Structural and Multidisciplinary Optimization

, Volume 50, Issue 5, pp 717–738 | Cite as

An efficient variable screening method for effective surrogate models for reliability-based design optimization

  • Hyunkyoo Cho
  • Sangjune Bae
  • K. K. Choi
  • David Lamb
  • Ren-Jye Yang


In the reliability-based design optimization (RBDO) process, surrogate models are frequently used to reduce the number of simulations because analysis of a simulation model takes a great deal of computational time. On the other hand, to obtain accurate surrogate models, we have to limit the dimension of the RBDO problem and thus mitigate the curse of dimensionality. Therefore, it is desirable to develop an efficient and effective variable screening method for reduction of the dimension of the RBDO problem. In this paper, requirements of the variable screening method for deterministic design optimization (DDO) and RBDO are compared, and it is found that output variance is critical for identifying important variables in the RBDO process. An efficient approximation method based on the univariate dimension reduction method (DRM) is proposed to calculate output variance efficiently. For variable screening, the variables that induce larger output variances are selected as important variables. To determine important variables, hypothesis testing is used in this paper so that possible errors are contained in a user-specified error level. Also, an appropriate number of samples is proposed for calculating the output variance. Moreover, a quadratic interpolation method is studied in detail to calculate output variance efficiently. Using numerical examples, performance of the proposed method is verified. It is shown that the proposed method finds important variables efficiently and effectively


Variable screening RBDO Surrogate model Output variance 1-D Surrogate model Partial output variance Hypothesis testing Univariate dimension reduction method 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Hyunkyoo Cho
    • 1
  • Sangjune Bae
    • 1
  • K. K. Choi
    • 1
  • David Lamb
    • 2
  • Ren-Jye Yang
    • 2
  1. 1.Department of Mechanical and Industrial EngineeringThe University of IowaIowa CityUSA
  2. 2.Research and Advanced EngineeringFord Motor CompanyDearbornUSA
  3. 3.Research and Advanced Engineering, Ford Motor CompanyDearbornUSA

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