TY - JOUR

T1 - Reliability analysis with consideration of asymmetrically dependent variables

T2 - Discussion and application to geotechnical examples

AU - Zhang, Yi

AU - Gomes, António Topa

AU - Neumann, Ingo

AU - Beer, Michael

AU - Nackenhorst, Udo

AU - Kim, Chul Woo

N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2018/12/27

Y1 - 2018/12/27

N2 - The consideration of multivariate models in the reliability analysis is quite essential from practical perspective. In principle, complete information regarding the joint probability distribution function should be known in prior to the analysis. However, in real practice, only the marginal distribution and covariance matrix are known in most cases. Such incomplete probabilistic information could lead to dubious results if dependences are not fully catered. Asymmetric dependence is one of these factors influencing the quality of reliability analysis. In this paper, the influences of asymmetric dependences to the reliability problem are investigated. The copula theory as well as the concept of asymmetric dependences is briefly introduced. The techniques of constructing asymmetric copulas are, thereafter, provided in details. Geotechnical problem is selected in this study as examples in the reliability analysis. Based on the given information, a group of symmetric and asymmetric copulas are selected to model the dependences between cohesion and friction angle, the parameters more commonly used to characterize soil strength. The reliability analysis of a continuous spread footing and an infinite slope are then presented to demonstrate the influence of asymmetric dependences on reliability. The results showed that the failure probabilities of the investigated geotechnical problems are very sensitive to the adopted dependence structure, either symmetrically or asymmetrically. The commonly applied one parameter symmetric copulas, such as Archimedean copulas, may underestimate the failure probabilities. Furthermore, the asymmetric copulas are more powerful in characterizing the tail dependences structures of variables especially for asymmetric dependent variables.

AB - The consideration of multivariate models in the reliability analysis is quite essential from practical perspective. In principle, complete information regarding the joint probability distribution function should be known in prior to the analysis. However, in real practice, only the marginal distribution and covariance matrix are known in most cases. Such incomplete probabilistic information could lead to dubious results if dependences are not fully catered. Asymmetric dependence is one of these factors influencing the quality of reliability analysis. In this paper, the influences of asymmetric dependences to the reliability problem are investigated. The copula theory as well as the concept of asymmetric dependences is briefly introduced. The techniques of constructing asymmetric copulas are, thereafter, provided in details. Geotechnical problem is selected in this study as examples in the reliability analysis. Based on the given information, a group of symmetric and asymmetric copulas are selected to model the dependences between cohesion and friction angle, the parameters more commonly used to characterize soil strength. The reliability analysis of a continuous spread footing and an infinite slope are then presented to demonstrate the influence of asymmetric dependences on reliability. The results showed that the failure probabilities of the investigated geotechnical problems are very sensitive to the adopted dependence structure, either symmetrically or asymmetrically. The commonly applied one parameter symmetric copulas, such as Archimedean copulas, may underestimate the failure probabilities. Furthermore, the asymmetric copulas are more powerful in characterizing the tail dependences structures of variables especially for asymmetric dependent variables.

KW - Asymmetric copula

KW - Geotechnical engineering

KW - Joint distribution

KW - Multivariate analysis

KW - Reliability analysis

UR - http://www.scopus.com/inward/record.url?scp=85059230430&partnerID=8YFLogxK

U2 - 10.1016/j.ress.2018.12.025

DO - 10.1016/j.ress.2018.12.025

M3 - Article

AN - SCOPUS:85059230430

VL - 185

SP - 261

EP - 277

JO - Reliability Engineering and System Safety

JF - Reliability Engineering and System Safety

SN - 0951-8320

ER -