A Vine Copula-Based Global Sensitivity Analysis Method for Structures with Multidimensional Dependent Variables

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

doi:10.3390/math9192489

Cited by 7 publications

(4 citation statements)

References 34 publications

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“…In the future, it would be appropriate to expand the combination of the three stochastic differential equations presented in this work to a larger number of variables with the help of the copula function (for example, additionally including the tree crown base height and crown width) using vine copulas and other techniques [4,31].…”

Section: Discussionmentioning

confidence: 99%

On the Construction of Growth Models via Symmetric Copulas and Stochastic Differential Equations

Rupšys

Petrauskas

2022

Symmetry

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By nature, growth regulatory networks in biology are dynamic and stochastic, and feedback regulates their growth function at different ages. In this study, we carried out a stochastic modeling of growth networks and demonstrated this method using three mixed effect four-parameter Gompertz-type diffusion processes and a combination thereof using the conditional normal copula function. Using the conditional normal copula, newly derived univariate distributions can be combined into trivariate and bivariate distributions, and their corresponding conditional bivariate and univariate distributions. The link between the predictor variable and the remaining one or two explanatory variables can be formalized using copula-type densities and a numerical integration procedure. In this study, for parameter estimation, we used a semiparametric maximum pseudo-likelihood estimator procedure, which was characterized by a two-step technique, namely, separately estimating the parameters of the marginal distributions and the parameters of the copula. The results were illustrated using two observed longitudinal datasets, the first of which included the age, diameter, and potentially available area of 39,437 trees (48 stands), while the second included the age, diameter, potentially available area, and height of 8604 trees (47 stands) covering uneven mixed-species (pine, spruce, and birch) stands. All results were implemented using the MAPLE symbolic algebra system.

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Section: Discussionmentioning

confidence: 99%

On the Construction of Growth Models via Symmetric Copulas and Stochastic Differential Equations

Rupšys

Petrauskas

2022

Symmetry

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“…27 This method enables the elimination of weakly correlated variables, thereby achieving a dimension reduction optimization. Bai et al 28 proposed a variance-based global sensitivity analysis (GSA) method based on Vine Copula and derived the primary and total indexes of GSA for addressing the importance of multidimensional variables. In the field of aero-engines, many researchers have also conducted studies on engine structures based on Copula theory.…”

Section: Introductionmentioning

confidence: 99%

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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“…A novel global sensitivity measure, called PAWN, was proposed to efficiently compute density-based sensitivity indices [18]. As for structural engineering, a novel vine copula-based approach for analyzing the variance-based global sensitivity measure is proposed [19]. In reliability engineering, a new reliability-oriented global sensitivity measure, which is obtained by replacing the variance with entropy, was proposed [20].…”

Section: Introductionmentioning

confidence: 99%

Derivative-Variance Hybrid Global Sensitivity Measure with Optimal Sampling Method Selection

Liu,

Zhang

et al. 2024

Mathematics

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This paper proposes a derivative-variance hybrid global sensitivity measure with optimal sampling method selection. The proposed sensitivity measure is as computationally efficient as the derivative-based global sensitivity measure, which also serves as the conservative estimation of the corresponding variance-based global sensitivity measure. Moreover, the optimal sampling method for the proposed sensitivity measure is studied. In search of the optimal sampling method, we investigated the performances of six widely used sampling methods, namely Monte Carlo sampling, Latin hypercube sampling, stratified sampling, Latinized stratified sampling, and quasi-Monte Carlo sampling using the Sobol and Halton sequences. In addition, the proposed sensitivity measure is validated through its application to a rural bridge.

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A Vine Copula-Based Global Sensitivity Analysis Method for Structures with Multidimensional Dependent Variables

Cited by 7 publications

References 34 publications

On the Construction of Growth Models via Symmetric Copulas and Stochastic Differential Equations

On the Construction of Growth Models via Symmetric Copulas and Stochastic Differential Equations

Fatigue reliability and sensitivity analysis of aero‐disk considering correlation

Derivative-Variance Hybrid Global Sensitivity Measure with Optimal Sampling Method Selection

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