Skip to main content
SpringerLink
Log in

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

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Zhao W, Fan F, Wang W (2017) Non-linear partial least squares response surface method for structural reliability analysis. Reliability Eng Syst Saf 161(Supplement C):69–77. https://doi.org/10.1016/j.ress.2017.01.004

    Article  Google Scholar 

  2. Ditlevsen O, Madsen HO (1996) Structural reliability methods, vol 178. Wiley, New York

    Google Scholar 

  3. Chakraborty S, Chowdhury R (2015) A semi-analytical framework for structural reliability analysis. Comput Methods Appl Mech Eng 289:475–497

    MathSciNet  MATH  Google Scholar 

  4. Zhang Z, Jiang C, Wang G, Han X (2015) First and second order approximate reliability analysis methods using evidence theory. Reliability Eng Syst Saf 137:40–49

    Google Scholar 

  5. Huang X, Li Y, Zhang Y, Zhang X (2018) A new direct second-order reliability analysis method. Appl Math Model 55:68–80

    MathSciNet  Google Scholar 

  6. Roudak MA, Shayanfar MA, Barkhordari MA, Karamloo M (2017) A robust approximation method for nonlinear cases of structural reliability analysis. Int J Mech Sci 133 (Supplement C):11–20. https://doi.org/10.1016/j.ijmecsci.2017.08.038

    Article  Google Scholar 

  7. Melchers RE, Beck AT (2017) Structural reliability analysis and prediction. Wiley, New York

    Google Scholar 

  8. Keshtegar B, Chakraborty S (2018) A hybrid self-adaptive conjugate first order reliability method for robust structural reliability analysis. Appl Math Model 53:319–332. https://doi.org/10.1016/j.apm.2017.09.017

    Article  MathSciNet  Google Scholar 

  9. Rashki M, Miri M, Moghaddam MA (2012) A new efficient simulation method to approximate the probability of failure and most probable point. Struct Saf 39:22–29

    Google Scholar 

  10. Xiao N-C, Zuo MJ, Zhou C (2018) A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis. Reliab Eng Syst Saf 169 (Supplement C):330–338. https://doi.org/10.1016/j.ress.2017.09.008

    Article  Google Scholar 

  11. Jian W, Zhili S, Qiang Y, Rui L (2017) Two accuracy measures of the Kriging model for structural reliability analysis. Reliability Eng Syst Saf 167 (Supplement C):494–505. https://doi.org/10.1016/j.ress.2017.06.028

    Article  Google Scholar 

  12. Keshtegar B, Kisi O (2017) M5 model tree and Monte Carlo simulation for efficient structural reliability analysis. Appl Math Model 48:899–910

    MathSciNet  Google Scholar 

  13. Green DK (2017) Efficient Markov Chain Monte Carlo for combined Subset Simulation and nonlinear finite element analysis. Comput Methods Appl Mech Eng 313:337–361

    MathSciNet  Google Scholar 

  14. Arab HG, Ghasemi MR (2015) A fast and robust method for estimating the failure probability of structures. Proc Inst Civil Eng Struct Build 168(4):298–309

    Google Scholar 

  15. Shields MD, Teferra K, Hapij A, Daddazio RP (2015) Refined stratified sampling for efficient Monte Carlo based uncertainty quantification. Reliability Eng Syst Saf 142:310–325

    Google Scholar 

  16. Olsson A, Sandberg G, Dahlblom O (2003) On Latin hypercube sampling for structural reliability analysis. Struct Saf 25(1):47–68

    Google Scholar 

  17. Papaioannou I, Papadimitriou C, Straub D (2016) Sequential importance sampling for structural reliability analysis. Struct Saf 62:66–75

    Google Scholar 

  18. Grooteman F (2011) An adaptive directional importance sampling method for structural reliability. Probab Eng Mech 26(2):134–141

    Google Scholar 

  19. Shayanfar MA, Barkhordari MA, Barkhori M, Barkhori M (2018) An adaptive directional importance sampling method for structural reliability analysis. Struct Saf 70:14–20

    Google Scholar 

  20. Okasha NM (2016) An improved weighted average simulation approach for solving reliability-based analysis and design optimization problems. Struct Saf 60:47–55

    Google Scholar 

  21. Li D-Q, Yang Z-Y, Cao Z-J, Au S-K, Phoon K-K (2017) System reliability analysis of slope stability using generalized subset simulation. Appl Math Model 46:650–664

