A copula-based uncertainty propagation method for structures with correlated parametric p-boxes

Li, Haibo; Chen, Ming; Du, Chunyu; Tang, Jiachang; Fu, Chunming; She, Gui-Lin

doi:10.1016/j.ijar.2021.08.002

Cited by 11 publications

(4 citation statements)

References 58 publications

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“…The non-negativity constraints (10), which are obviously required for p to be a probability mass function, are sometimes already implied by the general constraints ( 9), especially when the singletons are contained in E . However, this is not necessarily the case.…”

Section: Computation Of Extreme Points and Their Normal Conesmentioning

confidence: 99%

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A complete characterization of normal cones and extreme points for p-boxes

Škulj

2023

Fuzzy Sets and Systems

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Section: Computation Of Extreme Points and Their Normal Conesmentioning

confidence: 99%

“…Their applications include engineering [2,7], modeling risk and uncertainty [20,28], reliability [21], dynamical processes [6] and other fields. Recently, bivariate and multivariate generalizations have been proposed and related to imprecise copulas [5,10,[15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

A complete characterization of normal cones and extreme points for p-boxes

Škulj

2023

Fuzzy Sets and Systems

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“…50 Liu et al 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%

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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“…Their applications include engineering [5], modelling of risk and uncertainty [18], reliability [19]. Recently, bivariate and multivariate generalizations have been proposed and related to imprecise copulas [4,8,13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

A complete characterization of normal cones and extreme points for $p$-boxes

Škulj¹

2022

Preprint

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Probability boxes, also known as p-boxes, correspond to sets of probability distributions bounded by a pair of distribution functions. They fall into the class of models known as imprecise probabilities. One of the central questions related to imprecise probabilities are the intervals of values corresponding to expectations of random variables, and especially the interval bounds. In general, those are attained in extremal points of credal sets, which denote convex sets of compatible probabilistic models. The aim of this paper is a characterization and identification of extreme points corresponding to p-boxes on finite domains. To accomplish this, we utilize the concept of normal cones. In the settings of imprecise probabilities, those correspond to sets of random variables whose extremal expectations are attained in a common extreme point. Our main results include a characterization all possible normal cones of p-boxes, their relation with extreme points, and the identification of adjacency structure on the collection of normal cones, closely related to the adjacency structure in the set of extreme points.

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A copula-based uncertainty propagation method for structures with correlated parametric p-boxes

Cited by 11 publications

References 58 publications

A complete characterization of normal cones and extreme points for p-boxes

A complete characterization of normal cones and extreme points for p-boxes

Fatigue reliability and sensitivity analysis of aero‐disk considering correlation

A complete characterization of normal cones and extreme points for $p$-boxes

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