Identification of marginal and joint CDFs using Bayesian method for RBDO

  • Yoojeong Noh
  • K. K. ChoiEmail author
  • Ikjin Lee


In RBDO, input uncertainty models such as marginal and joint cumulative distribution functions (CDFs) need to be used. However, only limited data exists in industry applications. Thus, identification of the input uncertainty model is challenging especially when input variables are correlated. Since input random variables, such as fatigue material properties, are correlated in many industrial problems, the joint CDF of correlated input variables needs to be correctly identified from given data. In this paper, a Bayesian method is proposed to identify the marginal and joint CDFs from given data where a copula, which only requires marginal CDFs and correlation parameters, is used to model the joint CDF of input variables. Using simulated data sets, performance of the Bayesian method is tested for different numbers of samples and is compared with the goodness-of-fit (GOF) test. Two examples are used to demonstrate how the Bayesian method is used to identify correct marginal CDFs and copula.


Reliability-based design optimization Input model uncertainty Identification of marginal and joint CDFs Correlated input variables Copula Bayesian method Goodness-of-fit test 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Mechanical & Industrial Engineering, College of EngineeringThe University of IowaIowa CityUSA

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