Adapted design of experiments for dimension decomposition-based meta-model in structural reliability analysis

Document Type : Article


1 Department of Civil Engineering, Alzahra University, Tehran, P.O. Box 1993893973, Iran.

2 Department of Civil Engineering, Shiraz University of Technology, Shiraz, Iran.

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


Reliability analysis of structures is often problematic for the structures with nonlinear and complex limit state functions (LSF). For these cases, simulation methods often provide accurate failure probability, but with high number of structure’s LSF analysis. This paper presents an efficient combination of Monte Carlo Simulation (MCS) method and Univariate Dimension Reduction (UDR) based Meta-model to approximate the failure probability of structures with few LSFs evaluation. For this purpose, the design of experiment used in the Meta model is adapted such that the expected failure samples in MCS being approximated with higher accuracy. Several numerical and engineering reliability problems are solved by the proposed approach and the results are verified by MCS. Results show that the proposed approach highly reduces the required number of structural analysis to provide proper results.


Main Subjects

1. Ditlevsen, O. and Madsen, H.O., Structural Reliability Methods, New York, Wiley, 178, pp. 18-25 (1996). 2. Hasofer, A.M. and Lind, N.C. Exact and invariant second-moment code format", Journal of the Engineering Mechanics Division, 100(1), pp. 111-121 (1974). 3. Rackwitz, R. and Flessler, B. Structural reliability under combined random load sequences", Computers & Structures, 9(5), pp. 489-494 (1978). 4. Der Kiureghian, A., Lin, H.Z., and Hwang, S.J. Second-order reliability approximations", Journal of Engineering Mechanics, 113(8), pp. 1208-1225 (1987). 5. Liu, P.L. and Der Kiureghian, A. Optimization algorithms for structural reliability", Structural Safety, 9(3), pp. 161-177 (1991). 6. Wang, L. and Grandhi, R.V. Safety index calculation using intervening variables for structural reliability analysis", Computers & Structures, 59(6), pp. 1139- 1148 (1996). 7. Metropolis, N. and Ulam, S. The Monte Carlo method", Journal of the American Statistical Association, 44(247), pp. 335-341 (1949). 8. Yazdani, A., Nicknam, A., Khanzadi, M., and Motaghed, S. An arti_cial statistical method to estimate seismicity parameter from incomplete earthquake catalogs: A case study in metropolitan Tehran, Iran", Scientia Iranica, Transactions A, Civil Engineering, 22(2), p. 400 (2015). 9. Zuev, K. Subset simulation method for rare event estimation: An Introduction", ArXiv preprint arXiv: 1505.03506 (2015). 10. Wang, Z. and Song, J. Cross-entropy-based adaptive importance sampling using von Mises- Fisher mixture for high dimensional reliability analysis", Struct Saf, 59, pp. 42-52 (2016). 11. Fan, H. and Liang, R. Importance sampling based algorithm for e_cient reliability analysis of axially loaded piles", Computers and Geotechnics, 65, pp. 278-284 (2015). 12. Ibrahim, Y. Observations on applications of importance sampling in structural reliability analysis", Struct Safety, 9(4), pp. 269-281 (1991). 3070 M. Rakhshani Mehr et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 3060{3071 13. Nie, J. and Ellingwood, B.R. Directional methods for structural reliability analysis", Struct Safety, 22(3), pp. 233-249 (2000). 14. Depina, I., Le, T.M.H., Fenton, G., and Erikson, G. Reliability analysis with metamodel line sampling", Struct Saf, 60, pp. 1-15 (2016). 15. Pradlwarter, H.J., Schueller, G.I., Koutsourelakis, P.S., and Charmpis, D.C. Application of line sampling simulation method to reliability benchmark problems", Struct Safety, 29(3), pp. 208-221 (2007). 16. Rashki, M., Miri, M., and Moghaddam, M.A. A new e_cient simulation method to approximate the probability of failure and most probable point", Structural Safety, 39, pp. 22-29 (2012). 17. Au, S.K. and Beck, J.L. Estimation of small failure probabilities in high dimensions by subset simulation", Probabilistic Engineering Mechanics, 16(4), pp. 263- 277 (2001). 18. Ghanem, R. and Spanos, P.D. Polynomial chaos in stochastic _nite elements", Journal of Applied Mechanics, 57(1), pp. 197-202 (1990). 19. Kami_nski, M. and _Swita, P. Structural stability and reliability of the underground steel tanks with the stochastic _nite element method", Archives of Civil and Mechanical Engineering, 15(2), pp. 593-602 (2015). 20. Ghavidel, A., Mousavi, S.R., and Rashki, M. The e_ect of FEM mesh density on the failure probability analysis of structures", KSCE Journal of Civil Engineering, 22(7), pp. 2370-2383 (2018). 21. Gong, J.X. and Yi, P. A robust iterative algorithm for structural reliability analysis", Structural and Multidisciplinary Optimization, 43(4), pp. 519-527 (2011). 22. Johari, A., Momeni, M., and Javadi, A.A. An analytical solution for reliability assessment of pseudostatic stability of rock slopes using jointly distributed random variables method", Iranian Journal of Science and Technology Transactions of Civil Engineering, 39, pp. 351-363 (2015). 23. Hasofer, A.M. and Lind, N.C. Exact and invariant second-moment code format", Journal of the Engineering Mechanics Division, 100(1), pp. 111-121 (1974). 