The multi-objective optimization of the loading paths for T-shape tube hydroforming using adaptive support vector regression

The objective of this study is to introduce adaptive support vector regression, whose accuracy and efficiency are illustrated through a numerical example, to determine the Pareto optimal solution set for T-shape tube hydroforming process. A validated finite element model developed by the explicit finite element code LS-DYNA is used to conduct virtual T-shape tube hydroforming experiments. Multi-objective optimization problem considering contact area between the tube and counter punch, maximum thinning ratio, and protrusion height is formulated. Then, the Latin hypercube design is employed to construct the initial support vector regression model, and some extra sampling points are added to reconstruct the support vector regression model to obtain the Pareto optimal solution set during each iteration. Finally, the ideal point is used to obtain a compromise solution from the Pareto optimal solution set for the engineers.