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Neural Computing and Applications

, Volume 31, Issue 3, pp 777–791 | Cite as

New neural network-based response surface method for reliability analysis of structures

  • Hossein Beheshti Nezhad
  • Mahmoud MiriEmail author
  • Mohammad Reza Ghasemi
Original Article

Abstract

In this paper, a new algorithm is introduced for reliability analysis of structures using response surface method based on a group method of data handling-type neural networks with general structure (GS-GMDH-type NN). A multilayer network of quadratic neurons, GMDH, offers an effective solution to modeling nonlinear systems without an explicit limit state function. In the proposed method, the response surface function is determined using GMDH-type neural networks. This is then connected to a reliability method, such as first-order or second-order reliability methods (FORM or SORM) or Monte Carlo simulation method to predict the failure probability (Pf). In the proposed method, the use of the GMDH-type neural network with general structure, where all neurons from previous layers are used to produce neurons in the new layer, can improve the limit state function. In addition, the structure of the neural network and its weight are simultaneously optimized by genetic algorithm and singular value decomposition. As a result, the obtained model has no significant error, despite its simplicity. Moreover, the obtained limit state function is explicit and allows direct use of FORM and SORM methods. To determine the accuracy and efficiency of the proposed method, four numerical examples are solved and their results are compared to other conventional methods. The results show that the proposed method is simply applicable to analyzing the reliability of large complex and sophisticated structures without an explicit limit state function. The proposed approach is a high accurate method that can significantly reduce computing time compared with direct Monte Carlo method.

