[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Adaptive stability transformation method of chaos control for first order reliability method

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

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

The efficiency and robustness are two key performance indexes for first-order reliability method (FORM). In this study, two different algorithms, including the adaptive stability transformation method (ASTM) and enhanced adaptive stability transformation method (EASTM), are proposed to improve the efficiency and robustness of FORM. In both ASTM and EASTM, the computation of most probable failure point (MPFP) is converted to find a series of most probable target points (MPTPs), in which the chaos control factor is properly selected by proposing two different algorithms. Four benchmark examples with normal and non-normal random variables and one practical engineering application example are tested to verify the effectiveness of the proposed algorithms. The results illustrate that the proposed algorithms not only are more efficient than other advanced FORM algorithms, but also are very robust.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

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
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Rashki M, Miri M, Azhdary MM (2012) A new efficient simulation method to approximate the probability of failure and most probable point. Struct Saf 39(11):22–29

    Article  Google Scholar 

  2. Lee IJ, Shin J, Choi KK (2013) Equivalent target probability of failure to convert high-reliability model to low-reliability model for efficiency of sampling-based RBDO. Struct Multidiscip Optim 48(2):235–248

    Article  MathSciNet  Google Scholar 

  3. Keshtegar B, Baharom S, El-Shafie A (2017) Self-adaptive conjugate method for a robust and efficient performance measure approach for reliability-based design optimization. Eng Comput. https://doi.org/10.1007/s00366-017-0529-7

    Google Scholar 

  4. Zhang D, Han X, Jiang C, Liu J, Li Q (2017) Time-dependent reliability analysis through response surface method. J Mech Des 139(4):041404

    Article  Google Scholar 

  5. Lim J, Lee B, Lee I (2016) Post optimization for accurate and efficient reliability-based design optimization using second-order reliability method based on importance sampling and its stochastic sensitivity analysis. Int J Numer Meth Eng 107(2):93–108

    Article  MathSciNet  MATH  Google Scholar 

  6. Jiang C, Han S, Ji M, Han X (2015) A new method to solve the structural reliability index based on homotopy analysis. Acta Mech 226(4):1067–1083

    Article  MathSciNet  Google Scholar 

  7. Du XP, Chen W (2004) Sequential optimization and reliability assessment method for efficient probabilistic design. J Mech Des 126(2):225–233

    Article  Google Scholar 

  8. Li G, Meng Z, Hu H (2015) An adaptive hybrid approach for reliability-based design optimization. Struct Multidiscip Optim 51(5):1051–1065

    Article  MathSciNet  Google Scholar 

  9. Rashki M, Miri M, Moghaddam MA (2014) A simulation-based method for reliability based design optimization problems with highly nonlinear constraints. Autom Constr 47(11):24–36

    Article  Google Scholar 

  10. Meng Z, Zhou HL, 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

    Article  MathSciNet  MATH  Google Scholar 

  11. Lee JO, Yang YS, Ruy WS (2002) A comparative study on reliability-index and target-performance-based probabilistic structural design optimization. Comput Struct 80(3–4):257–269

    Article  Google Scholar 

  12. 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(1):32–43

    Article  Google Scholar 

  13. Hasofer AM, Lind NC (1974) Exact and invariant second moment code format. J Eng Mech Div Asce 100(1):111–121

    Google Scholar 

  14. Rackwitz R, Fiessler B (1978) Structural reliability under combined random load sequences. Comput Struct 9(5):489–494

    Article  MATH  Google Scholar 

  15. Zhang Y, Der Kiureghian A (1995) Two improved algorithms for reliability analysis. Reliability and optimization of structural systems. Springer, Berlin, pp 297–304

    Book  Google Scholar 

  16. Periçaro GA, Santos SR, Ribeiro AA, Matioli LC (2015) HLRF–BFGS optimization algorithm for structural reliability. Appl Math Model 39(7):2025–2035

    Article  MathSciNet  Google Scholar 

  17. Lopez RH, Torii AJ, Miguel LFF, Souza Cursi JE (2015) Overcoming the drawbacks of the FORM using a full characterization method. Struct Saf 54(5):57–63

    Article  Google Scholar 

  18. Santos SR, Matioli LC, Beck AT (2012) New optimization algorithms for structural reliability analysis. Cmes Comp Model Eng 83(1):23–55

    MathSciNet  MATH  Google Scholar 

  19. Yang DX, Li G, Cheng GD (2006) Convergence analysis of first order reliability method using chaos theory. Comput Struct 84(8–9):563–571

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  21. Keshtegar B (2017) A hybrid conjugate finite-step length method for robust and efficient reliability analysis. Appl Math Model 45(5):226–237

    Article  MathSciNet  Google Scholar 

  22. Keshtegar B (2016) Chaotic conjugate stability transformation method for structural reliability analysis. Comput Methods Appl Mech Eng 310:866–885

    Article  MathSciNet  Google Scholar 

  23. Keshtegar B (2017) Limited conjugate gradient method for structural reliability analysis. Eng Comput 33(3):621–629

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  25. Tu J, Choi KK, Park YH (1999) A new study on reliability-based design optimization. J Mech Des 121(4):557–564

    Article  Google Scholar 

  26. Petkov BH, Vitale V, Mazzola M, Lanconelli C, Lupi A (2015) Chaotic behaviour of the short-term variations in ozone column observed in Arctic. Commun Nonlinear Sci Numer Simulat 26(1–3):238–249

    Article  Google Scholar 

  27. Pingel D, Schmelcher P, Diakonos FK (2004) Stability transformation: a tool to solve nonlinear problems. Phys Rep 400(2):67–148

    Article  MathSciNet  Google Scholar 

  28. Schmelcher P, Diakonos FK (1998) General approach to the localization of unstable periodic orbits in chaotic dynamical systems. Phys Rev E 57(3):2739–2746

    Article  Google Scholar 

  29. Liu PL, Der Kiureghian A (1991) Optimization algorithms for structural reliability. Struct Saf 9(3):161–177

Download references

Acknowledgements

The supports of the National Natural Science Foundation of China (Grant Nos. 11602076 and 51605127), the Natural Science Foundation of Anhui Province (No. 1708085QA06) and the Fundamental Research Funds for the Central Universities of China (No. JZ2016HGBZ0751) are much appreciated.

Author information

Authors and Affiliations

  1. School of Civil Engineering, Hefei University of Technology, Hefei, 230009, People’s Republic of China

    Zeng Meng, Yuxue Pu & Huanli Zhou

Authors
  1. Zeng Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuxue Pu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Huanli Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zeng Meng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Meng, Z., Pu, Y. & Zhou, H. Adaptive stability transformation method of chaos control for first order reliability method. Engineering with Computers 34, 671–683 (2018). https://doi.org/10.1007/s00366-017-0566-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-017-0566-2

Keywords