Optimum design of pultrusion process via evolutionary multi-objective optimization



Pultrusion is one of the most cost-effective manufacturing techniques for producing fiber-reinforced composites with constant cross-sectional profiles. This obviously makes it more attractive for both researchers and practitioners to investigate the optimum process parameters, i.e., pulling speed, power, and dimensions of the heating platens, length and width of the heating die, design of the resin injection chamber, etc., to provide better understanding of the process, consequently to improve the efficiency of the process as well as the product quality. Using validated computer simulations is “cheap” and therefore is an attractive and efficient tool for autonomous (numerical) optimization. Optimization problems in engineering in general comprise multiple objectives often having conflict with each other. Evolutionary multi-objective optimization (EMO) algorithms provide an ideal way of solving this type of problems without any biased treatment of objectives such as weighting constants serving as pre-assumed user preferences. In this paper, first, a thermochemical simulation of the pultrusion process has been presented considering the steady-state conditions. Following that, it is integrated with a well-known EMO algorithm, i.e., nondominated sorting genetic algorithm (NSGA-II), to simultaneously maximize the pulling speed and minimize “total energy consumption” (TEC) which is defined as a measure of total heating area(s) and associated temperature(s). Finally, the results of the evolutionary computation step is used as starting guesses for a serial application of a of gradient-based classical algorithm to improve the convergence. As a result, a set of optimal solutions are obtained for different trade-offs between the conflicting objectives. The trade-off solution, thus obtained, would remain as a valuable source for a multi-criterion decision-making task for eventually choosing a single preferred solution for the pultrusion process.


Multi-objective optimization Evolutionary algorithm Mathematical programming Pultrusion process Simulation Thermochemical model 


