RBF surrogate model and EN1317 collision safety-based optimization of two guardrails

  • Sedat OzcananEmail author
  • Ali Osman Atahan
Industrial Application


The purpose of using roadside safety equipment is to protect vehicle occupants during an accident by reducing the severity of impact. Using poorly designed safety equipment can have serious consequences. While roadside safety elements are designed primarily for safety, cost-effectiveness cannot be overlooked. This study is aimed to optimize H1W4 and H2W4 performance level guardrails manufactured from S235JR, S275JR, and S355JR grade steel materials in terms of safety and economy. For this purpose, surrogate model-based optimization is utilized. In this context, the design variables are selected as post width (x1) and cross-sectional thickness of rail (x2), while objective functions are selected as working width (w) and vehicle exit angle (α). The design variables (x1, x2) are derived by full factorial design (FFD) method and crash test simulations are utilized to construct objective and constraint functions. Consequently, radial basis function (RBF)-based metamodels are created with the help of the obtained data and later the accuracy of the models is validated. Finally, the RBF metamodels are optimized using the multi-objective genetic algorithm (MOGA). As a result of the simulation-based design optimization (SBDO), the optimum designs of H1W4 and H2W4 guardrail systems for different steel material grades are achieved. It is concluded that the final guardrail designs meet the safety criteria as well as provide an economic advantage of up to 23% compared to existing guardrail designs.


Guardrails EN1317 safety criteria Radial basis function (RBF) Multi-objective optimization LS-DYNA 