    MathSciNet  MATH  Google Scholar 

  22. Zhao Y-G, Ang AH (2003) System reliability assessment by method of moments. J Struct Eng 129(10):1341–1349

    Google Scholar 

  23. Zhao Y-G, Ono T (2004) On the problems of the fourth moment method. Struct Saf 26(3):343–347

    Google Scholar 

  24. Goswami S, Ghosh S, Chakraborty S (2016) Reliability analysis of structures by iterative improved response surface method. Struct Saf 60 (Supplement C):56–66. https://doi.org/10.1016/j.strusafe.2016.02.002

    Article  Google Scholar 

  25. Meng Z, Li G, Yang D, Zhan L (2017) A new directional stability transformation method of chaos control for first order reliability analysis. Struct Multidiscip Optim 55(2):601–612

    MathSciNet  Google Scholar 

  26. Keshtegar B, Meng Z (2017) A hybrid relaxed first-order reliability method for efficient structural reliability analysis. Struct Saf 66:84–93. https://doi.org/10.1016/j.strusafe.2017.02.005

    Article  Google Scholar 

  27. Zhao Y-G, Lu Z-H (2007) Fourth-moment standardization for structural reliability assessment. J Struct Eng 133(7):916–924

    Google Scholar 

  28. Du X, Sudjianto A (2004) First-order saddlepoint approximation for reliability analysis. AIAA J 42(6):1199–1207

    Google Scholar 

  29. Huang B, Du X (2008) Probabilistic uncertainty analysis by mean-value first order saddlepoint approximation. Reliability Eng Syst Saf 93(2):325–336

    Google Scholar 

  30. Huang J, Griffiths D (2011) Observations on FORM in a simple geomechanics example. Struct Saf 33(1):115–119

    Google Scholar 

  31. Meng Z, Zhou H, Li G, Hu H (2017) A hybrid sequential approximate programming method for second-order reliability-based design optimization approach. Acta Mech 228(5):1965–1978

    MathSciNet  MATH  Google Scholar 

  32. Liu HB, Jiang C, Liu J, Mao JZ (2018) Uncertainty propagation analysis using sparse grid technique and saddlepoint approximation based on parameterized p-box representation. Struct Multidiscip Optim. https://doi.org/10.1007/s00158-018-2049-5

    Article  Google Scholar 

  33. Jiang Z, Li J (2017) High dimensional structural reliability with dimension reduction. Struct Saf 69 (Supplement C):35–46. https://doi.org/10.1016/j.strusafe.2017.07.007

    Article  Google Scholar 

  34. Rahman S, Xu H (2004) A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics. Probab Eng Mech 19(4):393–408

    Google Scholar 

  35. Hawchar L, El Soueidy C-P, Schoefs F (2017) Principal component analysis and polynomial chaos expansion for time-variant reliability problems. Reliab Eng Syst Saf 167(Supplement C):406–416. https://doi.org/10.1016/j.ress.2017.06.024

    Article  Google Scholar 

  36. Liu HB, Jiang C, Jia XY, Long XY, Zhang Z, Guan FJ (2018) A new uncertainty propagation method for problems with parameterized probability-boxes. Reliab Eng Syst Saf 172:64–73. https://doi.org/10.1016/j.ress.2017.12.004

    Article  Google Scholar 

  37. Keshtegar B, Chakraborty S (2018) Dynamical accelerated performance measure approach for efficient reliability-based design optimization with highly nonlinear probabilistic constraints. Reliab Eng Syst Saf 178:69–83. https://doi.org/10.1016/j.ress.2018.05.015

    Article  Google Scholar 

  38. Meng Z, Pu Y, Zhou H (2018) Adaptive stability transformation method of chaos control for first order reliability method. Eng Comput 34(4):671–683

    Google Scholar 

  39. Yang D (2010) Chaos control for numerical instability of first order reliability method. Commun Nonlinear Sci Numer Simul 15(10):3131–3141

    MATH  Google Scholar 

  40. Yaseen ZM, Keshtegar B (2018) Limited descent-based mean value method for inverse reliability analysis. Eng Comput. https://doi.org/10.1007/s00366-018-0661-z

    Article  Google Scholar 

  41. Keshtegar B, Chakraborty S (2018) An efficient-robust structural reliability method by adaptive finite-step length based on Armijo line search. Reliab Eng Syst Saf 172:195–206. https://doi.org/10.1016/j.ress.2017.12.014

    Article  Google Scholar 

  42. Gong J-X, Yi P (2011) A robust iterative algorithm for structural reliability analysis. Struct Multidiscip Optim 43(4):519–527

    MATH  Google Scholar 

  43. Keshtegar B (2018) Enriched FR conjugate search directions for robust and efficient structural reliability analysis. Eng Comput 34(1):117–128

