Refined first-order reliability method using cross-entropy optimization method

  • Hamed Ghohani ArabEmail author
  • Mohsen Rashki
  • Mehdi Rostamian
  • Alireza Ghavidel
  • Hossein Shahraki
  • Behrooz Keshtegar
Original Article


Generally, the first-order reliability method (FORM) is an efficient and accurate reliability method for problems with linear limit state functions (LSFs). It is showed that the FORM formula may produce inaccurate results when the LSF is defined by mathematical forms introduced as gray function. Thus, the original FORM formula may provide the results with huge errors. In this paper, a probabilistic optimization model as refined FORM (R-FORM) is presented to search most probable failure point (MPP) with the accurate results for gray LSFs. The cross-entropy optimization (CEO) method is utilized to search MPP in proposed R-FORM model. Several reliability problems are applied to illustrate the accuracy of the R-FORM compared to the conventional FORM formula. Results illustrate that the R-FORM provides more accurate results than the FORM for gray performance functions.


Failure probability Probabilistic model Refined FORM Cross-entropy optimization 



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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Hamed Ghohani Arab
    • 1
    Email author
  • Mohsen Rashki
    • 2
  • Mehdi Rostamian
    • 3
  • Alireza Ghavidel
    • 1
  • Hossein Shahraki
    • 4
  • Behrooz Keshtegar
    • 5
  1. 1.Civil Engineering DepartmentUniversity of Sistan and BaluchestanZahedanIran
  2. 2.Department of Architecture EngineeringUniversity of Sistan and BaluchestanZahedanIran
  3. 3.Department of Civil EngineeringUniversity of MemphisMemphisUSA
  4. 4.Civil Engineering DepartmentUniversity of BojnordBojnordIran
  5. 5.Department of Civil EngineeringUniversity of ZabolZabolIran

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