In this study, a dual response surface model-based multi-objective robust optimization method is introduced to deal with the uncertainties in the tube hydroforming process. The objective of this study is to maximize the protrusion height and minimize the thinning ratio; meanwhile, the variations of the objectives should be minimized. A valid finite element model obtained from experimental result and LS-DYNA is employed to simulate the T-shape tube hydroforming process. To improve computation efficiency, radial basis function combined with Latin hypercube and orthogonal design sampling strategies is employed to construct dual response surface model, which are the mean and standard deviation response of the hydroforming process, respectively. The robust Pareto solutions can be obtained using NSGA-II; meanwhile, the ideal point method is used to obtain the most satisfactory solution from the Pareto solutions for the design engineers. As a conclusion, a significant improvement of the robustness can be achieved; however, the mean performance of the protrusion height has to be sacrificed.

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. Multiobjective 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.

No abstract

No abstract