    Google Scholar 

  44. Keshtegar B (2017) A hybrid conjugate finite-step length method for robust and efficient reliability analysis. Appl Math Model 45:226–237. https://doi.org/10.1016/j.apm.2016.12.027

    Article  MathSciNet  Google Scholar 

  45. Keshtegar B (2018) Conjugate finite-step length method for efficient and robust structural reliability analysis. Struct Eng Mech 65:415–422. https://doi.org/10.12989/sem.2018.65.4.415

    Article  Google Scholar 

  46. Keshtegar B, Bagheri M (2018) Fuzzy relaxed-finite step size method to enhance the instability of the fuzzy first-order reliability method using conjugate discrete map. Nonlinear Dyn 91(3):1443–1459

    Google Scholar 

  47. Breitung K (2015) 40 years FORM: some new aspects? Probab Eng Mech 42:71–77

    Google Scholar 

  48. António CC (2001) A hierarchical genetic algorithm for reliability based design of geometrically non-linear composite structures. Compos Struct 54(1):37–47

    Google Scholar 

  49. Elegbede C (2005) Structural reliability assessment based on particles swarm optimization. Struct Saf 27(2):171–186

    Google Scholar 

  50. Meng Z, Li G, Wang BP, Hao P (2015) A hybrid chaos control approach of the performance measure functions for reliability-based design optimization. Comput Struct 146:32–43

    Google Scholar 

  51. Lopez R, Torii A, Miguel L, Cursi JS (2015) Overcoming the drawbacks of the FORM using a full characterization method. Struct Saf 54:57–63

    Google Scholar 

  52. Hao P, Wang Y, Liu X, Wang B, Li G, Wang L (2017) An efficient adaptive-loop method for non-probabilistic reliability-based design optimization. Comput Methods Appl Mech Eng 324(Supplement C):689–711. https://doi.org/10.1016/j.cma.2017.07.002

    Article  MathSciNet  Google Scholar 

  53. Rubinstein R (1999) The cross-entropy method for combinatorial and continuous optimization. Methodol Comput Appl Probab 1(2):127–190

    MathSciNet  MATH  Google Scholar 

  54. Benham T, Duan Q, Kroese DP, Liquet B (2015) CEoptim: cross-entropy R package for optimization. arXiv preprint 150301842

  55. Deng L-Y (2006) The cross-entropy method: a unified approach to combinatorial optimization, Monte-Carlo simulation, and machine learning. Taylor & Francis, Boca Raton

    Google Scholar 

  56. Ghidey H (2015) Reliability-based design optimization with cross-entropy method. NTNU

  57. Lopez-Garcia P, Onieva E, Osaba E, Masegosa AD, Perallos A (2016) GACE: a meta-heuristic based in the hybridization of genetic algorithms and cross entropy methods for continuous optimization. Expert Syst Appl 55:508–519

    Google Scholar 

  58. Hua L, Shao G (2017) The progress of operational forest fire monitoring with infrared remote sensing. J For Res 28(2):215–229. https://doi.org/10.1007/s11676-016-0361-8

    Article  Google Scholar 

  59. Depina I, Papaioannou I, Straub D, Eiksund G (2017) Coupling the cross-entropy with the line sampling method for risk-based design optimization. Struct Multidiscip Optim 55(5):1589–1612. https://doi.org/10.1007/s00158-016-1596-x

    Article  MathSciNet  Google Scholar 

  60. Gavin HP, Yau SC (2008) High-order limit state functions in the response surface method for structural reliability analysis. Struct Saf 30(2):162–179

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Civil Engineering Department, University of Sistan and Baluchestan, Zahedan, Iran

    Hamed Ghohani Arab & Alireza Ghavidel

  2. Department of Architecture Engineering, University of Sistan and Baluchestan, Zahedan, Iran

    Mohsen Rashki

  3. Department of Civil Engineering, University of Memphis, Memphis, TN, USA

    Mehdi Rostamian

  4. Civil Engineering Department, University of Bojnord, Bojnord, Iran

    Hossein Shahraki

  5. Department of Civil Engineering, University of Zabol, Zabol, Iran

    Behrooz Keshtegar

Authors
  1. Hamed Ghohani Arab
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohsen Rashki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mehdi Rostamian
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alireza Ghavidel
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hossein Shahraki
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Behrooz Keshtegar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hamed Ghohani Arab.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghohani Arab, H., Rashki, M., Rostamian, M. et al. Refined first-order reliability method using cross-entropy optimization method. Engineering with Computers 35, 1507–1519 (2019). https://doi.org/10.1007/s00366-018-0680-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-018-0680-9

Keywords

Search

Navigation