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  1. 1.
    Hackett RM, Prasad SN (1989) Pultrusion process modeling. Adv Thermoplast Matrix Compos Mater ASTM STP 1044:62–70CrossRefGoogle Scholar
  2. 2.
    Ding Z, Li S, Lee LJ (2002) Influence of heat transfer and curing on the quality of pultruded composites II: modeling and simulation. Polym Compos 23:957–969CrossRefGoogle Scholar
  3. 3.
    Liu XL, Crouch IG, Lam YC (2000) Simulation of heat transfer and cure in pultrusion with a general-purpose finite element package. Compos Sci Technol 60:857–864CrossRefGoogle Scholar
  4. 4.
    Carlone P, Palazzo GS, Pasquino R (2006) Pultrusion manufacturing process development by computational modelling and methods. Math Comput Model 44:701–709CrossRefMATHGoogle Scholar
  5. 5.
    Baran I, Tutum CC, Hattel JH (2013) The effect of thermal contact resistance on the thermosetting pultrusion process. Compos Part B Eng 45:995–1000CrossRefGoogle Scholar
  6. 6.
    Baran I, Hattel JH, Tutum CC (2013) Thermo-chemical modelling strategies for the pultrusion process. Appl Compos Mater. doi: 10.1007/s10443-013-9331-x
  7. 7.
    Valliappan M, Roux JA, Vaughan JG, Arafat ES (1996) Die and post-die temperature and cure in graphite-epoxy composites. Compos Part B-Eng 27:1–9CrossRefGoogle Scholar
  8. 8.
    Chachad YR, Roux JA, Vaughan JG, Arafat E (1995) Three-dimensional characterization of pultruded fiberglass-epoxy composite materials. J Reinf Plast Compos 14:495–512Google Scholar
  9. 9.
    Baran I, Tutum CC, Hattel JH (2013) The internal stress evaluation of the pultruded blades for a Darrieus wind turbine. Key Eng Mater 554–557:2127–2137CrossRefGoogle Scholar
  10. 10.
    Baran I, Tutum CC, Nielsen MW, Hattel JH (2013) Process induced residual stresses and distortions in pultrusion. Compos Part B Eng 51:148–161CrossRefGoogle Scholar
  11. 11.
    Baran I, Hattel JH, Tutum CC (2013) The impact of process parameters on the residual stresses and distortions in pultrusion. In: Proceedings of the 19th international conference on composite materials (ICCM19), Montreal, Canada, 28 July–02 AugustGoogle Scholar
  12. 12.
    Baran I, Tutum CC, Hattel JH (2012) Probabilistic thermo-chemical analysis of a pultruded composite rod. In: Proceedings of the 15th European conference on composite materials, ECCM-15, Venice, 24–28 JuneGoogle Scholar
  13. 13.
    Baran I, Tutum CC, Hattel JH (2013) Reliability estimation of the pultrusion process using the first-order reliability method (FORM). Appl Compos Mater 20:639–653CrossRefGoogle Scholar
  14. 14.
    Baran I, Hattel JH, Tutum CC (2013) Probabilistic modelling of the process induced variations in pultrusion. In: Proceedings of the 19th international conference on composite materials (ICCM19), Montreal-Canada, 28 July–02 AugustGoogle Scholar
  15. 15.
    Joshi SC, Lam YC, Win Tun U (2003) Improved cure optimization in pultrusion with pre-heating and die-cooler temperature. Compos Part A-Appl S 34:1151–1159CrossRefGoogle Scholar
  16. 16.
    Lam YC, Li J, Joshi SC (2003) Simultaneous optimization of die-heating and pull-speed in pultrusion of thermosetting composites. Polym Compos 24:199–209CrossRefGoogle Scholar
  17. 17.
    Li J, Joshi SC, Lam YC (2002) Curing optimization for pultruded composite sections. Compos Sci Technol 62:457–467CrossRefGoogle Scholar
  18. 18.
    Carlone P, Palazzo GS (2007) Pultrusion manufacturing process development: cure optimization by hybrid computational methods. Comput Math Appl 53:1464–1471CrossRefGoogle Scholar
  19. 19.
    Chen X, Xie H, Chen H, Zhang F (2010) Optimization for CFRP pultrusion process based on genetic algorithm-neural network. Int J Mater Form 3:1391–1399CrossRefGoogle Scholar
  20. 20.
    Baran I, Tutum CC, Hattel JH (2013) Optimization of the thermosetting pultrusion process by using hybrid and mixed integer genetic algorithms. Appl Compos Mater 20:449–463CrossRefGoogle Scholar
  21. 21.
    Tutum CC, Baran I, Hattel JH (2013) Utilizing multiple objectives for the optimization of the pultrusion process. Key Eng Mater 554–557:2165–2174CrossRefGoogle Scholar
  22. 22.
    Chankong V, Haimes YY (1983) Multiobjective decision making. Theory and methodology. North Holland, AmsterdamMATHGoogle Scholar
  23. 23.
    Deb K, Agarwal S, Pratap A, Meyarivan TA (2002) Fast and elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. IEEE Trans Evol Comput 6:182– 197CrossRefGoogle Scholar
  24. 24.
    Hattel JH (2005) Fundamentals of numerical modelling of casting processes, 1st edn. Polyteknisk Forlag, LyngbyGoogle Scholar
  25. 25.
    MATLAB (2011) Reference guide. The Mathworks Inc, Natick. ( Scholar
  26. 26.
    Tutum CC, Hattel JH (2011) State-of-the-art multi-objective optimisation of manufacturing processes based on thermo-mechanical simulations. In: Wang L, Ng A, Deb K (eds) Multi-objective evolutionary optimisation for product design and manufacturing. Springer, Berlin, pp 71–133CrossRefGoogle Scholar
  27. 27.
    Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New YorkMATHGoogle Scholar
  28. 28.
    Deb K (2003) Unveiling innovative design principles by means of multiple conflicting objectives. Eng Optim 35:445–470CrossRefGoogle Scholar
  29. 29.
    Branch MA, Grace A (2002) Optimization toolbox user’s guide, version 2, The Math Works, Inc., NatickGoogle Scholar
  30. 30.
    Deb K, Datta R (2012) Hybrid evolutionary multi-objective optimization and analysis of machining operations. Eng Optim 44:1–22CrossRefMathSciNetGoogle Scholar

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© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringMichigan State UniversityEast LansingUSA
  2. 2.Department of Mechanical EngineeringTechnical University of DenmarkKgs. LyngbyDenmark

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