Skip to main content
SpringerLink
Log in

Fuzzy relaxed-finite step size method to enhance the instability of the fuzzy first-order reliability method using conjugate discrete map

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Fuzzy reliability analysis can be implemented using two discrete optimization maps in the processes of reliability and fuzzy analysis. Actually, the efficiency and robustness of the iterative reliability methods are two main factors in the fuzzy-based reliability analysis due to the huge computational burdens and unstable results. In the structural fuzzy reliability analysis, the first-order reliability method (FORM) using discrete nonlinear map can provide a C membership function. In this paper, a discrete nonlinear conjugate map is proposed using a relaxed-finite step size method for fuzzy structural reliability analysis, namely Fuzzy conjugate relaxed-finite step size method fuzzy CRS. A discrete conjugate map is stabilized using two adaptive factors to compute the relaxed factor and step size in FORM. The framework of the proposed fuzzy structural reliability method is established using two linked iterative discrete maps as an outer loop, which constructs the membership function of the response using alpha level set optimization based on genetic operator, and the inner loop, implemented for reliability analysis using proposed conjugate relaxed-finite step size method. The fuzzy CRS and fuzzy HL-RF methods are compared to evaluate the membership functions of five structural problems with highly nonlinear limit state functions. Results demonstrated that the fuzzy CRS method is computationally more efficient and is strongly more robust than the HL-RF for fuzzy-based reliability analysis of the nonlinear structural reliability problems.

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
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Bulleit, W.M.: Uncertainty in structural engineering. Pract. Period. Struct. Des. Constr. 13(1), 24–30 (2008)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  4. Möller, B., Graf, W., Beer, M.: Fuzzy structural analysis using \(\alpha \)-level optimization. Comput. Mech. 26(6), 547–565 (2000)

    Article  MATH  Google Scholar 

  5. Wang, M., Huang, Q.: A new hybrid uncertain analysis method for structural-acoustic systems with random and interval parameters. Comput. Struct. 175, 15–28 (2016)

    Article  Google Scholar 

  6. Möller, B., Beer, M.: Fuzzy Randomness: Uncertainty in Civil Engineering and Computational Mechanics. Springer, Berlin (2013)

    MATH  Google Scholar 

  7. Möller, B., Graf, W., Beer, M.: Safety assessment of structures in view of fuzzy randomness. Comput. Struct. 81(15), 1567–1582 (2003)

    Article  Google Scholar 

  8. Cremona, C., Gao, Y.: The possibilistic reliability theory: theoretical aspects and applications. Struct. Saf. 19(2), 173–201 (1997)

    Article  Google Scholar 

  9. Yubin, L., Zhong, Q., Guangyuan, W.: Fuzzy random reliability of structures based on fuzzy random variables. Fuzzy Sets Syst. 86(3), 345–355 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)

    Article  MATH  Google Scholar 

  11. Kwakernaak, H.: Fuzzy random variables–I. Definitions and theorems. Inf. Sci. 15(1), 1–29 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kwakernaak, H.: Fuzzy random variables–II. Algorithms and examples for the discrete case. Inf. Sci. 17(3), 253–278 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  13. Freitag, S., Graf, W., Kaliske, M.: A material description based on recurrent neural networks for fuzzy data and its application within the finite element method. Comput. Struct. 124, 29–37 (2013)

    Article  Google Scholar 

  14. Serafinska, A., Kaliske, M., Zopf, C., Graf, W.: A multi-objective optimization approach with consideration of fuzzy variables applied to structural tire design. Comput. Struct. 116, 7–19 (2013)

    Article  Google Scholar 

  15. Massa, F., Lallemand, B., Tison, T.: Fuzzy multiobjective optimization of mechanical structures. Comput. Methods Appl. Mech. Eng. 198(5), 631–643 (2009)