Keywords

Reliability Response surface GMDH-type neural network Genetic algorithm 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Ji L, Yun L (2012) An improved adaptive response surface method for structural reliability analysis. J Cent South Univ T 19:1148–1154CrossRefGoogle Scholar
  2. 2.
    Hosni Elhewy A, Mesbahi E, Pu Y (2006) Reliability analysis of structures using neural network method. Probab Eng Mech 21:44–53CrossRefGoogle Scholar
  3. 3.
    Gomes HM, Awruch AM (2004) Comparison of response surface and neural network with other methods for structural reliability analysis. Struct Saf 26:49–67CrossRefGoogle Scholar
  4. 4.
    Cheng J, Li QS (2008) Reliability analysis of structures using artificial neural network based genetic algorithms. Comput Methods Appl Mech Eng 197:3742–3750CrossRefzbMATHGoogle Scholar
  5. 5.
    Zhao YG, Ono T (2001) Moment methods for structural reliability. Struct Saf 23:47–75CrossRefGoogle Scholar
  6. 6.
    Hasofer AM, Lind NC (1974) Exact and invariant second-moment code format. J Eng Mech Div ASCE 100:111–121Google Scholar
  7. 7.
    Nowak AS, Collins KR (2000) Reliability of structures. McGraw-Hill, New YorkGoogle Scholar
  8. 8.
    Rashki M, Miri M, Moghaddam MA (2012) A new efficient simulation method to approximate the probability of failure and most probable point. Struct Saf 39:22–29CrossRefGoogle Scholar
  9. 9.
    Rajashekhar MR, Ellingwood BRA (1993) A new look at the response surface approach for reliability analysis. Struct Saf 12:205–220CrossRefGoogle Scholar
  10. 10.
    Das PK, Zheng Y (2000) Cumulative formation of response surface and its use in reliability analysis. Probab Eng Mech 15:309–315CrossRefGoogle Scholar
  11. 11.
    Myers RH, Montgomery DC, Anderson-Cook CM (2007) Response surface methodology: process and product optimization using designed experiments. Wiley, New JerseyzbMATHGoogle Scholar
  12. 12.
    Yuan R, Guangchen B (2011) New neural network response surface methods for reliability analysis. Chin J Aeronaut 24:25–31CrossRefGoogle Scholar
  13. 13.
    Guan XL, Melchers RE (2001) Effect of response surface parameter variation on structural reliability estimate. Struct Saf 23:429–444CrossRefGoogle Scholar
  14. 14.
    Cheng J, R-ch Xiao (2005) Serviceability reliability analysis of cable-stayed bridges. Struct Eng Mech 20(6):609–630CrossRefGoogle Scholar
  15. 15.
    Li H, He Y, Nie X (2016) Structural reliability calculation method based on the dual neural network and direct integration method. Neural Comput Appl. doi: 10.1007/s00521-016-2554-7 Google Scholar
  16. 16.
    Cheng J, Li QS, Xiao R-Ch (2008) A new artificial neural network-based response surface method for structural reliability analysis. Probab Eng Mech 23:51–63CrossRefGoogle Scholar
  17. 17.
    Ivakhnenko AG (1971) Polynomial theory of complex system. IEEE Trans Syst Man Cybern SMC-1:364–378MathSciNetCrossRefGoogle Scholar
  18. 18.
    Muzzammil M, Alam J, Danish M (2015) The GMDH model for prediction of scour at bridge pier in cohesive bed. In: Hydro 2015 international, 20th international conference on hydraulics, water resources and river engineering, IIT Roorkee, IndiaGoogle Scholar
  19. 19.
    Nariman-zadeh N, Darvizeh A, Darvizeh M, Gharababaei H (2002) Modelling of explosive cutting process of plates using GMDH-type neural network and singular value decomposition. J Mater Process Tech 128(1–3):80–87CrossRefzbMATHGoogle Scholar
  20. 20.
    Beheshti Nezhad H, Nariman-Zadeh N, Ranjbar MM (2008) Prediction of concrete diffusion factor under aggressive environment with GMDH-type neural networks. In: Proceedings of the 8th international conference on creep, shrinkage and durability mechanics of concrete and concrete structures, pp 1131–1137. ISBN 978-0-415-48508-1Google Scholar
  21. 21.
    Golub GH, Reinesh C (1970) Singular value decomposition and least squares solutions. Numer Math 14(5):403–420MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Nariman-Zadeh N, Darvizeh A, Ahmad-Zadeh GR (2003) Hybrid genetic design of GMDH-type neural networks using singular value decomposition for modelling and prediction of the explosive cutting process. Proc Inst Mech Eng B J Eng 217:779–790CrossRefzbMATHGoogle Scholar
  23. 23.
    Melchers RE (1990) Search-based importance sampling. Struct Saf 9:117–128CrossRefGoogle Scholar
  24. 24.
    Richard B, Cremona CH, Adelaide L (2012) A response surface method based on support vector machines trained with an adaptive experimental design. Struct Saf 39:14–21CrossRefGoogle Scholar
  25. 25.
    Cheng J (2007) Hybrid genetic algorithms for structural reliability analysis. Comput Struct 85:1524–1533CrossRefGoogle Scholar
  26. 26.
    Shao S, Morutso Y (1997) Structural reliability analysis using a neural network. JSME Int J, Ser A 40(3):242–246CrossRefGoogle Scholar
  27. 27.
    Zhao G (1996) Reliability theory and its applications for engineering structures. Dalian university of technology press, DalianGoogle Scholar
  28. 28.
    Bucher U, Bourgund UA (1990) Fast and efficient response surface approach for structural reliability problems. Struct Saf 7:57–66CrossRefGoogle Scholar
  29. 29.
    Wei D, Rahman S (2007) Structural reliability analysis by univariate decomposition and numerical integration. Probab Eng Mech 22:27–38CrossRefGoogle Scholar
  30. 30.
    Blatman G, Sudret B (2010) An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis. Probab Eng Mech 25(2):183–197CrossRefGoogle Scholar
  31. 31.
    Nguyen X, Sellier A, Duprat F, Pons G (2009) Adaptive response surface method based on a double weighted regression technique. Probab Eng Mech 24:135–143CrossRefGoogle Scholar
  32. 32.
    Roussouly N, Petitjean F, Salaun M (2013) A new adaptive response surface method for reliability analysis. Probab Eng Mech 32:103–115CrossRefGoogle Scholar
  33. 33.
    Rahman S, Wei D (2006) A univariate approximation at most probable point for higher-order reliability analysis. Int J Solids Struct 43:2820–2839CrossRefzbMATHGoogle Scholar
  34. 34.
    Hohenbichler M, Gollwitzer S, Kruse W, Rackwitz R (1987) New light on first and second-order reliability methods. Struct Saf 4:267–284CrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2017

Authors and Affiliations

  • Hossein Beheshti Nezhad
    • 1
  • Mahmoud Miri
    • 1
    Email author
  • Mohammad Reza Ghasemi
    • 1
  1. 1.Department of Civil EngineeringUniversity of Sistan and BaluchestanZahedanIran

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