Structural Engineering and Mechanics

  • 제92권1호
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  • Pages.111-120
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  • 2024
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Optimal Latinized partially stratified sampling for structural reliability analysis

  • 투고 : 2024.03.25
  • 심사 : 2024.09.23
  • 발행 : 2024.10.10
⟨ 이전 논문 다음 논문 ⟩

초록

Sampling methods are powerful approaches to solving the problems of structural reliability analysis and estimating the failure probability of structures. In this paper, a new sampling method is proposed offering lower variance and lower computational cost for complex and high-dimensional problems. The method is called Optimal Latinized partially stratified sampling (OLPSS) as it is based upon the Latinized Partially Stratified Sampling (LPSS) which itself is based on merging Stratified Sampling (SS) and Latin Hypercube Sampling (LHS) algorithms. While LPSS has a low variance, it may suffer from a lack of good space-filling of its generated samples in some cases. In the OLPSS, this issue has been resolved by employing a new columnwise-pairwise exchange optimization procedure for sample generation. The efficiency of the OLPSS has been tested and reported under several benchmark mathematical functions and structural examples including structures with a large number of variables (e.g., a structure with 67 variables). The proposed method provides highly accurate estimates of the failure probability of structures with a significantly lower variance relative to the Monte Carlo simulations, Latin Hypercube, and standard LPSS.

