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Bivariate simulation using copula and its application to probabilistic pile settlement analysis

SUMMARY This paper aims to propose a procedure for modeling the joint probability distribution of bivariate uncertain data with a nonlinear dependence structure. First, the concept of dependence measures is briefly introduced. Then, both the Akaike Information Criterion and the Bayesian Information...

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Published in:International journal for numerical and analytical methods in geomechanics 2013-04, Vol.37 (6), p.597-617
Main Authors: Li, Dian-Qing, Tang, Xiao-Song, Phoon, Kok-Kwang, Chen, Yi-Feng, Zhou, Chuang-Bing
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container_title International journal for numerical and analytical methods in geomechanics
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description SUMMARY This paper aims to propose a procedure for modeling the joint probability distribution of bivariate uncertain data with a nonlinear dependence structure. First, the concept of dependence measures is briefly introduced. Then, both the Akaike Information Criterion and the Bayesian Information Criterion are adopted for identifying the best‐fit copula. Thereafter, simulation of copulas and bivariate distributions based on Monte Carlo simulation are presented. Practical application for serviceability limit state reliability analysis of piles is conducted. Finally, four load–test datasets of load–displacement curves of piles are used to illustrate the proposed procedure. The results indicate that the proposed copula‐based procedure can model and simulate the bivariate probability distribution of two curve‐fitting parameters underlying the load–displacement models of piles in a more general way. The simulated load–displacement curves using the proposed procedure are found to be in good agreement with the measured results. In most cases, the Gaussian copula, often adopted out of expedience without proper validation, is not the best‐fit copula for modeling the dependence structure underlying two curve‐fitting parameters. The conditional probability density functions obtained from the Gaussian copula differ considerably from those obtained from the best‐fit copula. The probabilities of failure associated with the Gaussian copula are significantly smaller than the reference solutions, which are very unconservative for pile safety assessment. If the strong negative correlation between the two curve‐fitting parameters is ignored, the scatter in the measured load–displacement curves cannot be simulated properly, and the probabilities of failure will be highly overestimated. Copyright © 2011 John Wiley & Sons, Ltd.
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First, the concept of dependence measures is briefly introduced. Then, both the Akaike Information Criterion and the Bayesian Information Criterion are adopted for identifying the best‐fit copula. Thereafter, simulation of copulas and bivariate distributions based on Monte Carlo simulation are presented. Practical application for serviceability limit state reliability analysis of piles is conducted. Finally, four load–test datasets of load–displacement curves of piles are used to illustrate the proposed procedure. The results indicate that the proposed copula‐based procedure can model and simulate the bivariate probability distribution of two curve‐fitting parameters underlying the load–displacement models of piles in a more general way. The simulated load–displacement curves using the proposed procedure are found to be in good agreement with the measured results. In most cases, the Gaussian copula, often adopted out of expedience without proper validation, is not the best‐fit copula for modeling the dependence structure underlying two curve‐fitting parameters. The conditional probability density functions obtained from the Gaussian copula differ considerably from those obtained from the best‐fit copula. The probabilities of failure associated with the Gaussian copula are significantly smaller than the reference solutions, which are very unconservative for pile safety assessment. If the strong negative correlation between the two curve‐fitting parameters is ignored, the scatter in the measured load–displacement curves cannot be simulated properly, and the probabilities of failure will be highly overestimated. Copyright © 2011 John Wiley &amp; Sons, Ltd.</description><identifier>ISSN: 0363-9061</identifier><identifier>EISSN: 1096-9853</identifier><identifier>DOI: 10.1002/nag.1112</identifier><identifier>CODEN: IJNGDZ</identifier><language>eng</language><publisher>Chichester: Blackwell Publishing Ltd</publisher><subject>Applied sciences ; Buildings. Public works ; Computation methods. Tables. Charts ; Computer simulation ; copula ; Criteria ; Density ; Earthwork. Foundations. Retaining walls ; Exact sciences and technology ; Failure ; Gaussian ; Geotechnics ; joint probability distribution ; Kendall rank correlation coefficient ; load-displacement curve ; Mathematical analysis ; Mathematical models ; Pearson correlation coefficient ; Piles ; probability of failure ; Soil mechanics. Rocks mechanics ; Structural analysis. 