24. Keshtegar, B. and Miri, M. Reliability analysis of corroded pipes using conjugate HL-RF algorithm based on average shear stress yield criterion", Engineering Failure Analysis, 46, pp. 104-117 (2014). 25. Johari, A., Mousavi, S., and Nejad, A.H. A seismic slope stability probabilistic model based on Bishop's method using analytical approach", Scientia Iranica. Transactions A, Civil Engineering, 22(3), p. 728 (2015). 26. Rackwitz, R. and Flessler, B. Structural reliability under combined random load sequences", Computers & Structures, 9(5), pp. 489-494 (1978). 27. Santosh, T.V., Saraf, R.K., Ghosh, A.K., and Kushwaha, H.S. Optimum step length selection rule in modi_ed HL-RF method for structural reliability", International Journal of Pressure Vessels and Piping, 83(10), pp. 742-748 (2006). 28. Yang, D. Chaos control for numerical instability of _rst order reliability method", Communications in Nonlinear Science and Numerical Simulation, 15(10), pp. 3131-3141 (2010). 29. Zhou, W., Gong, C., and Hong, H.P. New perspective on application of _rst-order reliability method for estimating system reliability", Journal of Engineering Mechanics, 143(9), p. 04017074 (2017). 30. Yun, W., Lu, Z., Jiang, X., and Zhao, L.F. Maximum probable life time analysis under the required timedependent failure probability constraint and its metamodel estimation", Structural and Multidisciplinary Optimization, 55(4), pp. 1439-1451 (2017). 31. Bhadra, A. and Ionides, E.L. Adaptive particle allocation in iterated sequential Monte Carlo via approximating meta-models", Statistics and Computing, 26(1- 2), pp. 393-407 (2016). 32. Dengiz, B., _I_c, Y.T., and Belgin, O. A meta-model based simulation optimization using hybrid simulationanalytical modeling to increase the productivity in automotive industry", Mathematics and Computers in Simulation, 120, pp. 120-128 (2016). 33. Sudret, B. Meta-models for structural reliability and uncertainty quanti_cation", arXiv preprint arXiv: 1203.2062 (2012). 34. Cadini, F., Santos, F., and Zio, E. An improved adaptive kriging-based importance technique for sampling multiple failure regions of low probability", Reliability Engineering & System Safety, 131, pp. 109-117 (2014). 35. Echard, B., Gayton, N., and Lemaire, M. AK-MCS: an active learning reliability method combining kriging and Monte Carlo simulation", Structural Safety, 33(2), pp. 145-154 (2011). 36. Bucher, C.G. and Bourgund, U. A fast and e_cient response surface approach for structural reliability problems", Structural Safety, 7(1), pp. 57-66 (1990). 37. Nguyen, X.S., Sellier, A., Duprat, F., and Pons, G. Adaptive response surface method based on a double weighted regression technique", Probabilistic Engineering Mechanics, 24(2), pp. 135-143 (2009). 38. Kang, S.C., Koh, H.M., and Choo, J.F. An ef- _cient response surface method using moving least squares approximation for structural reliability analysis", Probabilistic Engineering Mechanics, 25(4), pp. 365-371 (2010). 39. Allaix, D.L. and Carbone, V.I. An improvement of the response surface method", Structural Safety, 33(2), pp. 165-172 (2011). 40. Cai, W. A dimension reduction algorithm preserving both global and local clustering structure", Knowledge-Based Systems, 118, pp. 191-203 (2017). 41. Xu, H. and Rahman, S. A moment-based stochastic method for response moment and reliability analysis", M. Rakhshani Mehr et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 3060{3071 3071 In Proceedings of 2nd MIT Conference on Computational Fluid and Solid Mechanics, pp. 17-20 (2003). 42. Xu, H. and Rahman, S. A generalized dimensionreduction method for multidimensional integration in stochastic mechanics", International Journal for Numerical Methods in Engineering, 61(12), pp. 1992-2019 (2004). 43. Huang, B. and Du, X. Uncertainty analysis by dimension reduction integration and saddle point approximations", Journal of Mechanical Design, 128(1), pp. 26-33 (2006). 44. Lee, I., Choi, K.K., and Du, L. Alternative methods for reliability-based robust design optimization including dimension reduction method", In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 1235-1246 (2006). 45. GhohaniArab, H. and Ghasemi, M.R. A fast and robust method for estimating the failure probability of structures", P I Civil Eng Str B, 168(4), pp. 298-309 (2015). 46. Lv, Z., Lu, Z., and Wang, P. A new learning function for Kriging and its applications to solve reliability problems in engineering", Computers & Mathematics with Applications, 70(5), pp. 1182-1197 (2015). 47. Zou, T., Mahadevan, S., Mourelatos, Z., and Meernik, P. Reliability analysis of automotive body-door subsystem", Reliability Engineering & System Safety, 78(3), pp. 315-324 (2002). 48. Gavin, H.P. and Yau, S.C. High-order limit state functions in the response surface method for structural reliability analysis", Structural Safety, 30(2), pp. 162- 179 (2008). 49. Dubourg, V. and Sudret, B. Meta-model-based importance sampling for reliability sensitivity", Structural Safety, 49, pp. 27-36 (2014). 50. Wang, P., Lu, Z., and Tang, Z. An application of the Kriging method in global sensitivity analysis with parameter uncertainty", Applied Mathematical Modelling, 37, pp. 6543-6555 (2013).