키워드

참고문헌

  1. Arora, R.K. and Banerjee, S. (2023), "Reliability-based approach for fragility assessment of bridges under floods", Struct. Eng. Mech., 88(4), 311. https://doi.org/10.12989/sem.2023.88.4.311.
  2. Bates, S.J., Sienz, J. and Langley, D.S. (2003), "Formulation of the Audze-Eglais uniform Latin hypercube design of experiments", Adv. Eng. Softw., 34(8), 493-506. https://doi.org/10.1016/S0965-9978(03)00042-5.
  3. Chen, R.B., Hsieh, D.N., Hung, Y. and Wang, W. (2013), "Optimizing latin hypercube designs by particle swarm", Stat. Comput., 23(5), 663-676. https://doi.org/10.1007/s11222-012-9363-3.
  4. de Angelis, M., Patelli, E. and Beer, M. (2015), "Advanced line sampling for efficient robust reliability analysis", Struct. Saf., 52, 170-182. https://doi.org/10.1016/j.strusafe.2014.10.002.
  5. Etedali, S. (2022), "Probabilistic study on buildings with MTMD system in different seismic performance levels", Struct. Eng. Mech., 81(4), 429-441. https://doi.org/10.12989/sem.2022.81.4.429.
  6. Ghazaan, M.I. and Saadatmand, F. (2022), "A new performance measure approach with an adaptive step length selection method hybridized with decoupled reliability-based design optimization", Struct., 44(1), 977-987. https://doi.org/10.1016/j.istruc.2022.08.067.
  7. Grosso, A., Jamali, A. and Locatelli, M. (2009), "Finding maximin latin hypercube designs by iterated local search heuristics", Eur. J. Oper. Res., 197(2), 541-547. https://doi.org/10.1016/j.ejor.2008.07.028.
  8. Hadidi, A., Azar, B.F. and Rafiee, A. (2017), "Efficient response surface method for high-dimensional structural reliability analysis", Struct. Saf., 68, 15-27. https://doi.org/10.1016/j.strusafe.2017.03.006.
  9. Johnson, M.E., Moore, L.M. and Ylvisaker, D. (1990), "Minimax and maximin distance designs", J. Stat. Plann. Infer., 26(2), 131-148. https://doi.org/10.1016/0378-3758(90)90122-B.
  10. Khodam, A., Farajzadeh, M.S. and Shayanfar, M. (2023), "A new hybrid method for reliability-based optimal structural design with discrete and continuous variables", Struct. Eng. Mech., 85(3), 369-379. https://doi.org/10.12989/sem.2023.85.3.369.
  11. Liefvendahl, M. and Stocki, R. (2006), "A study on algorithms for optimization of Latin hypercubes", J. Stat. Plann. Infer., 136(9), 3231-3247. https://doi.org/10.1016/j.jspi.2005.01.007.
  12. McKay, M., Beckman, R. and Conover, W. (1979), "Acomparisonof three methodsforselecting valuesofinputvariablesinthe analysisofoutputfrom acomputercode", Technometrics, 21(2), 239-245. https://doi.org/10.1080/00401706.1979.10489755.
  13. Nguyen, T.T. and Dang, V.H. (2022), "Structural reliability analysis using temporal deep learning-based model and importance sampling", Struct. Eng. Mech., 84(3), 323. https://doi.org/10.12989/sem.2022.84.3.323.
  14. Nie, J. and Ellingwood, B.R. (2000), "Directional methods for structural reliability analysis", Struct. Saf., 22(3), 233-249. https://doi.org/10.1016/S0167-4730(00)00014-X.
  15. Pan, G., Ye, P. and Wang, P. (2014), "A novel Latin hypercube algorithm via translational propagation", Scientif. World J., 2014(1), 163949. https://doi.org/10.1155/2014/163949.
  16. Pholdee, N. and Bureerat, S. (2015), "An efficient optimum Latin hypercube sampling technique based on sequencing optimisation using simulated annealing", Int. J. Syst. Sci., 46(10), 1780-1789. https://doi.org/10.1080/00207721.2013.835003.
  17. Rosenbrock, H. (1960), "An automatic method for finding the greatest or least value of a function", Comput. J., 3(3), 175-184. https://doi.org/10.1093/comjnl/3.3.175.
  18. Shang, X., Chao, T., Ma, P. and Yang, M. (2019), "An efficient local search-based genetic algorithm for constructing optimal Latin hypercube design", Eng. Optimiz., https://doi.org/10.1080/0305215X.2019.1584618.
  19. Shields, M.D. and Zhang, J. (2016), "The generalization of Latin hypercube sampling", Reliab. Eng. Syst. Saf., 148, 96-108. https://doi.org/10.1016/j.ress.2015.12.002.
  20. Sun, Y., Meng, X., Long, T. and Wu, Y. (2020), "A fast optimal Latin hypercube design method using an improved translational propagation algorithm", Eng. Optim., 52(7), 1244-1260. https://doi.org/10.1080/0305215X.2019.1642881.
  21. Tang, B. (1993), "Orthogonal array-based Latin hypercubes", J. Am. Stat. Assoc., 88(424), 1392-1397. https://doi.org/10.1080/01621459.1993.10476423.
  22. Xu, J. and Dang, C. (2019), "A novel fractional moments-based maximum entropy method for high-dimensional reliability analysis", Appl. Math. Model., 75, 749-768. https://doi.org/10.1016/j.apm.2019.06.037.
  23. Yaseen, Z.M., Aldlemy, M.S. and Oukati Sadegh, M. (2020), "Non-gradient probabilistic Gaussian global-best harmony search optimization for first-order reliability method", Eng. Comput., 36(4), 1189-1200. https://doi.org/10.1007/s00366-019-00756-7.
  24. Zhang, Y., Sun, Z., Yan, Y., Yu, Z. and Wang, J. (2020), "A novel reliability analysis method based on Gaussian process classification for structures with discontinuous response", Struct. Eng. Mech., 75(6), 771-784. https://doi.org/10.12989/sem.2020.75.6.771.
  25. Zhang, Z., Tao, M., Wang, F., Yang, Y. and Ke, L. (2023), "Study on static and dynamic reliability of main girder of cable-stayed bridge based on subset simulation method", KSCE J. Civil Eng., 27(2), 657-669. https://doi.org/10.1007/s12205-022-0984-6.
  26. Zhu, H., Liu, L., Long, T. and Peng, L. (2012), "A novel algorithm of maximin Latin hypercube design using successive local enumeration", Eng. Optim., 44(5), 551-564. https://doi.org/10.1080/0305215X.2011.591790.