Design of experiment


European norm


Finite element analysis


Finite element model


Genetic algorithm


Latin hypercube design


Livermore software open code 3D finite element program


Maximum absolute error


Manual for assessing safety hardware


Multi-objective genetic algorithm


Multi-objective optimization


Post embedment depth


Radial basis function


Radial basis function—multiquadric


Relative error


Root mean square error


Root mean square cross-validation error


Sum of squared errors


Simulation-based design optimization


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. AASHTO MASH-1 (2009) Manual for assessing safety hardware (MASH). 1st ed. Washington (DC): American association of state highway transportation officials, Washington, USAGoogle Scholar
  2. Acar E (2014) Simultaneous optimization of shape parameters and weight factors in ensemble of radial basis functions. Struct Multidiscip Optim 49(6):969–978CrossRefGoogle Scholar
  3. Atahan AO (2002) Finite element simulation of a strong-post W-beam guardrail system. Simulation 78(10):587–599CrossRefGoogle Scholar
  4. Atahan AO (2003) Impact behaviour of G2 steel weak-post W-beam guardrail on nonlevel terrain. Int J Heavy Veh Syst 10(3):209–223CrossRefGoogle Scholar
  5. Atahan AO, Arslan T (2012) Collision behaviour of double W-beam transition. Int J Heavy Veh Syst 19(1):76–91CrossRefGoogle Scholar
  6. Atahan AO, Cansiz OF (2005a) Impact analysis of a vertical flared back bridge rail-to-guardrail transition structure using simulation. Finite Elem Anal Des 41:371–396CrossRefGoogle Scholar
  7. Atahan AO, Cansiz OF (2005b) Improvements to G4 (RW) strong-post round-wood, W beam guardrail system. J Transp Eng 131(1):63–73CrossRefGoogle Scholar
  8. Atahan AO, Musab Erdem M (2016) Evaluation of 12 m long turned down guardrail end terminal using full-scale crash testing and simulation. Lat Am J Solids Struct 13(16):3107–3125 ISSN: 1679–7825CrossRefGoogle Scholar
  9. Atahan AO, Yucel AO, Erdem MM (2014) Crash testing and evaluation of a new generation L1 containment level guardrail. Eng Fail Anal 38:25–37CrossRefGoogle Scholar
  10. Benki A, Habbal A, Mathis G (2017) A metamodel-based multicriteria shape optimization process for an aerosol can. Alexandria Eng J 57(3):1905–1915. CrossRefGoogle Scholar
  11. Bi J, Fang H, Wang Q, Ren X (2010) Modelling and optimization of foam-filled thinwalled columns for crashworthiness designs. Finite Elem Anal Des 46(9):698–709CrossRefGoogle Scholar
  12. Buth CE, Bullard DL, Menges WL (2006) NCHRP report 350 test 3–11 of the long-span guardrail with 5.7 m clear span and nested W-beams over 11.4 m. Report 405160–1-1. Texas Transportation Institute, USA, TexasGoogle Scholar
  13. Cansiz OF, Atahan AO (2006) Crash test simulation of a modified thrie-beam high containment level guardrail under NCHRP report 350 TL 4-12 conditions. Int J Heavy Veh Syst 13:2–18CrossRefGoogle Scholar
  14. Cao L, Jiang P, Chen Z, Zhou Q, Zhou H (2015) Metamodel assisted robust optimization under interval uncertainly based on reverse model. IFAC-Papers Online 48-28:1178–1183CrossRefGoogle Scholar
  15. CEN (2014) European Committee for Standardization. European standard EN1317, testing and evaluation of road restraint systems, BrusselsGoogle Scholar
  16. Committee on Guardrails and Guide Posts (1962) Proposed full-scale testing procedures for guardrails. Highway research correlation service circular 482. Washington (DC): Highway Research Board, USAGoogle Scholar
  17. Consolazio GR, Chung JH, Gurley KR (2003) Impact simulation and full scale crash testing of a low profile concrete work zone barrier. Comput Struct 81:1359–1374CrossRefGoogle Scholar
  18. CSI (2017) Crash testing of H1 and H2 guardrails systems. 0021\ME\HRB\17, Bollate, ItalyGoogle Scholar
  19. Davids WG, Botting JK, Peterson M (2006) Development and structural testing of a composite-reinforced timber highway guardrail. Constr Build Mater 20:733–743CrossRefGoogle Scholar
  20. Faller RK, Polivka KA, Kuipers BD, Bielenberg RW, Reid JD, Rohde JR, Sicking DL (2004) Midwest guardrail system for standard and special applications. Transp Res Rec 1890(1):19–33CrossRefGoogle Scholar
  21. Faller R, Sicking D, Bielenberg R, Rohde J, Polivka K, Reid J (2007) Performance of steel-post, W-beam guardrail systems. Transp Res Rec 2025:18–33CrossRefGoogle Scholar
  22. Faller R, Reid J, Kretschmann D, Hascall J, Sicking D (2009) Midwest guardrail system with round timber posts. Transp Res Rec 2120:47–59CrossRefGoogle Scholar
  23. Fang H, Rais-Rohani M, Liu Z, Horstemeyer MF (2005) A comparative study of metamodeling methods for multi-objective crashworthiness optimization. Comput Struct 83:2121–2136CrossRefGoogle Scholar
  24. Fang H, Wang Q, Weggel DC (2015) Crash analysis and evaluation of cable median barriers on sloped medians using an efficient finite element model. Adv Eng Softw 82:1–13CrossRefGoogle Scholar
  25. Forrester AIJ, Keane AJ (2009) Recent advances in surrogate-based optimization. Prog Aerosp Sci 45(1–3):50–79CrossRefGoogle Scholar
  26. Goel T, Haftka RT, Shyy W, Queipo NV (2007) Ensemble of surrogates. Struct Multidiscip Optim 33(3):199–216CrossRefGoogle Scholar
  27. Gutmann HM (2001) A radial basis function method for global optimization. J Glob Optim 19:201–227MathSciNetCrossRefzbMATHGoogle Scholar
  28. Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophys Res 76:1905–1915CrossRefGoogle Scholar
  29. Horstemeyer MF, Ren X, Fang H, Acar E, Wang PT (2009) A comparative study of design optimization methodologies for side-impact crashworthiness using injury-based versus energy-based criterion. Int J Crashworthiness 14(2):125–138CrossRefGoogle Scholar
