Abstract
The uncertainties in the load and resistant parameters of structures generally lead to a design with failure probability. In reliability-based design optimization (RBDO), the probability of structural failure is defined as an optimization constraint to consider the effect of these uncertainties. The smart improvement and combination of optimization and reliability methods in RBDO is very important and sensitive, especially for complex engineering structures. In the present study, the line sampling method has been improved using the horse optimization algorithm (HOA) to deal with the mentioned issue. The motivation for using these two methods is their high accuracy and speed in solving complex problems. The solution used to achieve this goal is in a way that the random samples are generated along the important direction vector (\(\alpha\)), and then HOA uses these points to find the position of the limit state function. Different problems including highly nonlinear, high dimensions, passive vehicle suspension system, and vehicle side impact are considered to evaluate the performance of the proposed method, and the answers are compared with that of the existing methods. Overall, the results indicate an increase in accuracy and speed of problem-solving by the present method.
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References
Azizyan G, Miarnaeimi F, Rashki M, Shabakhty N (2019) Flying Squirrel Optimizer (FSO): a novel SI-based optimization algorithm for engineering problems. Iran J Optim 11(2):177–205
Chen Z, Qiu H, Gao L, Su L, Li P (2013) An adaptive decoupling approach for reliability-based design optimization. Comput Struct 117(Feb 28):58–66. https://doi.org/10.1016/j.compstruc.2012.12.001
Chen XC, Hasselman TK, Neill DJ et al (1997) Reliability based structural design optimization for practical applications. In: Proceedings of the 38th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, vol 1, pp 2724–2732
Ching J, Hsu WC (2008) Approximate optimization of systems with high-dimensional uncertainties and multiple reliability constraints. Comput Methods Appl Mech Eng 198(1):52–71. https://doi.org/10.1016/j.cma.2008.01.004
Cho H, Bae S, Choi KK, Lamb D, Yang RJ (2014) An efficient variable screening method for effective surrogate models for reliability-based design optimization. Struct Multidiscip Optim 50(5):717–738. https://doi.org/10.1007/s00158-014-1096-9
Enevoldsen I, Sørensen JD (1994) Reliability-based optimization in structural engineering. Struct Saf 15(3):169–196
Fister I Jr, Yang X-S, Fister I, Brest J, Fister D (2013) A brief review of nature-inspired algorithms for optimization. ArXiv Preprint ArXiv:1307.4186
Gu L, Yang RJ, Tho C-H, Makowskit M, Faruquet O, Li Y (2001) Optimisation and robustness for crashworthiness of side impact. Int J Veh Des 26(4):348–360
Hamzehkolaei NS, Miri M, Rashki M (2016) An enhanced simulation-based design method coupled with meta-heuristic search algorithm for accurate reliability-based design optimization. Eng Comput 32(3):477–495
Ho-Huu V, Nguyen-Thoi T, Le-Anh L, Nguyen-Trang T (2016) An effective reliability-based improved constrained differential evolution for reliability-based design optimization of truss structures. Adv Eng Softw 92(Feb 29):48–56. https://doi.org/10.1016/j.advengsoft.2015.11.001
Keshtegar B (2017) A modified mean value of performance measure approach for reliability-based design optimization. Arab J Sci Eng 42(3):1093–1101
Keshtegar B, Hao P (2016) A hybrid loop approach using the sufficient descent condition for accurate, robust, and efficient reliability-based design optimization. J Mech Des 138(12):121401
Keshtegar B, Hao P (2017) A hybrid self-adjusted mean value method for reliability-based design optimization using sufficient descent condition. Appl Math Model 41(Jan 31):257–270. https://doi.org/10.1016/j.apm.2016.08.031
Keshtegar B, Lee I (2016) Relaxed performance measure approach for reliability-based design optimization. Struct Multidiscip Optim 54(6):1439–1454
Keshtegar B, Baharom S, El-Shafie A (2017) Self-adaptive conjugate method for a robust and efficient performance measure approach for reliability-based design optimization. Eng Comput Jul 4:1–16. https://doi.org/10.1007/s00366-017-0529-7
