Constrained Efficient Global Optimization for Pultrusion Process

Composite materials, as the name indicates, are composed of different materials which yield superior performance as compared to individual components. Pultrusion is one of the most costeffective 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’, therefore attractive and efficient tool for autonomous optimization. However, the complexity of the numerical models is increasing in parallel to the advances in the computer hardware and software, which in turn makes it still sometimes ‘expensive’ and forces us to use them sparingly. These relatively more complex models can be replaced with ‘surrogates’, which are less complex therefore faster to evaluate representative models, keeping in mind the trade-off between the accuracy and the computational expense. In this article, a previously validated thermo-chemical simulation of the pultrusion process (considering the steady-state conditions) has shortly been presented. Following this, the surrogate methodology which is composed of a statistical learning technique (i.e. Kriging) and a new constrained optimization technique based on this surrogate method are introduced. Next, a validation case is presented to clarify the working principles of the implementation, which also supports the upcoming main optimization test cases. These design problems involve the design of the heating die with one, two or three heaters together with the pulling speed. The results show that the proposed methodology is very efficient in finding the optimal process and design parameters.