  30. Hou S, Li Q, Long S, Yang X, Li W (2007) Design optimization of regular hexagonal thin-walled columns with crashworthiness criteria. Finite Elem Anal Des 43:555–565CrossRefGoogle Scholar
  31. Hou S, Li Q, Long S, Yang X, Li W (2008) Multiobjective optimization of multi-cell sections for the crashworthiness design. Int J Impact Eng 35(11):1355–1367CrossRefGoogle Scholar
  32. Hou S, Li Q, Long S, Yang X, Li W (2009) Crashworthiness design for foam filled thin-walled structures. Mater Des 30(6):2024–2032CrossRefGoogle Scholar
  33. Hou S, Zheng Y, Xie J, Han X (2013) Optimization design of NJ shaped guardrail based on collision safety consideration. Int J Comput Methods 11:1350083CrossRefGoogle Scholar
  34. Hou SJ, Liu TY, Dong D, Han X (2014a) Factor screening and multivariable crashworthiness optimization for vehicle side impact by factorial design. Struct Multidiscip Optim 49:147–167CrossRefGoogle Scholar
  35. Hou S, Tan W, Zheng Y, Han X, Li Q (2014b) Optimization design of corrugated beam guardrail based on RBF-MQ surrogate model and collision safety consideration. Adv Eng Softw 78:28–40CrossRefGoogle Scholar
  36. Ky VK, D’Ambrosio C, Hamadi Y, Liberti L (2016) Surrogate-based methods for black-box optimization. Int Trans Oper Res 24(3):393–424. MathSciNetzbMATHGoogle Scholar
  37. Liao X, Li Q, Yang X, Zhang W, Li W (2008) Multi-objective optimization for crash safety design of vehicles using stepwise regression model. Struct Multidiscip Optim 35(6):561–569CrossRefGoogle Scholar
  38. LSTC (2014) A general purpose dynamic finite element analysis program, LS-DYNA version 971 user’s manual. Livermore Software Technology Corporation, Livermore, California, USAGoogle Scholar
  39. MATLAB (2017) Matlab and statistics toolbox release (2017b) The MathWorks, Inc., Natick, Massachusetts, USAGoogle Scholar
  40. McDonald DB, Grantham WJ, Tabor WL, Murphy MJ (2007) Global and local optimization using radial basis function response surface models. Appl Math Model 31:2095–2110CrossRefzbMATHGoogle Scholar
  41. Meckesheimer M, Booker AJ, Barton RR, Simpson TW (2002) Computationally inexpensive metamodel assessment strategies. AIAA J 40(10):2053–2060CrossRefGoogle Scholar
  42. Mullur AA, Messac A (2005) Extended radial basis functions: more flexible and effective metamodeling. AIAA J 43(6):1306–1315CrossRefGoogle Scholar
  43. NCAC (2008) Finite element model archive, George Washington University FHWA/NHTSA National Crash Analysis Center,, Virginia (Accessed 2008)
  44. Plaxico CA, Ray MH, Hiranmayee K (2000) Comparison of the impact performance of the G4 1W and G4 2W guardrail systems: comparison under NCHRP report 350 test 3-11 conditions. Transp Res Rec 1720:7–18CrossRefGoogle Scholar
  45. Plaxico CA, Kennedy JC, Miele CR (2006) Development of an NCHRP report 350 TL-3 New Jersey shape 50-inch portable concrete barrier. Final report FHWA/OH- 2006/16. Ohio Department of Transportation, Ohio, USAGoogle Scholar
  46. Ray M. H., Patzner G. S (1997) Finite-element model of modified eccentric loader terminal MELT, Transportation Research Record 1599, Transportation Research Board, Washington, DC, 11–21Google Scholar
  47. Ray M, Engstrand K, Plaxico C, McGinnis R (2001) Improvements to the weak-post W-beam guardrail. Transp Res Rec 1743(1):88–96CrossRefGoogle Scholar
  48. Reid JD, Sicking DL, Faller RK, Pfeifer B (1997) Development of a new guardrail system. Transp Res Rec 1599(1):72–80CrossRefGoogle Scholar
  49. Ren Z, Vesenjak M (2005) Computational and experimental crash analysis of the road safety barrier. Eng Fail Anal 12:963–973CrossRefGoogle Scholar
  50. Ross Jr HE, Sicking DL, Zimmer RA, Michie JD (1993) Recommended procedures for the safety performance evaluation of highway features. NCHRP report 350. Washington (DC): Transportation Research Board, National Research Council, Washington DC, USAGoogle Scholar
  51. Rudholm J, Wojciechowski A (2007) A method for simulation based optimization using radial basis functions. Master’s Thesis, Göteborg University, Göteborg, SwedenGoogle Scholar
  52. Sicking, D. L. (1995) Applications of simulation in design and analysis of roadside safety features. Transportation Research Circular 435, TRB, National Research Council, Washington DCGoogle Scholar
  53. Sicking DL, Reid JD, Rohde JR (2002) Development of the midwest guardrail system. Transp Res Rec 1797:44–52CrossRefGoogle Scholar
  54. Soltani M, Moghaddam TB, Karim MR, Sulong NH (2013) The safety performance of guardrail systems: review and analysis of crash tests data. Int J Crashworthiness 18:530–543CrossRefGoogle Scholar
  55. Sui YK, Li SP, Guo YQ (2008) An efficient global optimization algorithm based on augmented radial basis function. Int J Simul Multidisci Des Optim 2:49–55CrossRefGoogle Scholar
  56. Xiang Y, Wang Q, Fan Z, Fang H (2006) Optimal crashworthiness design of a spot-welded thin-walled hat section. Finite Elem Anal Des 42(10):846–855CrossRefGoogle Scholar
  57. Yin H, Wen G, Hou S, Chen K (2011) Crushing analysis and multiobjective crashworthiness optimization of honeycomb-filled single and bitubular polygonal tubes. Mater Des 32:4449–4460CrossRefGoogle Scholar
  58. Yin H, Fang H, Wang Q, Wen G (2016) Design optimization of a MASH TL-3 concrete barrier using RBF-based metamodels and nonlinear finite element simulations. Eng Struct:0141–0296Google Scholar
  59. Yin H, Xiao Y, Wen G, Fang H (2017) Design optimization of a new W-beam guardrail for enhanced highway safety performance. Adv Eng Softw 112:154–164CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Istanbul Technical University Civil Engineering FacultySariyer/IstanbulTurkey

Personalised recommendations