Khatir S, Wahab MA (2019) Fast simulations for solving fracture mechanics inverse problems using POD-RBF XIGA and Jaya algorithm. Eng Fract Mech 205:285–300
Khatir S, Wahab MA, Boutchicha D, Khatir T (2019) Structural health monitoring using modal strain energy damage indicator coupled with teaching-learning-based optimization algorithm and isogoemetric analysis. J Sound Vib 448:230–246
Khatir S, Boutchicha D, Le Thanh C, Tran-Ngoc H, Nguyen TN, Abdel-Wahab M (2020) Improved ANN technique combined with Jaya algorithm for crack identification in plates using XIGA and experimental analysis. Theor Appl Fract Mech 107:102554
Koutsourelakis PS, Pradlwarter HJ, Schuëller GI (2004) Reliability of structures in high dimensions, part I: algorithms and applications. Probab Eng Mech 19(4):409–417. https://doi.org/10.1016/j.probengmech.2004.05.001
Krueger K, Heinze J (2008) Horse sense: social status of horses (Equus caballus) affects their likelihood of copying other horses’ behavior. Anim Cogn 11(3):431–439
Lee J-O, Yang Y-S, Ruy W-S (2002) A comparative study on reliability-index and target-performance-based probabilistic structural design optimization. Comput Struct 80(3):257–269
Lee I, Choi KK, Du L, Gorsich D (2008) Inverse analysis method using MPP-based dimension reduction for reliability-based design optimization of nonlinear and multi-dimensional systems. Comput Methods Appl Mech Eng 198(1):14–27. https://doi.org/10.1016/j.cma.2008.03.004
Levine MA (2005) Domestication and early history of the horse. In: Mills DS, McDonnell SM (eds) The domestic horse: the origins, development and management of its behaviour. Cambridge University Press, Cambridge, pp 5–22
Li L, Lu Z (2014) Interval optimization based line sampling method for fuzzy and random reliability analysis. Appl Math Model 38(13):3124–3135
Li F, Wu T, Hu M, Dong J (2010) An accurate penalty-based approach for reliability-based design optimization. Res Eng Des 21(2):87–98. https://doi.org/10.1007/s00163-009-0083-4
Li X, Chen Z, Ming W, Qiu H, Ma J, He W (2017) An efficient moving optimal radial sampling method for reliability-based design optimization. Int J Perform Eng 13(6):864–877. https://doi.org/10.23940/ijpe.17.06.p8.864877
Lu Z, Song S, Yue Z, Wang J (2008) Reliability sensitivity method by line sampling. Struct Saf 30(6):517–532
McDonnell SM (2003) The equid ethogram: a practical field guide to horse behavior. Eclipse Press
Meng Z, Zhou H, Li G, Yang D (2016) A decoupled approach for non-probabilistic reliability-based design optimization. Comput Struct 175(October 15):65–73. https://doi.org/10.1016/j.compstruc.2016.06.008
MiarNaeimi F, Azizyan G, Rashki M (2019) Reliability sensitivity analysis method based on subset simulation hybrid techniques. Appl Math Model 75:607–626
MiarNaeimi F, Azizyan G, Rashki M (2021) Horse herd optimization algorithm: a nature-inspired algorithm for high-dimensional optimization problems. Knowl Based Syst 213:106711. https://doi.org/10.1016/j.knosys.2020.106711
Mirjalili S (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl Based Syst 89:228–249
Mohammed H, Rashid T (2020) A novel hybrid GWO with WOA for global numerical optimization and solving pressure vessel design. Neural Comput Appl 32:14701–14718. https://doi.org/10.1007/s00521-020-04823-9
Mourelatos ZP, Liang J (2006) A methodology for trading-off performance and robustness under uncertainty. J Mech Des 128(4):856–863. https://doi.org/10.1115/1.2202883
Nikolaidis E, Burdisso R (1988) Reliability based optimization: a safety index approach. Comput Struct 28(6):781–788
Parand A, Seraji M, Dashti H (n.d.) A modified multi-level cross-entropy algorithm for optimization of problems with discrete variables. Eng Comput 1–16
Pradlwarter HJ, Schuëller GI, Koutsourelakis PS, Charmpis DC (2007) Application of line sampling simulation method to reliability benchmark problems. Struct Saf 29(3):208–221. https://doi.org/10.1016/j.strusafe.2006.07.009
Rajan A, Ooi MP-L, Kuang YC, Demidenko SN (2017) Reliability-based design optimisation of technical systems: Analytical response surface moments method. J Eng 2017(3):36–46
Rashki M, Miri M, Moghaddam MA (2014) A simulation-based method for reliability based design optimization problems with highly nonlinear constraints. Autom Constr 47:24–36. https://doi.org/10.1016/j.autcon.2014.07.004
