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Non-gradient probabilistic Gaussian global-best harmony search optimization for first-order reliability method

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Abstract

The performances of first-order reliability method (FORM) are highly important owing to its accuracy and efficiency in the structural reliability analysis. In the gradient methods-based sensitivity analysis, the iterative formula of FORM is established using the gradient vector which it may not compute for some structural problems with discrete or non-continuous performance functions. In this study, the probabilistic Gaussian global-best harmony search (GGHS) optimization is implemented to search for the most probable point in the structural reliability analysis. The proposed GGHS approach for reliability analyses is performed based on two main adjusted processes using the random Gaussian generation. The accuracy and efficiency of the GGHS are compared with original harmony search (HS) algorithm and three modified versions of HS as improved HS, global-best HS, and improved global-best HS based on a mathematical and three structural problems. The obtained results illustrated that the PGGHS is more efficient than other modified versions of HS and provides the accurate results for discrete performance functions compared to original FORM-based gradient method.

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References

  1. Jiang C, Qiu H, Li X, Chen Z, Gao L, Li P (2019) Iterative reliable design space approach for efficient reliability-based design optimization. Eng Comput. https://doi.org/10.1007/s00366-018-00691-z

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. Keshtegar B (2017) A modified mean value of performance measure approach for reliability-based design optimization. Arab J Sci Eng 42(3):1093–1101

    Google Scholar 

  4. 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

    MathSciNet  MATH  Google Scholar 

  5. Jiang C, Qiu H, Yang Z, Chen L, Gao L, Li P (2019) A general failure-pursuing sampling framework for surrogate-based reliability analysis. Reliab Eng Syst Saf 183:47–59

    Google Scholar 

  6. Zhu S-P, Liu Q, Peng W, Zhang X-C (2018) Computational-experimental approaches for fatigue reliability assessment of turbine bladed disks. Int J Mech Sci 142:502–517

    Google Scholar 

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

    Google Scholar 

  8. 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 

  9. Keshtegar B, Kisi O (2018) RM5Tree: radial basis M5 model tree for accurate structural reliability analysis. Reliab Eng Syst Saf 180:49–61

    Google Scholar 

  10. Seghier El Amine Ben, Keshtegar MB, Correia JAFO, Lesiuk G, De Jesus AMP (2019) Reliability analysis based on hybrid algorithm of M5 model tree and Monte Carlo simulation for corroded pipelines: case of study X60 Steel grade pipes. Eng Fail Anal 97:793–803. https://doi.org/10.1016/j.engfailanal.2019.01.061

    Article  Google Scholar 

  11. Au S-K, Beck JL (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech 16(4):263–277

    Google Scholar 

  12. Hamzehkolaei NS, Miri M, Rashki M (2018) New simulation-based frameworks for multi-objective reliability-based design optimization of structures. Appl Math Model 62:1–20. https://doi.org/10.1016/j.apm.2018.05.015

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  14. Engelund S, Rackwitz R (1993) A benchmark study on importance sampling techniques in structural reliability. Struct Saf 12(4):255–276

    Google Scholar 

  15. Dey A, Mahadevan S (1998) Ductile structural system reliability analysis using adaptive importance sampling. Struct Saf 20(2):137–154

    Google Scholar 

  16. Nie J, Ellingwood BR (2000) Directional methods for structural reliability analysis. Struct Saf 22(3):233–249

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  19. 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 

  20. 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 

  21. Keshtegar B, Meng Z (2017) A hybrid relaxed first-order reliability method for efficient structural reliability analysis. Struct Saf 66:84–93

    Google Scholar 

  22. 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 

  23. 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  MATH  Google Scholar 

  24. 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 

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

    MathSciNet  MATH  Google Scholar 

  26. Ghohani Arab H, Rashki M, Rostamian M, Ghavidel A, Shahraki H, Keshtegar B (2018) Refined first-order reliability method using cross-entropy optimization method. Eng Comput. https://doi.org/10.1007/s00366-018-0680-9

    Article  Google Scholar 

  27. 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 

  28. 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 

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

    Google Scholar 

  30. Huang X, Li Y, Zhang Y, Zhang X (2018) A new direct second-order reliability analysis method. Appl Math Model. https://doi.org/10.1016/j.apm.2017.10.026

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  33. Keshtegar B, Lee I (2016) Relaxed performance measure approach for reliability-based design optimization. Struct Multidiscip Optim 54(6):1439–1454

    MathSciNet  Google Scholar 

  34. 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 

  35. Keshtegar B, Hao P (2017) A hybrid self-adjusted mean value method for reliability-based design optimization using sufficient descent condition. Appl Math Model 41:257–270

    MathSciNet  MATH  Google Scholar 

  36. Meng Z, Keshtegar B (2019) Adaptive conjugate single-loop method for efficient reliability-based design and topology optimization. Comput Methods Appl Mech Eng 344:95–119. https://doi.org/10.1016/j.cma.2018.10.009

