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Multiobjective optimization for crash safety design of vehicles using stepwise regression model

  • Industrial Application
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Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

In automotive industry, structural optimization for crashworthiness criteria is of special importance. Due to the high nonlinearities, however, there exists substantial difficulty to obtain accurate continuum or discrete sensitivities. For this reason, metamodel or surrogate model methods have been extensively employed in vehicle design with industry interest. This paper presents a multiobjective optimization procedure for the vehicle design, where the weight, acceleration characteristics and toe-board intrusion are considered as the design objectives. The response surface method with linear and quadratic basis functions is employed to formulate these objectives, in which optimal Latin hypercube sampling and stepwise regression techniques are implemented. In this study, a nondominated sorting genetic algorithm is employed to search for Pareto solution to a full-scale vehicle design problem that undergoes both the full frontal and 40% offset-frontal crashes. The results demonstrate the capability and potential of this procedure in solving the crashworthiness design of vehicles.

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References

  • Altair Engineering (2004) Hypermesh 7.0 Tutorial

  • Athan TW, Papalambros PY (1999) A note on weighted criteria methods for compromise solutions in multi-objective optimization. Eng Opt 27(2):155–176

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Currin C, Mitchell T, Morris M, Ylvisaker D (1991) Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments. J Am Stat Assoc 86(416):953–963

    Article  MathSciNet  Google Scholar 

  • Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New York

    MATH  Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  • Dias JP, Pereira MS (2004) Optimization methods for crashworthiness design using multibody models. Comput Struct 82(17–19):1371–1380

    Article  Google Scholar 

  • Fang H, Rais-Rohani M, Liu Z, Horstemeyer MF (2005a) A comparative study of metamodeling methods for multiobjective crashworthiness optimization. Comput Struct 83(25–26):2121–2136

    Article  Google Scholar 

  • Fang H, Solanki K, Horstemeyer MF (2005b) Numerical simulations of multiple vehicle crashes and multidisciplinary crashworthiness optimization. Int J Crashworthiness 10(2):161–171

    Article  Google Scholar 

  • Fu Y, Sahin KH (2004) Better optimization of nonlinear uncertain systems (BONUS) for vehicle structural design. Ann Oper Res 132(1–4):69–84

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Hamza K, Hossoy I, Reyes-Luna JF, Papalambros PY (2004) Combined maximization of interior comfort and frontal crashworthiness in preliminary vehicle design. Int J Veh Des 35(3):167–185

    Google Scholar 

  • Hong JH, Mun MS, Song SH (2001) An optimum design methodology development using a statistical technique for vehicle occupant safety. Proc Inst Mech Eng D J Automot Eng 215:795–801

    Article  Google Scholar 

  • Hou SJ, Li Q, Long SY, Yang XJ, Li W (2007) Design optimization of regular hexagonal thin-walled columns with crashworthiness criteria. Finite Elem Anal Des 43(6–7):555–565

    Google Scholar 

  • Kodiyalam S, Yang RJ, Gu L (2004a) High-performance computing and surrogate modeling for rapid visualization with multidisciplinary optimization. AIAA J 42(11):2347–2354

    Google Scholar 

  • Kodiyalam S, Yang RJ, Gu L, Tho CH (2004b) Multidisciplinary design optimization of a vehicle system in a scalable, high performance computing environment. Struct Multidiscipl Optim 26(3–4):256–263

    Article  Google Scholar 

  • Krishnaiah PR (1982) Selection of variables under univariate regression models. Handbook of statistics, vol 2

  • Lanzi L, Castelletti LML, Anghileri M (2004) Multi-objective optimisation of composite absorber shape under crashworthiness requirements. Compstruct 65(3–4):433–441

    Google Scholar 

  • Latchford J, Chirwa EC (2000) Airbag head restraint system. Proc Inst Mech Eng D J Automot Eng 214(D3):229–241

    Article  Google Scholar 

  • Li W, Li Q, Steven GP, Xie YM (2005) An evolutionary shape optimization for elastic contact problems subject to multiple load cases. Comput Methods Appl Mech Eng 194:3394–3415

    Article  MATH  Google Scholar 

  • Mao M, Chirwa EC, Wang W (2006) Assessment of vehicle roof crush test protocols using FE models: inverted drop tests versus updated FMVSS no. 216. Int J Crashworthiness 11(1):49–63

    Article  Google Scholar 

  • Marklund PO, Nilsson L (2001) Optimization of a car body component subjected to side impact. Struct Multidiscipl Optim 21(5):383–392

    Article  Google Scholar 

  • Myers RH, Montgomery DC (2002) Response surface methodology: process and product optimization using designed experiments. Wiley, New York

    Google Scholar 

  • Redhe M, Nilsson L (2004) Optimization of the new Saab 9–3 exposed to impact load using a space mapping technique. Struct Multidiscipl Optim 27(5):411–420

    Article  Google Scholar 

  • Redhe M, Giger M, Nilsson L (2004) An investigation of structural optimization in crashworthiness design using a stochastic approach — A comparison of stochastic optimization and the response surface methodology. Struct Multidisc Optim 27(6):446–459

    Google Scholar 

  • Rudenko O, Schoenauer M, Bosio T, Fontana R (2002) A multiobjective evolutionary algorithm for car front end design. In: P Collet, C Fonlupt, J-K Hao, E Lutton, and M Schoenauer (eds) Artificial Evolution. 5th International Conference, Evolution Artificielle, EA'2001. Lecture notes in computer science, vol 2310. Springer, Berlin pp 205–216 (Selected Papers)

  • Simpson TW, Peplinski JD, Koch PN, Allen JK (2001) Metamodels for computer-based engineering design: survey and recommendations. Eng Comput 17(2):129–150

    Article  MATH  Google Scholar 

  • Sobieszczanski-Sobieski J, Kodiyalam S, Yang RY (2001) Optimization of car body under constraints of noise, vibration, and harshness (NVH), and crash. Struct Multidiscipl Optim 22(4):295–306

    Article  Google Scholar 

  • United Nations Economic Commission for Europe (1998) ECE R94: uniform provisions concerning the approval of vehicles with regard to the protection of the occupants in the event of a frontal collision

  • Yang RJ, Wang N, Tho CH, Bobineau JP (2005) Metamodeling development for vehicle frontal impact simulation. J Mec Des 127(5):1014–1020

    Article  Google Scholar 

  • Yoshimura M, Nishiwaki S, Izui K (2005) A multiple cross-sectional shape optimization method for automotive body frames. J Mec Des 127:49–57

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Yu Q, Koizumi N, Yajima H, Shiratori M (2001) Optimum design of vehicle frontal structure and occupant restraint system for crashworthiness (A multilevel approach using SDSS). JSME Int J Ser A Solid Mech Mater Eng 44(4):594–601

    Google Scholar 

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Correspondence to Qing Li.

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Liao, X., Li, Q., Yang, X. et al. Multiobjective optimization for crash safety design of vehicles using stepwise regression model. Struct Multidisc Optim 35, 561–569 (2008). https://doi.org/10.1007/s00158-007-0163-x

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  • DOI: https://doi.org/10.1007/s00158-007-0163-x

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