Evaluation of the Performance of Methods based on Reliability and Simulation Methods in Calculating the Reliability of Structures

Document Type : Original Research

Authors
K. yazdannejad 1
P. Ebadi 2
A. rashidi 3
1 Postdoc Researcher - Department of Civil Engineering - University of Kurdistan
2 Assistant Professor, Faculty of Engineering, Department of Civil Engineering, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran
3 Master of Structural Engineering, Faculty of Engineering, Department of Civil Engineering, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran
10.22034/23.6.3
Abstract
Calculating the failure probability of structural problems with linear boundary condition functions is usually done at a low level and by first-order methods due to simple concepts and the need for few calculations. These methods are only suitable for providing an estimate of the probability of structural failure, and especially when the function expressing the performance of the structure is linear, they are accurate in providing the final answer. But when the limit function is nonlinear, due to inherent problems in this method, they are unable to accurately estimate the safety level of the structure. For such problems, it is necessary to use accurate methods of estimating the probability of failure, such as simulation

methods. The use of concepts in the first and second order methods of reliability along with the use of an optimization algorithm will reduce the volume of calculations, but this factor causes assumptions and simplifications, derivation of functions and estimating the sensitivity of failure probability is also a part of the structure design process. It can be proven that for many design problems with nonlinear boundary condition function, the answer provided by these methods will not satisfy the probabilistic constraints of the problem, or the answer provided is not the most economical design option. Also, many existing

methods in this group are unable to provide answers for problems with low failure probability, especially when the variables of the problem have non-normal density functions. Therefore, the present study has investigated the performance of these methods in dealing with various structural problems, and the strengths and weaknesses of each method are discussed. Three different issues have been studied in this research with seven analytical and simulation method, to achieve this goal. The first problem is to verify the results. In this case, the failure probability of a reinforced concrete beam was calculated by the Monte Carlo Simulation (MCS) and compared with the results obtained from the precise gradient method used in previous studies. The results of this problem showed a 0.5% error in the results, indicating the accuracy of the responses. The existence of very small differences between the results obtained from Monte Carlo and the results of previous researchers in estimating the integral of failure probability related to the discussed problems, indicates the high accuracy of the Monte Carlo method, and it is possible to use the results obtained from Monte Carlo as a suitable criterion in the analysis of these problems. used to compare the results. Also, analysis of two problems including three-span steel beam, two-degree-of-freedom seismic system using seven methods including MCS, SS, IS, LS, WSM, FORM and SORM were also put on the agenda. The results indicate that SS has high accuracy in solving nonlinear and complex problems. WSM has shown a significant decrease in the number of function calls. The LS method has a great performance in calculating the reliability of problems with a low failure probability. Therefore, in general, it can be stated that the first-order method (FORM) is the simplest safety estimation method (with low accuracy for non-linear functions) and simulation methods are the most accurate methods (with conceptual complexity or high calculations).

