Archives of Computational Methods in Engineering

, Volume 23, Issue 4, pp 723–734 | Cite as

A Comparative Study of Non-traditional Methods for Vehicle Crashworthiness and NVH Optimization

  • Morteza Kiani
  • Ali R. Yildiz
Original Paper


In this paper, metamodeling and five well-known metaheuristic optimization algorithms were used to reduce the weight and improve crash and NVH attributes of a vehicle simultaneously. A high-fidelity full vehicle model is used to analyze peak acceleration, intrusion and component’s internal-energy under Full-Frontal, Offset-Frontal, and Side crash scenarios as well as vehicle natural frequencies. The radial basis functions method is used to approximate the structural responses. A nonlinear surrogate-based mass minimization was formulated and solved by five different optimization algorithms under crash-vibration constraints. The performance of these algorithms is investigated and discussed.


Particle Swarm Optimization Radial Basis Function Differential Evolution Particle Swarm Optimization Algorithm Training Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Fang H, Solanki K, Horstemeyer MF, Rais-Rohani M (2004) Multi-impact crashworthiness optimization with full-scale finite element simulations. In: Proceedings of the 6th World congress on computational mechanics, Beijing, ChinaGoogle Scholar
  2. 2.
    Kiani M, Motoyama K, Rais-Rohani M, Shiozaki H (2014) Joint stiffness analysis and optimization as a mechanism for improving the structural design and performance of a vehicle. Proc IMech Part D J Automob Eng 228(6):689–700CrossRefGoogle Scholar
  3. 3.
    Yildiz AR, Solanki KN (2011) Multi-objective optimization of vehicle crash- worthiness using a new particle swarm based approach. Int J Adv Manuf Technol 59(1–4):367–376Google Scholar
  4. 4.
    Lee KH, Kang DH (2007) Structural optimization of an automotive door using the kriging interpolation method. Proc Inst Mech Eng Part D J Automob Eng 221(12):1525–1534CrossRefGoogle Scholar
  5. 5.
    Yildiz AR (2013) A new hybrid artificial bee colony algorithm for robust optimal design and manufacturing. Appl Soft Comput 13(5):2906–2912CrossRefGoogle Scholar
  6. 6.
    Kiani M, Gandikota I, Parrish A, Motoyama K, Rais-Rohani M (2013) Surrogate-based optimisation of automotive structures under multiple crash and vibration design criteria. Int J Crashworthiness 18(5):473–482CrossRefGoogle Scholar
  7. 7.
    Kiani M, Gandikota I, Rais-Rohani M, Motoyama K (2014) Design of lightweight magnesium car body structure under crash and vibration constraints. J Magnesium Alloys 2(2):99–108CrossRefGoogle Scholar
  8. 8.
    Gandikota I, Rais-Rohani M, DorMohammadi S, Kiani M (2014) Multilevel vehicle–dummy design optimization for mass and injury criteria minimization. Proc IMech Part D J Automob Eng 229(3):283–295CrossRefGoogle Scholar
  9. 9.
    Storn RM, Price KV (1995) Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces technical report TR-95-12, International Computer Science, Berkeley, CaliforniaGoogle Scholar
  10. 10.
    Yildiz AR (2013) Comparison of evolutionary-based optimization algorithms for structural design optimization. Eng Appl Artif Intell 26(1):327–333CrossRefGoogle Scholar
  11. 11.
    Fender J, Duddeck F, Zimmermann M (2014) On the calibration of simplified vehicle crash models. Struct Multidiscip Optim 49(3):455–469CrossRefGoogle Scholar
  12. 12.
    Sigmund O (2011) On the usefulness of non-gradient approaches in topology optimization. Struct Multidiscip Optim 43(5):589–596MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Yildiz AR (2013) A new hybrid differential evolution algorithm for the selection of optimal machining parameters in milling operations. Appl Soft Comput 13(3):1561–1566CrossRefGoogle Scholar
  14. 14.
    Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical report TR06, Erciyes University Press, ErciyesGoogle Scholar
  15. 15.
    Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39(3):459–471MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8(1):687–697CrossRefGoogle Scholar
  17. 17.
    Karaboga D, Ozturk C (2011) A novel clustering approach: Artificial Bee Colony (ABC) algorithm. Appl Soft Comput 11(1):652–657CrossRefGoogle Scholar
  18. 18.
    Price KV, Storn RM (1997) Differential evolution. Dr. Dobb.s J Softw Tools Prof Program 22(4):18–24Google Scholar
  19. 19.
    Price KV, Storn RM, Lampinen JA (2005) Differential evolution a practical approach to global optimization. Springer, BerlinzbMATHGoogle Scholar
  20. 20.
    Huang FZ, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186(1):340–356MathSciNetzbMATHGoogle Scholar
  21. 21.
