Hierarchical Metamodeling of the Air Bending Process

Despite the tremendous effort of researchers and manufacturing engineers in improving the predictability of the air bending process, there is still a strong need for comprehensive and dependable prediction models. Currently, available modeling approaches all present some relevant limitations in practical applications. In this paper, we propose a new method, which represents an improvement over all existing modeling and prediction techniques. The proposed method can be used for accurate prediction of the main response variables of the air bending process: the angle α after springback and the bend deduction BD. The metamodeling method is based on the hierarchical fusion of different kinds of data: the deterministic low-fidelity response of numerical finite element method (FEM) simulations and the stochastic high fidelity response of experimental tests. The metamodel has been built over a very large database, unprecedented in the scientific literature on air bending, made of more than 500 numerical simulations and nearly 300 experimental tests. The fusion is achieved first by interpolating the FEM simulations with a kriging predictor; then, the hierarchical metamodel is built as a linear regression model of the experimental data, using the kriging predictor among the regressors. The accuracy of the method has been proved using a variant of the leave-one-out cross validation technique. The quality of the prediction yielded by the proposed method significantly over-performs the current prediction of the press brake on-line numerical control.