    Article  MATH  Google Scholar 

  16. Hurtado, J.E., Alvarez, D.A., RamíRez, J.: Fuzzy structural analysis based on fundamental reliability concepts. Comput. Struct. 112, 183–192 (2012)

    Article  Google Scholar 

  17. Biondini, F., Bontempi, F., Malerba, P.G.: Fuzzy reliability analysis of concrete structures. Comput. Struct. 82(13), 1033–1052 (2004)

    Article  MATH  Google Scholar 

  18. Marano, G.C., Quaranta, G.: A new possibilistic reliability index definition. Acta Mech. 210(3–4), 291–303 (2010)

    Article  MATH  Google Scholar 

  19. Shuxiang, G., Zhenzhou, L., Lifu, F.: A fuzzy reliability approach for structures in the possibility context. Chin. J. Comput. Mech. 19(1), 189–193 (2002)

    Google Scholar 

  20. Aliev, I.M., Kara, Z.: Fuzzy system reliability analysis using time dependent fuzzy set. Control Cybern. 33(4), 653–662 (2004)

    MathSciNet  MATH  Google Scholar 

  21. Zhang, M., Beer, M., Quek, S., Choo, Y.: Comparison of uncertainty models in reliability analysis of offshore structures under marine corrosion. Struct. Saf. 32(6), 425–432 (2010)

    Article  Google Scholar 

  22. Möller, B., Beer, M., Graf, W., Sickert, J.-U.: Time-dependent reliability of textile-strengthened RC structures under consideration of fuzzy randomness. Comput. Struct. 84(8), 585–603 (2006)

    Article  Google Scholar 

  23. Marano, G.C., Quaranta, G., Mezzina, M.: Fuzzy time-dependent reliability analysis of RC beams subject to pitting corrosion. J. Mater. Civ. Eng. 20(9), 578–587 (2008)

    Article  Google Scholar 

  24. Bagheri, M., Miri, M., Shabakhty, N.: Modeling of epistemic uncertainty in reliability analysis of structures using a robust genetic algorithm. Iran. J. Fuzzy Syst. 12(2), 23–40 (2015)

    Google Scholar 

  25. Meng, Z., Li, G., Yang, D., Zhan, L.: A new directional stability transformation method of chaos control for first order reliability analysis. Struct. Multidiscip. Optim. 1–12 (2016). https://doi.org/10.1007/s00158-00016-01525-z

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  29. Keshtegar, B., Meng, Z.: Conjugate and directional chaos control methods for reliability analysis of CNT-reinforced nanocomposite beams under buckling forces; a comparative study. J. Appl. Comput. Mech. 2(3), 144–151 (2016)

    Google Scholar 

  30. Keshtegar, B.: Stability iterative method for structural reliability analysis using a chaotic conjugate map. Nonlinear Dyn. 84(4), 2161–2174 (2016). https://doi.org/10.1007/s11071-016-2636-1

    Article  MathSciNet  Google Scholar 

  31. Lin, G., Huang, C., Zhan, S., Lu, X., Lu, Y.: Ranking based selection genetic algorithm for capacity flow assignments. In: International Symposium on Intelligence Computation and Applications, pp. 97–107. Springer (2010)

  32. Hao, P., Wang, B., Li, G., Meng, Z., Wang, L.: Hybrid framework for reliability-based design optimization of imperfect stiffened shells. AIAA J. 53(10), 2878–2889 (2015)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  34. Gandomi, A.H., Yun, G.J., Yang, X.-S., Talatahari, S.: Chaos-enhanced accelerated particle swarm optimization. Commun. Nonlinear Sci. Numer. Simul. 18(2), 327–340 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  36. Keshtegar, B.: Enriched FR conjugate search directions for robust and efficient structural reliability analysis. Eng. Comput. (2017). https://doi.org/10.1007/s00366-017-0524-z

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

    Article  MathSciNet  Google Scholar 

  38. Keshtegar, B., Miri, M.: Reliability analysis of corroded pipes using conjugate HL-RF algorithm based on average shear stress yield criterion. Eng. Fail. Anal. 46, 104–117 (2014)

