Abstract
It is important to consider the performances of lightweight, stiffness, strength and rollover safety when designing a bus body. In this paper, the finite element (FE) analysis models including strength, stiffness and rollover crashworthiness of a bus body are first built and then validated by physical tests. Based on the FE models, the design of experiment is implemented and multiple surrogate models are created with response surface method and hybrid radial basis function according to the experimental data. After that, a multi-objective optimization problem (MOP) of the bus body is formulated in which the objective is to minimize the weight and maximize the torsional stiffness of the bus body under the constraints of strength and rollover safety. The MOP is solved by employing multi-objective evolutionary algorithms to obtain the Pareto optimal set. Finally, an optimal solution of the set is chosen as the final design and compared with the original design.
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References
Aguiar FHV, Spinelli DM, Pazian A, Gimenez MC (2002) Frame structure optimization for bus chassis. In: 11th international mobility technology congress and exhibition. SAE International, São Paulo, Brazil
Chen S, Chng ES, Alkadhimi K (1996) Regularized orthogonal least squares algorithm for constructing radial basis function networks. Int J Control 64(5):829–837
Coello C, Pulido GT, Lechuga MS (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8(3):256–279
Corne D, Knowles J, Oates M (2000) The Pareto envelope-based selection algorithm for multiobjective optimization. Parallel Problem Solving from Nature PPSN VI, Springer Berlin/Heidelberg, 1917/2000:839–848
Craig K, Stander N, Dooge D, Varadappa S (2002) MDO of automotive vehicle for crashworthiness and NVH using response surface methods. In: 9th AIAA/ISSMO symposium on multidisciplinary analysis and optimization, Atlanta, Georgia, 4–6 September, AIAA-2002-5607
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
Deb K (2005) Chapter 10: multi-objective optimization. In: Burke EK, Kendall G (eds) Search methodologies: introductory tutorials in optimization and decision support techniques. Springer, New York, pp 273–316
Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. Parallel Problem Solving from Nature PPSN VI, Springer Berlin/Heidelberg, 1917:849–858
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 (2005) On polynomial response surfaces and Kriging for use in structural optimization of crashworthiness. Struct Multidisc Optim 29(3):232–243
Forsberg J, Nilsson L (2007) Topology optimization in crashworthiness design. Struct Multidisc Optim 33(1):1–12
Gong MG, Jiao LC, Du HF, Bo LF (2008) Multiobjective immune algorithm with nondominated neighbor-based selection. Evol Comput 16(2):225–255
Guler MA, Elitok K, Bayram B, Stelzmann U (2007) The influence of seat structure and passenger weight on the rollover crashworthiness of an intercity coach. Int J Crashworthiness 12(6):567–580
Hart C, Vlahopoulos N (2010) An integrated multidisciplinary particle swarm optimization approach to conceptual ship design. Struct Multidisc Optim 41(3):481–494
** R, Chen W, Simpson TW (2001) Comparative studies of metamodelling techniques under multiple modelling criteria. Struct Multidisc Optim 23(1):1–13
Krishnamurthy T (2003) Response surface approximation with augmented and compactly supported radial basis functions. In: 44th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference. Norfolk, Virginia
Kutner MH, Nachtsheim CJ, Neter J (2004) Applied linear regression models. McGraw-Hill/Irwin, Boston
Lan F, Chen J, Lin J (2004) Comparative analysis for bus side structures and lightweight optimization. Proc Inst Mech Eng Part D-J Automobile Eng 218(D10):1067–1075
Laxman S, Iyengar RM, Morgans S (2009) Achieving light-weight design of automotive bodies with advanced high strength steels via structural optimization. SAE International, 2009-01-0795
Liao XT, Li Q, Yang XJ, Zhang WG, Li W (2008) Multiobjective optimization for crash safety design of vehicles using stepwise regression model. Struct Multidisc Optim 35(6):561–569
Martinez L, Aparicio F, Garcia A, Paez J, Ferichola G (2003) Improving occupant safety in coach rollover. Int J Crashworthiness 8(2):121–132
Park JS (1994) Optimal Latin-hypercube designs for computer experiments. J Stat Plan Inference 39(1):95–111
Park J, Sandberg IW (1993) Approximation and radial-basis-function networks. Neural Comput 5(2):305–316
Park SJ, Yoo WS (2008) Rollover analysis for the body section structure of a large bus using beam and non-linear spring elements. Proc Inst Mech Eng Part D-J Automobile Eng 222(D6):955–962
Pedersen C (2003) Topology optimization for crashworthiness of frame structures. Int J Crashworthiness 8(1):29–39
Pedersen C (2004) Crashworthiness design of transient frame structures using topology optimization. Comput Methods Appl Mech Eng 193(6–8):653–678
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
Roux WJ, Stander N, Haftka RT (1998) Response surface approximations for structural optimization. Int J Numer Methods Eng 42(3):517–534
Saito M, Iwatsuki S, Yasunaga K, Andoh K (2000) Development of aluminum body for the most fuel efficient vehicle. JSAE Rev 21(4):511–516
Sindhya K, Deb K, Miettinen K (2008) A local search based evolutionary multi-objective optimization approach for fast and accurate convergence. In: 10th international conference on parallel problem solving from nature, PPSN X, Springer, Dortmund, 13–17 September 2008
Sobieszczanski-Sobieski J, Kodiyalam S, Yang RY (2001) Optimization of car body under constraints of noise, vibration, and harshness (NVH), and crash. Struct Multidisc Optim 22(4):295–306
Su R, Wang X, Gui L, Fan Z (2010) Multi-objective topology and sizing optimization of truss structures based on adaptive multi-island search strategy. Struct Multidisc Optim. Online First 12 August 2010. doi:10.1007/s00158-010-0544-4
Tan KC, Goh CK, Mamun AA, Ei EZ (2008) An evolutionary artificial immune system for multi-objective optimization. Eur J Oper Res 187(2):371–392
Unite Nations Economic Commission for Europe (1996) Uniform provisions concerning the approval of large passenger vehicles with regard to the strength of their superstructure. Regulation No. 66. Geneva
Wang GCS, Jain CL (2003) Regression analysis: modeling & forecasting. Graceway Publishing Company, Inc, New York
Wang H, Li GY, Li EY (2010) Time-based metamodeling technique for vehicle crashworthiness optimization. Comput Methods Appl Mech Eng 199(37–40):2497–2509
Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength Pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich
Acknowledgement
This work was supported in part by the National High Technology Research and Development Program (“863” Program) of China under Grant no. 2007AA04Z133.
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Su, R., Gui, L. & Fan, Z. Multi-objective optimization for bus body with strength and rollover safety constraints based on surrogate models. Struct Multidisc Optim 44, 431–441 (2011). https://doi.org/10.1007/s00158-011-0627-x
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DOI: https://doi.org/10.1007/s00158-011-0627-x