Sequential metamodelling application to improve porthole die design

Abstract The conventional trial—error method and empirical approaches are time consuming for the design of complex shaped products like porthole dies. These methods are associated with higher production costs, lower efficiency, and design inaccuracies pertaining to ambiguity and uncertainty. Owing to these deficiencies, there is a need for a more reliable and better design approach. In this article, a Kriging metamodel and differential evolution-based random simulation design methodology is proposed in order to reduce the cognitive load on the designer. The proposed methodology helps in selecting the set of parameters to be used to perform a simulation such that an improved design is delivered with reduced time and effort. The combination of the input parameters and their probable effect on the final design is evaluated and provided to the designer beforehand. This information, when juxtaposed with the designer's knowledge, gives greater opportunities to produce an optimal design. The sequential sampling strategy is used to select this set of parameters. It depends on the confidence value: a function of the design variables and the desired performance parameter. A Kriging metamodel is employed for modelling a random simulation of porthole extrusion with different influencing parameters. It converts the black-box region (no information zone in the design space) into a grey region (design space with some available information). Differential evolution (an evolutionary algorithm) is used to search for the black-box region carrying the least information in the design space. Three-dimensional extrusion of aluminium is considered in this article for designing a porthole die. The effect of variation of the design parameters is described, sampling points are generated, and the effective set of parameters are evaluated. The results obtained with the proposed sequential methodology are comparable with the simulation results presented in the literature for porthole extrusion.