Abstract
This paper introduces a new method for reliability-based design optimization (RBDO) of structures. In RBDO of structural problems unlike the conventional two-level approaches, sometimes it is not necessary to carry out reliability analysis for each deterministic design. The proposed method may be categorized as a decoupled method for reliable optimum design; however, it is based on the safety factor (SF) concept. To briefly describe the proposed method, a deterministic design optimization (DDO) point is obtained based on an arbitrary SF. The corresponding failure probability (P f) is then determined using Monte Carlo simulation (MCS). The P f is then compared with the targeted P f. If the relative distance error is greater than a desirable tolerance, the cubic B-spline interpolation concept is then employed as a result of which a modified SF is extracted. For the modified SF found, DDO procedure is carried out. The above procedure is iteratively repeated until convergence occurs and the reliable optimum point is found. Finally, the proposed method was applied to solving some structural problems. The obtained results were favourably in accordance with those recorded in the literature while only a fraction of P f computations was necessary.
Similar content being viewed by others
References
Tu J, Choi KK, Park YH (1999) A new study on reliability-based design optimization. J Mech Des 121(4):557–564. doi:10.1115/1.28294992
Kharmanda G, Mohamed A, Lemaire M (2002) Efficient reliability-based design optimization using a hybrid space with application to finite element analysis. Struct Multidiscp Optim 24(3):233–245. doi:10.1007/s00158-002-0233-z
Kirjner-Neto C, Polak E, Kiureghian AD (1998) An outer approximations approach to reliability-based optimal design of structures. J Optim Theory Appl 98(1):1–16. doi:10.1023/A:10226477284194
Kuschel N, Rackwitz R (1997) Two basic problems in reliability-based structural optimization. Math Methods Oper Res 46(3):309–333. doi:10.1007/BF01194859
Madsen HO, Hansen PF (1992) A comparison of some algorithms for reliability based structural optimization and sensitivity analysis. In: Rackwitz R, Thoft-Christensen P (eds) Reliability and optimization of structural systems’91. Lecture notes in engineering, vol 76. Springer, Berlin, Heidelberg, pp 443–451. doi:10.1007/978-3-642-84753-0_34
Shan S, Wang GG (2008) Reliable design space and complete single-loop reliability-based design optimization. Reliab Eng Syst Saf 93(8):1218–1230. doi:10.1016/j.ress.2007.07.006
Aoues Y, Chateauneuf A (2010) Benchmark study of numerical methods for reliability-based design optimization. Struct Multidiscp Optim 41(2):277–294. doi:10.1007/s00158-009-0412-2
Du X, Chen W (2004) Sequential optimization and reliability assessment method for efficient probabilistic design. J Mech Des 126(2):225–233. doi:10.1115/1.1649968
Dubourg V, Sudret B, Bourinet J-M (2011) Reliability-based design optimization using kriging surrogates and subset simulation. Struct Multidiscip Optim 44(5):673–690. doi:10.1007/s00158-011-0653-8
Cheng G, Xu L, Jiang L (2006) A sequential approximate programming strategy for reliability-based structural optimization. Comput Struct 84(21):1353–1367. doi:10.1016/j.compstruc.2006.03.006
Bucher CG, Bourgund U (1990) A fast and efficient response surface approach for structural reliability problems. Struct Saf 7(1):57–66. doi:10.1016/0167-4730(90)90012-E
Faravelli L (1989) Response-surface approach for reliability analysis. J Eng Mech 115(12):2763–2781. doi:10.1061/(ASCE)0733-9399(1989)115:12(2763)
Guan XL, Melchers RE (2001) Effect of response surface parameter variation on structural reliability estimates. Struct Saf 23(4):429–444. doi:10.1016/S0167-4730(02)00013-9
Rajashekhar MR, Ellingwood BR (1993) A new look at the response surface approach for reliability analysis. Struct Saf 12(3):205–220. doi:10.1016/0167-4730(93)90003-J
Nguyen XS, Sellier A, Duprat F, Pons G (2009) Adaptive response surface method based on a double weighted regression technique. Probab Eng Mech 24(2):135–143. doi:10.1016/j.probengmech.2008.04.001
Roussouly N, Petitjean F, Salaun M (2013) A new adaptive response surface method for reliability analysis. Probab Eng Mech 32:103–115. doi:10.1016/j.probengmech.2012.10.001
Wong SM, Hobbs RE, Onof C (2005) An adaptive response surface method for reliability analysis of structures with multiple loading sequences. Struct Saf 27(4):287–308. doi:10.1016/j.strusafe.2005.02.001
Kang S-C, Koh H-M, Choo JF (2010) An efficient response surface method using moving least squares approximation for structural reliability analysis. Probab Eng Mech 25(4):365–371. doi:10.1016/j.probengmech.2010.04.002
Yinga L (2012) Application of stochastic response surface method in the structural reliability. Proc Eng 28:661–664. doi:10.1016/j.proeng.2012.01.787
Zhao W, Qiu Z (2013) An efficient response surface method and its application to structural reliability and reliability-basedoptimization. Finite Elem Anal Des 67:34–42. doi:10.1016/j.finel.2012.12.004
Der Kiureghian A (1996) Structural reliability methods for seismic safety assessment: a review. Eng Struct 18(6):412–424. doi:10.1016/0141-0296(95)00005-4
Qu X, Haftka RT (2004) Reliability-based design optimization using probabilistic sufficiency factor. Struct Multidiscp Optim 27(5):314–325. doi:10.1007/s00158-004-0390-3
Wu Y, Shin Y, Sues R, Cesare M (2001) Safety-factor based approach for probability-based design optimization. In: Proceedings of the 42nd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, number AIAA-2001-1522, Seattle, WA, pp 199–342
Nowak AS, Collins KR (2012) Reliability of structures, 2nd edn. Taylor & Francis, New York
Choi S-K, Grandhi R, Canfield RA (2006) Reliability-based structural design. Springer Science & Business Media, Berlin
de Boor C (2001) A practical guide to splines. Springer, New York
Metropolis N, Ulam S (1949) The Monte Carlo method. J Am Stat Assoc 44(247):335–341
Nakib R, Frangopol DM (1990) RBSA and RBSA-OPT: two computer programs for structural system reliability analysis and optimization. Comput Struct 36(1):13–27. doi:10.1016/0045-7949(90)90170-7
Ghorbani A, Ghasemi MR (2010) An efficient method for reliability based optimization of structures using adaptive neuro-fuzzy systems. J Model Simul Syst 1(1):13–21
Shayanfar M, Abbasnia R, Khodam A (2014) Development of a GA-based method for reliability-based optimization of structures with discrete and continuous design variables using OpenSees and Tcl. Finite Elem Anal Des 90:61–73. doi:10.1016/j.finel.2014.06.010
Author information
Authors and Affiliations
Corresponding author
Additional information
Technical Editor: Marcelo A. Trindade.
Rights and permissions
About this article
Cite this article
Dizangian, B., Ghasemi, M.R. A fast decoupled reliability-based design optimization of structures using B-spline interpolation curves. J Braz. Soc. Mech. Sci. Eng. 38, 1817–1829 (2016). https://doi.org/10.1007/s40430-015-0423-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40430-015-0423-4