    Article  Google Scholar 

  39. Wu, G.-C., Baleanu, D.: Discrete fractional logistic map and its chaos. Nonlinear Dyn. 75(1), 283–287 (2014). https://doi.org/10.1007/s11071-013-1065-7

    Article  MathSciNet  MATH  Google Scholar 

  40. Wang, Y., Liu, Z., Ma, J., He, H.: A pseudorandom number generator based on piecewise logistic map. Nonlinear Dyn. 83(4), 2373–2391 (2016). https://doi.org/10.1007/s11071-015-2488-0

    Article  MathSciNet  MATH  Google Scholar 

  41. He, Y., Yang, S., Xu, Q.: Short-term cascaded hydroelectric system scheduling based on chaotic particle swarm optimization using improved logistic map. Commun. Nonlinear Sci. Numer. Simul. 18(7), 1746–1756 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  42. Bagheri, M., Miri, M., Shabakhty, N.: Fuzzy reliability analysis using a new alpha level set optimization approach based on particle swarm optimization. J. Intell. Fuzzy Syst. 30(1), 235–244 (2015)

    Article  Google Scholar 

  43. Zhang, B.T., Kim, J.J.: Comparison of selection methods for evolutionary optimization. Evol. Optim. 2(1), 55–70 (2000)

    Google Scholar 

  44. Vasant, P.: Handbook of Research on Novel Soft Computing Intelligent Algorithms: Theory and Practical Applications. Hershey, IGI Global (2013)

    Google Scholar 

  45. Keshtegar, B., Hao, P., Meng, Z.: A self-adaptive modified chaos control method for reliability-based design optimization. Struct. Multidiscip. Optim. 55(51), 63–75 (2017)

    Article  MathSciNet  Google Scholar 

  46. Keshtegar, B., Miri, M.: An enhanced HL-RF Method for the computation of structural failure probability based on relaxed approach. Civ. Eng. Infrastruct. J. 46(1), 69–80 (2013)

    Google Scholar 

  47. Zhang, L., Lu, Z., Wang, P.: Efficient structural reliability analysis method based on advanced Kriging model. Appl. Math. Model. 39(2), 781–793 (2015)

    Article  MathSciNet  Google Scholar 

  48. Shayanfar, M.A., Barkhordari, M.A., Roudak, M.A.: An efficient reliability algorithm for locating design point using the combination of importance sampling concepts and response surface method. Commun. Nonlinear Sci. Numer. Simul. 47, 223–237 (2017)

    Article  Google Scholar 

  49. Zamanian, M., Kolahchi, R., Bidgoli, M.R.: Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with SiO2 nano-particles. Wind Struct. 24(1), 43–57 (2017)

    Article  Google Scholar 

  50. Kolahchi, R., Bidgoli, A.M.: Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes. Appl. Math. Mech. 37(2), 265–274 (2016)

    Article  MathSciNet  Google Scholar 

  51. Kolahchi, R., Safari, M., Esmailpour, M.: Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium. Compos. Struct. 150, 255–265 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by University of Zabol under Grant No. UOZ-GR-9517-3.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Faculty of Engineering, University of Zabol, P.B. 9861335856, Zabol, Iran

    Behrooz Keshtegar

  2. Department of Civil Engineering, Birjand University of Technology, P.B. 9719866981, Birjand, Iran

    Mansour Bagheri

Authors
  1. Behrooz Keshtegar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mansour Bagheri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Behrooz Keshtegar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Keshtegar, B., Bagheri, M. Fuzzy relaxed-finite step size method to enhance the instability of the fuzzy first-order reliability method using conjugate discrete map. Nonlinear Dyn 91, 1443–1459 (2018). https://doi.org/10.1007/s11071-017-3957-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-017-3957-4

Keywords

Search

Navigation