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منابع
[1] F. MiarNaeimi, G. Azizyan, M. Rashki, Reliability sensitivity analysis method based on subset simulation hybrid techniques, Appl. Math. Model. 75 (2019) 607–626.
[2] A. Abdollahi, M.A. Moghaddam, S.A.H. Monfared, M. Rashki, Y. Li, Subset simulation method including fitness-based seed selection for reliability analysis, Eng. Comput. (2020) 1–17.
[3] J. Zhang, M. Xiao, L. Gao, A new method for reliability analysis of structures with mixed random and convex variables, Appl. Math. Model. 70 (2019) 206–220.
[4] P. Hosseini, S.H. Ghasemi, M. Jalayer, A.S. Nowak, Performance-based reliability analysis of bridge pier subjected to vehicular collision: Extremity and failure, Eng. Fail. Anal. 106 (2019) 104176.
[5] T. Zhang, Robust reliability-based optimization with a moment method for hydraulic pump sealing design, Struct. Multidiscip. Optim. 58 (2018) 1737–1750.
[6] M. Bagheri, M. Miri, N. Shabakhty, Fuzzy time dependent structural reliability analysis using alpha level set optimization method based on genetic algorithm, J. Intell. Fuzzy Syst. 32 (2017) 4173–4182.
[7] M. Rashki, M. Miri, M.A. Moghaddam, A new efficient simulation method to approximate the probability of failure and most probable point, Struct. Saf. 39 (2012) 22–29.
[8] R.E. Melchers, Importance sampling in structural systems, Struct. Saf. 6 (1989) 3–10.
[9] S.-K. Au, J.L. Beck, Estimation of small failure probabilities in high dimensions by subset simulation, Probabilistic Eng. Mech. 16 (2001) 263–277.
[10] P.S. Koutsourelakis, H.J. Pradlwarter, G.I. Schuëller, Reliability of structures in high dimensions, part I: Algorithms and applications, Probabilistic Eng. Mech. 19 (2004) 409–417. https://doi.org/10.1016/j.probengmech.2004.05.001.
[11] A.M. Hasofer, N.C. Lind, Exact and invariant second-moment code format, J. Eng. Mech. Div. 100 (1974) 111–121.
[12] R. Rackwitz, B. Flessler, Structural reliability under combined random load sequences, Comput. Struct. 9 (1978) 489–494.
[13] X. Chen, N.C. Lind, Fast probability integration by three-parameter normal tail approximation, Struct. Saf. 1 (1982) 269–276.
[14] Y.-G. Zhao, T. Ono, Moment methods for structural reliability, Struct. Saf. 23 (2001) 47–75.
[15] R. Chowdhury, B.N. Rao, Structural failure probability estimation using HDMR and FFT, Electron J Struct Eng. 8 (2008) 67–76.
[16] D. Wei, S. Rahman, A multi-point univariate decomposition method for structural reliability analysis, Int. J. Press. Vessel. Pip. 87 (2010) 220–229.
[17] D. Yang, Chaos control for numerical instability of first order reliability method, Commun. Nonlinear Sci. Numer. Simul. 15 (2010) 3131–3141.
[18] M. Jirgl, Z. Bradac, K. Stibor, M. Havlikova, Reliability analysis of systems with a complex structure using Monte Carlo approach, IFAC Proc. Vol. 46 (2013) 461–466.
[19] D.-Q. Li, F.-P. Zhang, Z.-J. Cao, W. Zhou, K.-K. Phoon, C.-B. Zhou, Efficient reliability updating of slope stability by reweighting failure samples generated by Monte Carlo simulation, Comput. Geotech. 69 (2015) 588–600.
[20] B. Xu, L. Zhao, W. Li, J. He, Y.M. Xie, Dynamic response reliability based topological optimization of continuum structures involving multi-phase materials, Compos. Struct. 149 (2016) 134–144.
[21] X.-Y. Zhou, P.D. Gosling, Z. Ullah, L. Kaczmarczyk, C.J. Pearce, Stochastic multi-scale finite element based reliability analysis for laminated composite structures, Appl. Math. Model. 45 (2017) 457–473.
[22] C. Li, S. Mahadevan, An efficient modularized sample-based method to estimate the first-order Sobol׳ index, Reliab. Eng. Syst. Saf. 153 (2016) 110–121.
]23[ ف. میارنعیمی, غ. عزیزیان, م. راشکی, بهینه‌سازی سازه‌های هیدرولیکی بر مبنای قابلیت اطمینان با استفاده از الگوریتمی نو, 1398.
[24] A.S. Nowak, K.R. Collins, Reliability of structures, CRC Press, 2012.
[25] M. Rashki, Hybrid control variates-based simulation method for structural reliability analysis of some problems with low failure probability, Appl. Math. Model. 60 (2018) 220–234.
[26] N. Metropolis, S. Ulam, The monte carlo method, J. Am. Stat. Assoc. 44 (1949) 335–341.
[27] N.S. Hamzehkolaei, M. Miri, M. Rashki, An enhanced simulation-based design method coupled with meta-heuristic search algorithm for accurate reliability-based design optimization, Eng. Comput. 32 (2016) 477–495.
[28] X. Li, Z. Chen, W. Ming, H. Qiu, J. Ma, W. He, An efficient moving optimal radial sampling method for reliability-based design optimization, Int. J. Performability Eng. 13 (2017) 864–877. https://doi.org/10.23940/ijpe.17.06.p8.864877.
[29] V. Dubourg, B. Sudret, Meta-model-based importance sampling for reliability sensitivity analysis, Struct. Saf. 49 (2014) 27–36.
[30] M.A. Shayanfar, M.A. Barkhordari, M.A. Roudak, Locating design point in structural reliability analysis by introduction of a control parameter and moving limited regions, Int. J. Mech. Sci. 126 (2017) 196–202. https://doi.org/10.1016/j.ijmecsci.2017.04.003.
[31] H.-S. Li, Z.-J. Cao, Matlab codes of Subset Simulation for reliability analysis and structural optimization, Struct. Multidiscip. Optim. 54 (2016) 391–410.
[32] T.M. Aljohani, M.J. Beshir, Matlab code to assess the reliability of the smart power distribution system using monte carlo simulation, J. Power Energy Eng. 5 (2017) 30–44.
[33] B. Keshtegar, S. Chakraborty, A hybrid self-adaptive conjugate first order reliability method for robust structural reliability analysis, Appl. Math. Model. 53 (2018) 319–332.
[34] X. Huang, Y. Li, Y. Zhang, X. Zhang, A new direct second-order reliability analysis method, Appl. Math. Model. 55 (2018) 68–80.
[35] B.S. Dhillon, Reliability, quality, and safety for engineers, CRC Press, 2004.
[36] B. Keshtegar, O. Kisi, M5 model tree and Monte Carlo simulation for efficient structural reliability analysis, Appl. Math. Model. 48 (2017) 899–910.
[37] S.K. Au, J. Ching, J.L. Beck, Application of subset simulation methods to reliability benchmark problems, Struct. Saf. 29 (2007) 183–193.
[38] B. Keshtegar, O. Kisi, RM5Tree: Radial basis M5 model tree for accurate structural reliability analysis, Reliab. Eng. Syst. Saf. 180 (2018) 49–61.
Modares Civil Engineering journal
Volume 23, Issue 6
November and December 2023
Pages 35-51