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J. Numer. Anal. Meth. Geomech</addtitle><description>SUMMARY This paper aims to propose a procedure for modeling the joint probability distribution of bivariate uncertain data with a nonlinear dependence structure. First, the concept of dependence measures is briefly introduced. Then, both the Akaike Information Criterion and the Bayesian Information Criterion are adopted for identifying the best‐fit copula. Thereafter, simulation of copulas and bivariate distributions based on Monte Carlo simulation are presented. Practical application for serviceability limit state reliability analysis of piles is conducted. Finally, four load–test datasets of load–displacement curves of piles are used to illustrate the proposed procedure. The results indicate that the proposed copula‐based procedure can model and simulate the bivariate probability distribution of two curve‐fitting parameters underlying the load–displacement models of piles in a more general way. The simulated load–displacement curves using the proposed procedure are found to be in good agreement with the measured results. In most cases, the Gaussian copula, often adopted out of expedience without proper validation, is not the best‐fit copula for modeling the dependence structure underlying two curve‐fitting parameters. The conditional probability density functions obtained from the Gaussian copula differ considerably from those obtained from the best‐fit copula. The probabilities of failure associated with the Gaussian copula are significantly smaller than the reference solutions, which are very unconservative for pile safety assessment. If the strong negative correlation between the two curve‐fitting parameters is ignored, the scatter in the measured load–displacement curves cannot be simulated properly, and the probabilities of failure will be highly overestimated. Copyright © 2011 John Wiley &amp; Sons, Ltd.</description><subject>Applied sciences</subject><subject>Buildings. Public works</subject><subject>Computation methods. Tables. Charts</subject><subject>Computer simulation</subject><subject>copula</subject><subject>Criteria</subject><subject>Density</subject><subject>Earthwork. Foundations. Retaining walls</subject><subject>Exact sciences and technology</subject><subject>Failure</subject><subject>Gaussian</subject><subject>Geotechnics</subject><subject>joint probability distribution</subject><subject>Kendall rank correlation coefficient</subject><subject>load-displacement curve</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Pearson correlation coefficient</subject><subject>Piles</subject><subject>probability of failure</subject><subject>Soil mechanics. Rocks mechanics</subject><subject>Structural analysis. 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Public works</topic><topic>Computation methods. Tables. Charts</topic><topic>Computer simulation</topic><topic>copula</topic><topic>Criteria</topic><topic>Density</topic><topic>Earthwork. Foundations. Retaining walls</topic><topic>Exact sciences and technology</topic><topic>Failure</topic><topic>Gaussian</topic><topic>Geotechnics</topic><topic>joint probability distribution</topic><topic>Kendall rank correlation coefficient</topic><topic>load-displacement curve</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Pearson correlation coefficient</topic><topic>Piles</topic><topic>probability of failure</topic><topic>Soil mechanics. Rocks mechanics</topic><topic>Structural analysis. 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J. Numer. Anal. Meth. Geomech</addtitle><date>2013-04-25</date><risdate>2013</risdate><volume>37</volume><issue>6</issue><spage>597</spage><epage>617</epage><pages>597-617</pages><issn>0363-9061</issn><eissn>1096-9853</eissn><coden>IJNGDZ</coden><abstract>SUMMARY This paper aims to propose a procedure for modeling the joint probability distribution of bivariate uncertain data with a nonlinear dependence structure. First, the concept of dependence measures is briefly introduced. Then, both the Akaike Information Criterion and the Bayesian Information Criterion are adopted for identifying the best‐fit copula. Thereafter, simulation of copulas and bivariate distributions based on Monte Carlo simulation are presented. Practical application for serviceability limit state reliability analysis of piles is conducted. Finally, four load–test datasets of load–displacement curves of piles are used to illustrate the proposed procedure. The results indicate that the proposed copula‐based procedure can model and simulate the bivariate probability distribution of two curve‐fitting parameters underlying the load–displacement models of piles in a more general way. The simulated load–displacement curves using the proposed procedure are found to be in good agreement with the measured results. In most cases, the Gaussian copula, often adopted out of expedience without proper validation, is not the best‐fit copula for modeling the dependence structure underlying two curve‐fitting parameters. The conditional probability density functions obtained from the Gaussian copula differ considerably from those obtained from the best‐fit copula. The probabilities of failure associated with the Gaussian copula are significantly smaller than the reference solutions, which are very unconservative for pile safety assessment. If the strong negative correlation between the two curve‐fitting parameters is ignored, the scatter in the measured load–displacement curves cannot be simulated properly, and the probabilities of failure will be highly overestimated. Copyright © 2011 John Wiley &amp; Sons, Ltd.</abstract><cop>Chichester</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1002/nag.1112</doi><tpages>21</tpages></addata></record>
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subjects Applied sciences
Buildings. Public works
Computation methods. Tables. Charts
Computer simulation
copula
Criteria
Density
Earthwork. Foundations. Retaining walls
Exact sciences and technology
Failure
Gaussian
Geotechnics
joint probability distribution
Kendall rank correlation coefficient
load-displacement curve
Mathematical analysis
Mathematical models
Pearson correlation coefficient
Piles
probability of failure
Soil mechanics. Rocks mechanics
Structural analysis. Stresses
title Bivariate simulation using copula and its application to probabilistic pile settlement analysis
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