A non-parametric copula approach to dependence modelling of shear strength parameters and its implications for geotechnical reliability under incomplete probability information
This paper aims to evaluate the potential of the non-parametric copula approach to dependence modelling of shear strength parameters and address the problem of copula selection for geotechnical reliability under incomplete probability information. The optimal non-parametric copula is determined by t...
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| Published in | Computers and geotechnics Vol. 116; p. 103185 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Elsevier Ltd
01.12.2019
Elsevier BV |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0266-352X 1873-7633 |
| DOI | 10.1016/j.compgeo.2019.103185 |
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| Abstract | This paper aims to evaluate the potential of the non-parametric copula approach to dependence modelling of shear strength parameters and address the problem of copula selection for geotechnical reliability under incomplete probability information. The optimal non-parametric copula is determined by truncating the basis functions in the kernel according to the Akaike information criterion and Bayesian information criterion. The fitting of copulas to the same dataset shows that the non-parametric approach generally gives better copula models. As the non-parametric copula maximizes its relative entropy (Kullback–Leibler divergence) with respect to the independence copula subject to given constraints, the approximated copula should be the best model according to the principle of maximum entropy. The interpretation of the incomplete probability information as constraints on the expectation of a basis function is later provided, and the non-parametric copula approach is applied to solve two geotechnical reliability problems under incomplete probability information. By measuring the relative entropy of the copulas, the best reliability result and reliability-based design under incomplete probability information can be selected. The comparison between the parametric and non-parametric copula shows that the non-parametric copula almost always encodes the minimum dependence information in the context of given probability information. |
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| AbstractList | This paper aims to evaluate the potential of the non-parametric copula approach to dependence modelling of shear strength parameters and address the problem of copula selection for geotechnical reliability under incomplete probability information. The optimal non-parametric copula is determined by truncating the basis functions in the kernel according to the Akaike information criterion and Bayesian information criterion. The fitting of copulas to the same dataset shows that the non-parametric approach generally gives better copula models. As the non-parametric copula maximizes its relative entropy (Kullback–Leibler divergence) with respect to the independence copula subject to given constraints, the approximated copula should be the best model according to the principle of maximum entropy. The interpretation of the incomplete probability information as constraints on the expectation of a basis function is later provided, and the non-parametric copula approach is applied to solve two geotechnical reliability problems under incomplete probability information. By measuring the relative entropy of the copulas, the best reliability result and reliability-based design under incomplete probability information can be selected. The comparison between the parametric and non-parametric copula shows that the non-parametric copula almost always encodes the minimum dependence information in the context of given probability information. |
| ArticleNumber | 103185 |
| Author | Wang, Fan Li, Heng |
| Author_xml | – sequence: 1 givenname: Fan orcidid: 0000-0002-6335-600X surname: Wang fullname: Wang, Fan email: fan.v.wang@polyu.edu.hk – sequence: 2 givenname: Heng orcidid: 0000-0002-3187-9041 surname: Li fullname: Li, Heng |
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| CitedBy_id | crossref_primary_10_1007_s10064_020_01976_8 crossref_primary_10_1007_s00477_024_02789_x crossref_primary_10_1016_j_asoc_2021_107524 crossref_primary_10_1016_j_compgeo_2024_106530 crossref_primary_10_1016_j_compgeo_2024_106451 crossref_primary_10_1016_j_geoen_2024_213085 crossref_primary_10_1016_j_measurement_2021_109652 crossref_primary_10_1016_j_oceaneng_2023_114067 crossref_primary_10_1002_nag_3966 crossref_primary_10_1061_JENMDT_EMENG_7455 crossref_primary_10_1080_17499518_2023_2272986 crossref_primary_10_1061_AJRUA6_RUENG_1064 |
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| Keywords | Shear strength parameters Non-parametric copula approach Principle of maximum entropy Reliability Incomplete probability information |
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| Snippet | This paper aims to evaluate the potential of the non-parametric copula approach to dependence modelling of shear strength parameters and address the problem of... |
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| SubjectTerms | Basis functions Bayesian analysis Criteria Dependence Divergence Entropy Geotechnical engineering Incomplete probability information Mathematical models Maximum entropy Modelling Non-parametric copula approach Nonparametric statistics Parameters Principle of maximum entropy Probability theory Reliability Reliability analysis Shear strength Shear strength parameters |
| Title | A non-parametric copula approach to dependence modelling of shear strength parameters and its implications for geotechnical reliability under incomplete probability information |
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