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Reliability analysis with consideration of asymmetrically dependent variables: Discussion and application to geotechnical examples

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  • Zhang, Yi
  • Gomes, António Topa
  • Beer, Michael
  • Neumann, Ingo
  • Nackenhorst, Udo
  • Kim, Chul-Woo

Abstract

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.

Suggested Citation

  • Zhang, Yi & Gomes, António Topa & Beer, Michael & Neumann, Ingo & Nackenhorst, Udo & Kim, Chul-Woo, 2019. "Reliability analysis with consideration of asymmetrically dependent variables: Discussion and application to geotechnical examples," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 261-277.
    • Handle: RePEc:eee:reensy:v:185:y:2019:i:c:p:261-277
    DOI: 10.1016/j.ress.2018.12.025
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    1. Mazo, Gildas & Girard, Stéphane & Forbes, Florence, 2015. "A class of multivariate copulas based on products of bivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 363-376.
    2. Lu, Zhenzhou & Xinyao Li,, 2018. "Failure-mode importance measures in structural system with multiple failure modes and its estimation using copulaAuthor-Name: He, Liangli," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 53-59.
    3. Zhang, Yi, 2018. "Investigating dependencies among oil price and tanker market variables by copula-based multivariate models," Energy, Elsevier, vol. 161(C), pages 435-446.
    4. Trivedi, Pravin K. & Zimmer, David M., 2007. "Copula Modeling: An Introduction for Practitioners," Foundations and Trends(R) in Econometrics, now publishers, vol. 1(1), pages 1-111, April.
    5. Wang, Fan & Li, Heng, 2018. "System reliability under prescribed marginals and correlations: Are we correct about the effect of correlations?," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 94-104.
    6. Charpentier, A. & Fougères, A.-L. & Genest, C. & Nešlehová, J.G., 2014. "Multivariate Archimax copulas," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 118-136.
    7. Wang, Cao & Zhang, Hao & Li, Quanwang, 2017. "Reliability assessment of aging structures subjected to gradual and shock deteriorations," Reliability Engineering and System Safety, Elsevier, vol. 161(C), pages 78-86.
    8. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    9. Yanqin Fan & Andrew J. Patton, 2014. "Copulas in Econometrics," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 179-200, August.
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    4. Alibeikloo, Mehrnaz & Khabbaz, Hadi & Fatahi, Behzad & Le, Thu Minh, 2021. "Reliability Assessment for Time-Dependent Behaviour of Soft Soils Considering Cross Correlation between Visco-Plastic Model Parameters," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    5. Zhao, Tengyuan & Wang, Yu, 2020. "Non-parametric simulation of non-stationary non-gaussian 3D random field samples directly from sparse measurements using signal decomposition and Markov Chain Monte Carlo (MCMC) simulation," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    6. Zarghami, Seyed Ashkan & Dumrak, Jantanee, 2021. "Aleatory uncertainty quantification of project resources and its application to project scheduling," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    7. Ramadhani, Adhitya & Khan, Faisal & Colbourne, Bruce & Ahmed, Salim & Taleb-Berrouane, Mohammed, 2022. "Resilience assessment of offshore structures subjected to ice load considering complex dependencies," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    8. Liu, Fuchao & Wei, Pengfei & Tang, Chenghu & Wang, Pan & Yue, Zhufeng, 2019. "Global sensitivity analysis for multivariate outputs based on multiple response Gaussian process model," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 287-298.

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