Structural and Multidisciplinary Optimization

, Volume 47, Issue 2, pp 175–189 | Cite as

Comparison study between probabilistic and possibilistic methods for problems under a lack of correlated input statistical information

Research Paper


In most industrial applications, only limited statistical information is available to describe the input uncertainty model due to expensive experimental testing costs. It would be unreliable to use the estimated input uncertainty model obtained from insufficient data for the design optimization. Furthermore, when input variables are correlated, we would obtain non-optimum design if we assume that they are independent. In this paper, two methods for problems with a lack of input statistical information—possibility-based design optimization (PBDO) and reliability-based design optimization (RBDO) with confidence level on the input model—are compared using mathematical examples and an Abrams M1A1 tank roadarm example. The comparison study shows that PBDO could provide an unreliable optimum design when the number of samples is very small. In addition, PBDO provides an optimum design that is too conservative when the number of samples is relatively large. Furthermore, the obtained PBDO designs do not converge to the optimum design obtained using the true input distribution as the number of samples increases. On the other hand, RBDO with confidence level on the input model provides a conservative and reliable optimum design in a stable manner. The obtained RBDO designs converge to the optimum design obtained using the true input distribution as the number of samples increases.


Identification of joint and marginal CDFs Confidence level Reliability-based design optimization (RBDO) Possibility-based design optimization (PBDO) Correlated input Copula 



Research is supported by the Automotive Research Center, which is sponsored by the U.S. Army Tank Automotive Research, Development and Engineering Center (TARDEC). This research was also partially supported by the World Class University Program through the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education, Science and Technology (Grant Number R32-2008-000-10161-0 in 2009).


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Ikjin Lee
    • 1
  • K. K. Choi
    • 2
    • 3
  • Yoojeong Noh
    • 4
  • David Lamb
    • 5
  1. 1.Department of Mechanical EngineeringThe University of ConnecticutStorrsUSA
  2. 2.Department of Mechanical & Industrial EngineeringThe University of IowaIowa CityUSA
  3. 3.Department of Naval Architecture and Ocean EngineeringSeoul National UniversitySeoulKorea
  4. 4.Department of Mechanical & Automotive EngineeringKeimyung UniversityDaeguKorea

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