Reliability Analysis of Flexural Steel Frames by Using the Weighted Simulation Method and Radial Basis Function Interpolation

Document Type : Civil Article

Authors

Abstract

Flexural steel frames are one of the most commonly used building’s structural systems. The safety of this structural system could be affected by the uncertainties such as imperfectness in construction (especially for imperfect rigid connection), material properties and effect of unexpected loads. By considering these uncertainties and combination them with the probability theories and structural engineering, structural reliability investigates the safety level of structure. In this paper by employing the weighted simulation method, reliability and reliability-based design optimization of the flexural steel frames is investigated. For this purpose, by simultaneously using the firefly algorithm and the Radial Basis Function Meta-Model, a hybrid algorithm to approximate the failure probability and design point is proposed. The efficiency of proposed framework firstly evaluated by solving several numerical examples and then the safety and parameters sensitivity of a three-story steel frame under an artificial acceleration is investigated. The results of the safety evaluation presented good agreement with the accurate results obtained by the Monte Carlo simulation. Results of the safety evaluation and sensitivity analysis show that the imperfectness in connections rigidity highly affects the failure probability of the frame.

Keywords


]1[ لطف اللهی یقین؛ محمد علی؛ نگین؛ مسعود؛"مطالعه اثر انحنای اولیه تصادفی اعضا بر قابلیت اعتماد قاب های فولادی"، مجله علمی- پژوهشی عمران مدرس، دوره دهم (۴)، ۱۳۸9، 57-69.
[2] Nowak, A.S., Collins, K.R. (2000). “Reliability of Structures”. New York: McGraw-Hill.
[3] Hasofer, A.M., Lind, N.C. (1974). “Exact and invariant second-moment code format”. Engrg Mech Division ASCE; Vol. 100, Page. 111-121.
[4] Rahman, S., Wei, D. (2006). “A univariate approximation at most probable point for higher-order reliability analysis”. Solids and Structures, Vol. 43, Page. 2820-2839.
[5] Choi, S.K., Grandhi, R.V., Canfield, R.A. (2007). “Reliability-based Structural Design”. London, Springer.
[6] Ibrahim, Y. (1991). “Observations on applications of importance sampling in structural reliability analysis”. Structural Safety, Vol. 9, Page. 269-281.
[7] Zio, E., Pedroni, N. (2010). “An optimized Line Sampling method for the estimation of the failure probability of nuclear passive systems”. Reliability Engineering & System Safety, Vol. 95 (12), Page. 1300-1313.
[8] Angelis, M., Patelli, E., Beer, M. (2015). “Advanced Line Sampling for efficient robust reliability analysis”. Structural Safety, Vol. 52, Page. 170–182.
[9] Miao, F., Ghosn, M. (2011). “Modified subset simulation method for reliability analysis of structural systems”. Structural Safety, Vol. 33, Page. 251–260.
[10] Li, H.S., Ma, Y.Z., Cao, Z. (2015). “A generalized Subset Simulation approach for estimating small failure probabilities of multiple stochastic responses”. Computers & Structures, Vol. 153, Page. 239-251.
[11] Elegbede, C. (2005). “Structural reliability assessment based on particles swarm optimization”.  Structural Safety, Vol. 27, Page. 171–186.
[12] Zuev, K.M., Katafygiotis, L.S. (2011). “The horseracing simulation algorithm for evaluation of small failure probabilities”. Probabilistic Engineering Mechanics, Vol. 26, Page, 157-164.
[13] Cheng, j., Li, Q,S,. (2008). “Reliability analysis of structures using artificial neural network based genetic algorithms”. Computer Methods in Applied Mechanics and Engineering, Vol. 197, Page, 3742–3750.
[14] Schueremans, L., Van Gemert, D. (2005). “Benefit of splines and neural networks in simulation based structural reliability analysis”. Structural Safety, Vol. 27, Page. 246-261.
[15] Allaix, D.L., Carbone, V.I. (2011). “An improvement of the response surface method”. Structural Safety, Vol. 33, Page. 165-172.
[16] Zhang, J., Chen, H.Z., Huang, H.W., Luo, Z. (2015). “Efficient response surface method for practical geotechnical reliability analysis”. Computers & Geotechnics, Vol. 69, Page. 496–505.
[17] Elhewy A,H., Mesbahi, E., Pu, Y. (2006). “Reliability analysis of structures using neural network method”. Probabilistic Engineering Mechanics. Vol. 21(1), Page. 44-53.
[18] Kaymaz, I. (2005). “Application of Kriging method to structural reliability problems”. Structural Safety, Vol. 27(2), Page. 133-151.
[19] Gavin, H,P., Yau, S,C. (2008). “High-order limit state functions in the response surface method for structural reliability analysis”. Structural Safety, Vol. 30(2), Page, 162-179.
[20] Rashki, M. Miri, M. Azhdary Moghaddam, M. (2012). “A new efficient simulation method to approximate the probability of failure and most probable point”. Structural Safety, Vol. 39, Page. 22-29.
]21[ راشکی، م. میری، م. اژدری­مقدم، م. (1393). "ارائه روشی جهت رتبه بندی اهمیت و تاثیر متغیرهای تصادفی بر احتمال خرابی سازه ها". روش‌های عددی در مهندسی، سال 33، شمارة 2.
[22] Yang, X.S. (2008). “Nature-Inspired Metaheuristic Algorithms”. Luniver Press, UK.
]23[ فورگی­نژاد، ا، امیرآبادی، ح. خلیلی، خ. (1393). "مدل سازی فرآیند ماشینکاری تخلیه الکتریکی با شبکه عصبی و بهینه سازی آن با استفاده از الگوریتم کرم شب تاب". مجله مدل سازی در مهندسی، سال 12، شماره 73.
[24] Kiureghian, A.D., Dakessian. T. (1998). “ Multiple design points in structural reliability”. Structural safety and reliability, Rotterdam, Balkema.
[25] Kim, S.H., Na, S.W. (1997) “Response surface method using vector projected sampling point”. Structural Safety, Vol. 19(1), Page. 3-19.
[26] Gayton, N., Bourinet, J.M., Lemaire, M. (2003). “CQ2RS: a new statistical approach to the response surface method for reliability analysis”. Structural Safety, Vol. 25(1), Page. 99-121.
[27] Rofooei, F.R., Aghababaii Mobarake, A., Ahmadi, G. (2001). “Generation of artificial earthquake records with a nonstationary Kanai Tajimi model”. Engineering Structures, Vol. 23, Page. 827-837.
[28] Nagarajaiah, S., Narasimhan, S. (2006). “Smart base-isolated benchmark building
part II: phase I, sample controllers for linear isolation”. Structural
Control and Health Monitoring, Vol. 13, Page. 589-604.
[29] Kartal, M.E., Basaga, H.B., Bayraktar,  A., Muvafık, M. (2010). “Effects of Semi-Rigid Connection on Structural Responses”. Electronic Journal of Structural Engineering, Vol. 17(10).
[30] Mazzolani, F., Piluso V. (1996). “Theory and Design of Seismic Resistant Steel Frames”. CRC Press.