‐disk is a key component of aero‐engine. Due to its complex working conditions, aero‐disk is prone to structural failures. Therefore, it is essential to analyze the reliability and importance input variables of aero‐disk. In this paper, a framework of aero‐disk reliability analysis and global sensitivity analysis (GSA) was established. First, the hazardous regions of aero‐disk were determined by finite element analysis, and the limit state function of aero‐disk was defined by the life interference model. Then D‐Vine model was utilized to establish the correlation model for aero‐disk hazardous regions to evaluate the reliability of aero‐disk. In addition, two GSA methods based on Copula and space partition were proposed to identify important input random variables considering underlying correlation, and the accuracy of the proposed method was verified by two examples. Finally, the proposed method was applied to the GSA of aero‐disk. The results show that the established framework fills in the gap of uncertainty analysis of aero‐disk, which can be extended to other engineering fields. The proposed GSA methods have both high efficiency and accuracy and can realize multi‐dimensional GSA when the correlation of input variables is considered.

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Section: Gsa Based On Sp Considering Correlationmentioning

confidence: 99%

Section: Gsa Based On Space Partition Considering Correlationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fatigue reliability and sensitivity analysis of aero‐disk considering correlation

Di,

Li,

Nan

et al. 2024

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

A bivariate dependent degradation model based on artificial neural network supported stochastic process and Copula function

Liu,

Duan,

Wang

et al. 2024

Quality & Reliability Eng

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In order to use the high ability of the artificial neural network (ANN) in data fitting, this paper introduces an ANN in stochastic process to describe the mean function for degradation modeling. Due to the fact that the existing method cannot handle the bivariate dependent degradation conditions, a bivariate dependent degradation model based on Copula function and ANN‐supported stochastic processes is proposed. Considering the random effects caused by individual difference, it is assumed that the unknown parameters in the stochastic processes and Copula functions are randomly distributed. Based on the maximum likelihood and moment estimation methods, a related statistical inference method for ANN training and parameter estimation is developed to use the bivariate dependent degradation model. An actual fatigue crack dataset is used to demonstrate the validity of the proposed method. The obtained results show that the dependent relationship between two degradation indicators should not be neglected, and it can be efficiently handled by the proposed method. Furthermore, the proposed degradation model can provide reliability and degradation intervals with enough precision due to the fact that it considers the random effects caused by individual difference.

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Aerospace structural reliability analysis method based on regular vine copula model with the asymmetric tail correlation

LIU,

LAI,

Wang

et al. 2023

Aerospace Science and Technology

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Copula-based methods for global sensitivity analysis with correlated random variables and stochastic processes under incomplete probability information

Cited by 5 publications

References 28 publications

Fatigue reliability and sensitivity analysis of aero‐disk considering correlation

Fatigue reliability and sensitivity analysis of aero‐disk considering correlation

A bivariate dependent degradation model based on artificial neural network supported stochastic process and Copula function

Aerospace structural reliability analysis method based on regular vine copula model with the asymmetric tail correlation

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