A hybrid multi-fidelity approach to the optimal design of warm forming processes using a knowledge-based artificial neural network

In this paper, a hybrid multi-fidelity optimization approach based on a knowledge-based artificial neural network (KBNN) was used to determine the optimal heating strategy in warm forming processes. First, a less costly, but less accurate isothermal finite element analysis (FEA), which neglected the complex heat transfer between the part and tooling elements, was performed to obtain overall knowledge about the effect of temperature on forming performance. Then, a small number of more accurate and expensive (i.e., longer computational time) non-isothermal FEA results were utilized in an artificial neural network (ANN), along with the prior knowledge from the isothermal FEA, to improve the accuracy in defining the non-linear relationship between the design variables (i.e., regional temperatures on the tooling) and the response (i.e., part depth value before failure). The accuracy of the non-isothermal FEA was validated by comparing its prediction results to the experimental findings. This approach was demonstrated for forming a rectangular cup, where it offered a rapid and accurate recommendation of the optimal temperature distribution on the tooling elements for improved formability. The individual and interaction effects of the regional temperatures on formability were also evaluated in detail by constructing the response surfaces near the optimal design point using the multi-fidelity system developed. Finally, a comparison of the temperature and thickness strain distributions on the formed parts was made under various operating conditions, to acquire detailed information on the deformation characteristics of the material.