Abstract
Although deterministic optimization has to a considerable extent been successfully applied in various crashworthiness designs to improve passenger safety and reduce vehicle cost, the design could become less meaningful or even unacceptable when considering the perturbations of design variables and noises of system parameters. To overcome this drawback, we present a multiobjective robust optimization methodology to address the effects of parametric uncertainties on multiple crashworthiness criteria, where several different sigma criteria are adopted to measure the variations. As an example, a full front impact of vehicle is considered with increase in energy absorption and reduction of structural weight as the design objectives, and peak deceleration as the constraint. A multiobjective particle swarm optimization is applied to generate robust Pareto solution, which no longer requires formulating a single cost function by using weighting factors or other means. From the example, a clear compromise between the Pareto deterministic and robust designs can be observed. The results demonstrate the advantages of using multiobjective robust optimization, with not only the increase in the energy absorption and decrease in structural weight from a baseline design, but also a significant improvement in the robustness of optimum.
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References
Avalle M, Chiandussi G, Belingardi G (2002) Design optimization by response surface methodology: application to crashworthiness design of vehicle structures. Struct Multidisc Optim 24(4):325–332
Craig KJ, Stander N, Dooge DA, Varadappa S (2005) Automotive crashworthiness design using response surface-based variable screening and optimization. Eng Comput 22(1–2):38–61
Doltsinis I, Kang Z (2004) Robust design of structures using optimization methods. Comput Methods Appl Mech Eng 193(23–26):2221–2237
Doltsinis L, Kang Z, Cheng GD (2005) Robust design of non-linear structures using optimization methods. Comput Methods Appl Mech Eng 194(12–16):1779–1795
Duddeck F (2008) Multidisciplinary optimization of car bodies. Struct Multidisc Optim 35(4):375–389
Fang H, Rais-Rohani M, Liu Z, Horstemeyer MF (2005) A comparative study of metamodeling methods for multiobjective crashworthiness optimization. Comput Struct 83(25–26):2121–2136
Forsberg J, Nilsson L (2006) Evaluation of response surface methodologies used in crashworthiness optimization. Int J Impact Eng 32(5):759–777
Gu L, Yang RJ, Tho CH, Makowski M, Faruque O, Li Y (2001) Optimization and robustness for crashworthiness of side impact. Int J Veh Des 26(4):348–360
Gunawan S, Azarm S (2005) Multi-objective robust optimization using a sensitivity region concept. Struct Multidisc Optim 29(1):50–60
Hou SJ, Li Q, Long SY, Yanga XJ, Li W (2008) Multiobjective optimization of multi-cell sections for the crashworthiness design. Int J Impact Eng 35(11):1355–1367
Jansson T, Nilsson L, Redhe M (2003) Using surrogate models and response surfaces in structural optimization—with application to crashworthiness design and sheet metal forming. Struct Multidisc Optim 25(2):129–140
Kapur KC, Cho BR (1996) Economic design of the specification region for multiple quality characteristics. IIE Trans 28(3):237–248
Kim KJ, Lin DKJ (1998) Dual response surface optimization: a fuzzy modeling approach. J Qual Technol 30(1):1–10
Koch PN, Yang RJ, Gu L (2004) Design for six sigma through robust optimization. Struct Multidisc Optim 26(3–4):235–248
Koksoy O (2006) Multiresponse robust design: mean square error (MSE) criterion. Appl Math Comput 175(2):1716–1729
Koksoy O (2008) A nonlinear programming solution to robust multi-response quality problem. Appl Math Comput 196(2):603–612
Koksoy O, Yalcinoz T (2006) Mean square error criteria to multiresponse process optimization by a new genetic algorithm. Appl Math Comput 175(2):1657–1674
Kovach J, Cho BR, Antony J (2008) Development of an experiment-based robust design paradigm for multiple quality characteristics using physical programming. Int J Adv Manuf Technol 35(11–12):1100–1112
Kurtaran H, Eskandarian A, Marzougui D, Bedewi NE (2002) Crashworthiness design optimization using successive response surface approximations. Comput Mech 29(4–5):409–421