Royset JO, Der Kiureghian A, Polak E (2001) Reliability-based optimal structural design by the decoupling approach. Reliab Eng Syst Saf 73(3):213–221. https://doi.org/10.1016/S0951-8320(01)00048-5
Safaeian Hamzehkolaei N, Miri M, Rashki M (2017) Reliability-based design optimization of structures using modified weighted simulation method. J Comput Methods Eng 35(2):1–23. https://doi.org/10.18869/acadpub.jcme.35.2.1
Safaeian Hamzehkolaei N, Miri M, Rashki M (2018) An improved binary bat flexible sampling algorithm for reliability-based design optimization of truss structures with discrete-continuous variables. Eng Comput 35(2):641–671. https://doi.org/10.1108/EC-06-2016-0207
Shehab M, Alshawabkah H, Abualigah L, Nagham A-M (2021) Enhanced a hybrid moth-flame optimization algorithm using new selection schemes. Eng Comput 37:2931–2956. https://doi.org/10.1007/s00366-020-00971-7
Shi Z, Gu C, Zheng X, Qin D (2016) Multiple failure modes analysis of the dam system by means of line sampling simulation. Optik 127(11):4710–4715
Tu J, Choi KK, Park YH (1999) A new study on reliability-based design optimization. J Mech Des 121(4):557–564
Van den Berg M, Giagos V, Lee C, Brown WY, Cawdell-Smith AJ, Hinch GN (2016) The influence of odour, taste and nutrients on feeding behaviour and food preferences in horses. Appl Anim Behav Sci 184:41–50
Waring GH (1983) Horse behaviour. The behavioral traits and adaptations of domestic and wild horses, including ponies. Noyes Publications, Mill Road
Xiao M, Zhang J, Gao L, Lee S, Eshghi AT (2019) An efficient Kriging-based subset simulation method for hybrid reliability analysis under random and interval variables with small failure probability. Struct Multidiscip Optim 59(6):2077–2092
Xiao M, Zhang J, Gao L (2020) A system active learning Kriging method for system reliability-based design optimization with a multiple response model. Reliab Eng Syst Saf 199:106935
Yang I-T, Hsieh Y-H, Kuo C-G (2016) Integrated multiobjective framework for reliability-based design optimization with discrete design variables. Autom Constr 63:162–172. https://doi.org/10.1016/j.autcon.2015.12.010
Yang M, Zhang D, Han X (2020) New efficient and robust method for structural reliability analysis and its application in reliability-based design optimization. Comput Methods Appl Mech Eng 366:113018
Yang M, Zhang D, Cheng C, Han X (2021a) Reliability-based design optimization for RV reducer with experimental constraint. Struct Multidiscip Optim 63(4):2047–2064
Yang M, Zhang D, Jiang C, Han X, Li Q (2021b) A hybrid adaptive Kriging-based single loop approach for complex reliability-based design optimization problems. Reliab Eng Syst Saf 215(3):107736. https://doi.org/10.1016/j.ress.2021.107736
Youn BD, Choi KK (2004) An investigation of nonlinearity of reliability-based design optimization approaches. J Mech Des 126(3):403. https://doi.org/10.1115/1.1701880
Youn BD, Choi KK, Yang R-J, Gu L (2004) Reliability-based design optimization for crashworthiness of vehicle side impact. Struct Multidiscip Optim 26(3–4):272–283
Youn BD, Choi KK, Du L (2005) Enriched performance measure approach for reliability-based design optimization. AIAA J 43(4):874–884
Zhang J, Xiao M, Gao L, Fu J (2018) A novel projection outline based active learning method and its combination with Kriging metamodel for hybrid reliability analysis with random and interval variables. Comput Methods Appl Mech Eng 341:32–52
Zhang J, Xiao M, Gao L, Chu S (2019) A combined projection-outline-based active learning Kriging and adaptive importance sampling method for hybrid reliability analysis with small failure probabilities. Comput Methods Appl Mech Eng 344:13–33
Zou T, Mahadevan S (2006) Versatile formulation for multiobjective reliability-based design optimization. J Mech Des 128(6):1217. https://doi.org/10.1115/1.2218884
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Parand, A., Seraji, M., Dashti, H. et al. A New Developed Line Sampling Method for Reliability-Based Design Optimization of Structures. Iran J Sci Technol Trans Civ Eng 46, 3537–3553 (2022). https://doi.org/10.1007/s40996-021-00805-6
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DOI: https://doi.org/10.1007/s40996-021-00805-6