    Storn R (2008) Differential evolution research-trends and open questions. Advances in differential evolution. Springer, Berlin, pp 1–31CrossRefGoogle Scholar
  22. 22.
    Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, Michigan; re-issued by MIT PressGoogle Scholar
  23. 23.
    Pham DT, Karaboga D (1991) Optimum design of fuzzy logic controllers using genetic algorithms. J Syst Eng 1(2):114–118Google Scholar
  24. 24.
    Kennedy J, Eberhart RC (1995) Particle swarm optimization. Proceedings IEEE international conference on neural networks, Piscataway, 1942–1948Google Scholar
  25. 25.
    Kennedy J, Eberhart R (1997) A discrete binary version of the particle swarm algorithm. In: IEEE Systems, Man, and Cybernetics, Computational Cybernetics and Simulation, Orlando, FL, vol 5, pp 4104–4108Google Scholar
  26. 26.
    Clerc M, Kennedy J (2002) The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58–73CrossRefGoogle Scholar
  27. 27.
    Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculation by fast computing machines. J Chem Phys 21:1087–1091CrossRefGoogle Scholar
  28. 28.
    Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Aarts E, Korst J (2002) Selected topics in simulated annealing. Essays and surveys in metaheuristics. Springer, New York, pp 1–37CrossRefGoogle Scholar
  30. 30.
    Menon S, Gupta R (2004) Assigning cells to switches in cellular networks by incorporating a pricing mechanism into simulated annealing. IEEE Trans Syst Man Cybern Part B Cybern 34(1):558–565CrossRefGoogle Scholar
  31. 31.
    Ceranic B, Fryer C, Baines RW (2001) An application of simulated annealing to the optimum design of reinforced concrete retaining structures. Comput Struct 79(17):1569–1581CrossRefGoogle Scholar
  32. 32.
    Lundy M, Mees A (1986) Convergence of an annealing algorithm. Math Program 34:111–124MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Van Laarhoven P, Aarts E (1987) Simulated annealing: theory and applications. Kluwer Academic Publishers, NorwellGoogle Scholar
  34. 34.
    Strenski P, Kirkpatrick S (1991) Analysis of finite length annealing schedules. Algoritmica 6:346–366MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    NCAC, Finite Element Model of Dodge Neon: Model Year 1996 Version 7. FHWA/NHTSA National Crash Analysis Center, Ashburn, VA, 2006.
  36. 36.
    NHTSA (1997) Frontal Barrier Forty Percent Offset Impact Test: 1996 Dodge Neon, prepared by Kargo Engineering for the U.S. Department of Transportation, Washington, DCGoogle Scholar
  37. 37.
    MGA (1997) Safety compliance testing for FMVSS 214. Side impact protection—passenger cars: 1997 dodge neon, prepared by MGA proving grounds for the U.S. Department of Transportation, Washington, DCGoogle Scholar
  38. 38.
    Hurnall J, Draheim A, Case M, Del Beato J (2003) A review of ‘B’-pillar and front seat belt loads measured in ANCAP offset frontal crash tests. In: Proceedings of 18th international technical conference on the enhanced safety of vehicles, Nagoya, JapanGoogle Scholar
  39. 39.
    Bertocci GE, Esteireiro J, Cooper RA, Young TM, Thomas C (1999) Testing and evaluation of wheelchair caster assemblies subjected to dynamic crash loading. J Rehab Res Dev 36(1):32–41Google Scholar
  40. 40.
    Draheim A, Hurnall J, Case M, Beato JD (2005) Structural energy absorption trends in NCAP crashed vehicles. In: 19th Enhanced safety of vehicles conference, NHTSA, Washington, DC, USA, Paper 05-0317Google Scholar
  41. 41.
    Liao X, Li X, Yang Q, Li W, Zhang W (2008) A two-stage multi-objective optimisation of vehicle crashworthiness under frontal impact. Int J Crashworthiness 13(3):279–288CrossRefGoogle Scholar
  42. 42.
    Kiani M, Shiozaki H, Motoyama K (2013) Simulation-based design optimization to develop a lightweight body-in-white structure focusing on dynamic and static stiffness. Int J Veh Des 67(3):219–236. doi: 10.1504/IJVD.2015.069467
  43. 43.
    Duddeck F (2007) Multidisciplinary optimization of car bodies. Struct Multidisc Optim 35:375–389CrossRefGoogle Scholar
  44. 44.
    Baskin D, Reed D, Seel T, Hunt M (2008) A case study in structural optimization of an automotive body-in-white design, SAE technical paper 2008-01-0880. SAE International, Warrendale, PAGoogle Scholar
  45. 45.
    Parrish A, Rais-Rohani M, Najafi A (2012) Crashworthiness optimisation of vehicle structures with magnesium alloy parts. Int J Crashworthiness 17:259–281CrossRefGoogle Scholar

Copyright information

© CIMNE, Barcelona, Spain 2015

Authors and Affiliations

  1. 1.Engineering Technology Associates Inc. (ETA)TroyUSA
  2. 2.Mechanical Engineering DepartmentBursa Technical UniversityBursaTurkey

Personalised recommendations