Liao XT, Li Q, Yang XJ, Li W, Zhang WG (2008a) A two-stage multi-objective optimization of vehicle crashworthiness under front impact. Int J Crashworthiness 13(3):279–288
Liao XT, Li Q, Yang XJ, Zhang WG, Li W (2008b) Multiobjective optimization for crash safety design of vehicles using stepwise regression model. Struct Multidisc Optim 35(6):561–569
Lin DKJ, Tu WZ (1995) Dual response-surface optimization. J Qual Technol 27(1):34–39
Liu DS, Tan KC, Goh CK, Ho WK (2007) A multiobjective memetic algorithm based on particle swarm optimization. IEEE Trans Syst Man Cybern B Cybern 37(1):42–50
LS-DYNA (2003) Keyword user’s manual, v. 970. Livermore Software Technology Corporation, Livermore
Marklund PO, Nilsson L (2001) Optimization of a car body component subjected to side impact. Struct Multidisc Optim 21(5):383–392
Raquel C, Naval P (2005) An effective use of crowding distance in multiobjective particle swarm optimization. In: Proceedings of the 2005 conference on genetic and evolutionary computation. Washington DC, USA
Redhe M, Forsberg J, Jansson T, Marklund PO, Nilsson L (2002) Using the response surface methodology and the D-optimality criterion in crashworthiness related problems—an analysis of the surface approximation error versus the number of function evaluations. Struct Multidisc Optim 24(3):185–194
Shimoyama K, Oyama A, Fujii K (2005) A new efficient and useful robust optimization approach—design for multi-objective six sigma. In: Proceedings of the 2005 IEEE congress on evolutionary computation. Edinburgh
Siddall JN (1984) A new approach to probability in engineering design and optimization. J Mech Transmissions Automation Des Trans ASME 106(1):5–10
Sun GY, Li GY, Gong ZH, Cui XY, Yang XJ, Li Q (2010a) Multiobjective robust optimization method for drawbead design in sheet metal forming. Mater Des 31(4):1917–1929
Sun GY, Li GY, Hou SJ, Zhou SW, Li W, Li Q (2010b) Crashworthiness design for functionally graded foam-filled thin-walled structures. Mater Sci Eng Struct Mater Prop Microstruct Process 527(7–8):1911–1919
Sun GY, Li GY, Stone M, Li Q (2010c) A two-stage multi-fidelity optimization procedure for honeycomb-type cellular materials. Comput Mater Sci 49(3):500–511
Vining GG, Myers RH (1990) Combining taguchi and response-surface philosophies—a dual response approach. J Qual Technol 22(1):38–45
Wang GG, Shan S (2007) Review of metamodeling techniques in support of engineering design optimization. J Mech Des 129(4):370–380
Yang RJ, Akkerman A, Anderson DF, Faruque OM, Gu L (2000) Robustness optimization for vehicular crash simulations. Comput Sci Eng 2(6):8–13
Yang RJ, Wang N, Tho CH, Bobineau JP (2005a) Metamodeling development for vehicle frontal impact simulation. J Mech Des 127(5):1014–1020
Yang TH, Chou PH (2005) Solving a multiresponse simulation-optimization problem with discrete variables using a multiple-attribute decision-making method. Math Comput Simul 68(1): 9–21
Yang TH, Kuo YY, Chou PH (2005b) Solving a multiresponse simulation problem using a dual-response system and scatter search method. Simul Model Pract Theory 13(4):356–369
Yeniay O, Unal R, Lepsch RA (2006) Using dual response surfaces to reduce variability in launch vehicle design: a case study. Reliab Eng Syst Saf 91(4):407–412
Youn BD, Choi KK (2004) A new response surface methodology for reliability-based design optimization. Comput Struct 82(2–3):241–256
Youn BD, Choi KK, Yang RJ, Gu L (2004) Reliability-based design optimization for crashworthiness of vehicle side impact. Struct Multidisc Optim 26(3–4):272–283
Zang C, Friswell MI, Mottershead JE (2005) A review of robust optimal design and its application in dynamics. Comput Struct 83(4–5):315–326
Acknowledgements
The support from National 973 Project of China (2010CB328005), Key Project of National Science Foundation of China (60635020) and Program for Changjiang Scholar Innovative Research Team in Hunan University. The first author is also grateful the supports from China Scholarship Council (CSC).
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Sun, G., Li, G., Zhou, S. et al. Crashworthiness design of vehicle by using multiobjective robust optimization. Struct Multidisc Optim 44, 99–110 (2011). https://doi.org/10.1007/s00158-010-0601-z
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DOI: https://doi.org/10.1007/s00158-010-0601-z