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  38. 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 

  39. Keshtegar B, Baharom S, El-Shafie A (2018) Self-adaptive conjugate method for a robust and efficient performance measure approach for reliability-based design optimization. Eng Comput 34(1):187–202

    Google Scholar 

  40. 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  MATH  Google Scholar 

  41. 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 

  42. Meng Z, Zhang D, Li G, Yu B (2019) An importance learning method for non-probabilistic reliability analysis and optimization. Struct Multidiscip Optim 59(4):1255–1271

    Google Scholar 

  43. 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. https://doi.org/10.1016/j.compstruc.2014.08.011

    Article  Google Scholar 

  44. Meng Z, Yang D, Zhou H, Wang BP (2018) Convergence control of single loop approach for reliability-based design optimization. Struct Multidiscip Optim 57(3):1079–1091

    MathSciNet  Google Scholar 

  45. Meng Z, Zhang D, Liu Z, Li G (2018) An adaptive directional boundary sampling method for efficient reliability-based design optimization. J Mech Des 140(12):121406

    Google Scholar 

  46. Keshtegar B, Hao P, Meng Z (2017) A self-adaptive modified chaos control method for reliability-based design optimization. Struct Multidiscip Optim 55(1):63–75

    MathSciNet  Google Scholar 

  47. Keshtegar B, Hao P (2018) A hybrid descent mean value for accurate and efficient performance measure approach of reliability-based design optimization. Comput Methods Appl Mech Eng 336:237–259

    MathSciNet  MATH  Google Scholar 

  48. Seghier El Amine Ben, Keshtegar MB, Elahmoune B (2018) Reliability analysis of low, mid and high-grade strength corroded pipes based on plastic flow theory using adaptive nonlinear conjugate map. Eng Fail Anal 90:245–261. https://doi.org/10.1016/j.engfailanal.2018.03.029

    Article  Google Scholar 

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

    MATH  Google Scholar 

  50. 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 

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

    Google Scholar 

  52. J-x Gong, Yi P, Zhao N (2014) Non-gradient–based algorithm for structural reliability analysis. J Eng Mech 140(6):04014029

    Google Scholar 

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

    Google Scholar 

  54. Santosh T, Saraf R, Ghosh A, Kushwaha H (2006) Optimum step length selection rule in modified HL–RF method for structural reliability. Int J Press Vessels Pip 83(10):742–748

    Google Scholar 

  55. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68

    Google Scholar 

  56. Geem ZW, Choi J-Y (2007) Music composition using harmony search algorithm. In: workshops on applications of evolutionary computation, Springer, pp 593–600

  57. Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579

    MathSciNet  MATH  Google Scholar 

  58. Wang C-M, Huang Y-F (2010) Self-adaptive harmony search algorithm for optimization. Expert Syst Appl 37(4):2826–2837

    Google Scholar 

  59. Omran MG, Mahdavi M (2008) Global-best harmony search. Appl Math Comput 198(2):643–656

    MathSciNet  MATH  Google Scholar 

  60. Zou D, Gao L, Wu J, Li S, Li Y (2010) A novel global harmony search algorithm for reliability problems. Comput Ind Eng 58(2):307–316

    Google Scholar 

  61. Zou D, Gao L, Wu J, Li S (2010) Novel global harmony search algorithm for unconstrained problems. Neurocomputing 73(16–18):3308–3318

    Google Scholar 

  62. El-Abd M (2013) An improved global-best harmony search algorithm. Appl Math Comput 222:94–106

    MATH  Google Scholar 

  63. Keshtegar B, Hao P, Wang Y, Li Y (2017) Optimum design of aircraft panels based on adaptive dynamic harmony search. Thin Walled Struct 118:37–45

    Google Scholar 

  64. Keshtegar B, Ozbakkaloglu T, Gholampour A (2017) Modeling the behavior of FRP-confined concrete using dynamic harmony search algorithm. Eng Comput 33(3):415–430

    Google Scholar 

  65. 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 

  66. White DW, Jeong WY, Toğay O (2016) Comprehensive stability design of planar steel members and framing systems via inelastic buckling analysis. Int J Steel Struct 16(4):1029–1042

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Sustainable Developments in Civil Engineering Research Group, Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Zaher Mundher Yaseen

  2. Department of Mechanical Engineering, Technical Collage of Mechanical Engineering, Benghazi, Libya

    Mohammed Suleman Aldlemy

  3. Department of Electrical and Electronic Engineering, University of Sistan and Baluchestan, Zahedan, Iran

    Mahmoud Oukati Sadegh

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  1. Zaher Mundher Yaseen
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  2. Mohammed Suleman Aldlemy
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Yaseen, Z.M., Aldlemy, M.S. & Oukati Sadegh, M. Non-gradient probabilistic Gaussian global-best harmony search optimization for first-order reliability method. Engineering with Computers 36, 1189–1200 (2020). https://doi.org/10.1007/s00366-019-00756-7

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