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Conjugate finite-step length method for efficient and robust structural reliability analysis

  • Keshtegar, Behrooz (Department of Civil Engineering, Faculty of Engineering, University of Zabol)
  • Received : 2016.08.23
  • Accepted : 2017.11.29
  • Published : 2018.02.25

Abstract

The Conjugate Finite-Step Length" (CFSL) algorithm is proposed to improve the efficiency and robustness of first order reliability method (FORM) for reliability analysis of highly nonlinear problems. The conjugate FORM-based CFSL is formulated using the adaptive conjugate search direction based on the finite-step size with simple adjusting condition, gradient vector of performance function and previous iterative results including the conjugate gradient vector and converged point. The efficiency and robustness of the CFSL algorithm are compared through several nonlinear mathematical and structural/mechanical examples with the HL-RF and "Finite-Step-Length" (FSL) algorithms. Numerical results illustrated that the CFSL algorithm performs better than the HL-RF for both robust and efficient results while the CFLS is as robust as the FSL for structural reliability analysis but is more efficient.

Keywords

Acknowledgement

Supported by : University of Zabol

References

  1. Du, X., (2010), "System reliability analysis with Saddlepoint approximation", Struct. Multidiscip. Optim., 42(2), 193-208. https://doi.org/10.1007/s00158-009-0478-x
  2. Gong, J.X. and Yi, P. (2011), "A robust iterative algorithm for structural reliability analysis", Struct. Multidisc. Optim., 43, 519-527. https://doi.org/10.1007/s00158-010-0582-y
  3. Hasofer, A.M. and Lind, N.C. (1974), "Exact and invariant second-moment code format", ASCE J. Eng. Mech. Div., 100(1), 111-121.
  4. Keshtegar, B. and Bagheri, M. (2017), "Fuzzy relaxed-finite step size method to enhance the instability of the fuzzy first order reliability method using conjugate discrete map", Nonlin. Dyn.
  5. Keshtegar, B. and Chakraborty, S. (2018), "A hybrid self-adaptive conjugate first order reliability method for robust structural reliability analysis", Appl. Math. Modell., 53(1), 319-332. https://doi.org/10.1016/j.apm.2017.09.017
  6. Keshtegar, B. and Meng, Z. (2017), "A hybrid relaxed first-order reliability method for efficient structural reliability analysis", Struct. Safety, 66(1), 84-93. https://doi.org/10.1016/j.strusafe.2017.02.005
  7. Keshtegar, B. (2016a), "Chaotic conjugate stability transformation method for structural reliability analysis", Comput. Meth. Appl. Mech. Eng., 310(1), 866-885. https://doi.org/10.1016/j.cma.2016.07.046
  8. Keshtegar, B. (2016b), "Stability iterative method for structural reliability analysis using a chaotic conjugate map", Nonlin. Dyn., 84(4), 2161-2174. https://doi.org/10.1007/s11071-016-2636-1
  9. Keshtegar, B. (2017a), "A hybrid conjugate finite-step length method for robust and efficient reliability analysis", Appl. Math. Modell., 45(1), 226-237. https://doi.org/10.1016/j.apm.2016.12.027
  10. Keshtegar, B. (2017b), "Enriched FR conjugate search directions for robust and efficient structural reliability analysis", Eng. Comput., 1-16.
  11. Keshtegar, B. (2017c), "Limited conjugate gradient method for structural reliability analysis", Eng. Comput., 33(3), 621-709. https://doi.org/10.1007/s00366-016-0493-7
  12. Keshtegar, B. and Kisi, O. (2017), "M5 model tree and Monte Carlo simulation for efficient structural reliability analysis", Appl. Math. Modell., 48(1), 899-910 https://doi.org/10.1016/j.apm.2017.02.047
  13. Keshtegar, B. and Miri, M. (2014), "Introducing conjugate gradient optimization for modified HL-RF method", Eng. Comput., 31(4), 775-790. https://doi.org/10.1108/EC-09-2012-0225
  14. Kiureghian, A.D. and Stefano, M.D. (1991), "Efficient algorithm for second-order reliability analysis", J. Eng. Mech., 117(12), 2904-2923. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:12(2904)
  15. Koduru, S.D. and Haukaas, T. (2010), "Feasibility of FORM in finite element reliability analysis", Struct. Safety, 32(1), 145-153. https://doi.org/10.1016/j.strusafe.2009.10.001
  16. Liu, D. and Peng, Y. (2012), "Reliability analysis by mean-value second-order expansion", J. Mech. Des., 134(6), 1-8
  17. Liu, P.L. and Der Kiureghian, A. (1991), "Optimization algorithms for structural reliability", Struct. Safety, 9(3), 161-177. https://doi.org/10.1016/0167-4730(91)90041-7
  18. Meng, Z., Li, G., Yang, D. and Zhan, L. (2017), "A new directional stability transformation method of chaos control for first order reliability analysis", Struct. Multidiscipl. Optim., 55(2), 601-612. https://doi.org/10.1007/s00158-016-1525-z
  19. Pericaro, G.A., Santos, S.R., Ribeiro, A.A. and Matioli, L.C. (2015), "HLRF-BFGS optimization algorithm for structural reliability", Appl. Math. Modell., 39(7), 2025-2035. https://doi.org/10.1016/j.apm.2014.10.024
  20. Rackwitz, R. and Fiessler, B. (1978), "Structural reliability under combined load sequences", Comput. Struct., 9(8), 489-494. https://doi.org/10.1016/0045-7949(78)90046-9
  21. Rao, B.N. and Chowdhury, R. (2009), "Enhanced high-dimensional model representation for reliability analysis", J. Numer. Meth. Eng., 77(5), 719-750. https://doi.org/10.1002/nme.2440
  22. Santos, S.R., Matioli, L.C. and Beck, A.T. (2012), "New optimization algorithms for structural reliability analysis", Comput. Model. Eng. Sci., 83(1), 23-56.
  23. Santosh, T.V., Saraf, R.K., Ghosh, A.K. and Kushwaha, H.S. (2006), "Optimum step length selection rule in modified HL-RF method for structural reliability", J. Press Vess. Pip., 83, 742-748. https://doi.org/10.1016/j.ijpvp.2006.07.004
  24. Wang, L.P. and Grandhi, R.V. (1994), "Efficient safety index calculation for structural reliability analysis", Comput. Struct., 52(1), 103-111. https://doi.org/10.1016/0045-7949(94)90260-7
  25. Wang, L.P. and Grandhi, R.V. (1996), "Safety index calculation using intervening variables for structural reliability analysis", Comput. Struct., 59(6), 1139-1148. https://doi.org/10.1016/0045-7949(96)00291-X
  26. Xiao, N.C., Huang, H.Z., Wang, Z., Pang, Y. and He, L. (2011), "Reliability sensitivity analysis for structural systems in interval probability form", Struct. Multidiscipl. Optim., 44, 691-705. https://doi.org/10.1007/s00158-011-0652-9
  27. Yang, D. (2010), "Chaos control for numerical instability of first order reliability method", Commun. Nonlin. Sci. Numer. Simulat., 5, 3131-3141.

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