The multi-objective non-probabilistic interval optimization of the loading paths for T-shape tube hydroforming

The focus of presented paper is to find a reliable Pareto front of the loading paths for T-shape tube hydroforming (THF) process using multi-objective non-probabilistic interval optimization method. Three indicators are included to measure the forming quality of THF process: the contact area is used to evaluate the calibration degree; bursting failure is estimated by the maximum thinning ratio and the protrusion height is also taken into consideration. The reliability-based degree of interval of constraints is employed to guarantee the reliability of THF process. A validated finite element model is adopted to conduct virtual experiments. The percentage contributions of the loading parameters for each indicators are calculated by the Taguchi method, and some significant parameters are identified and the dimensionality of the design variables can be reduced. The support vector regression model whose accuracy is calculated by leave-one-out cross-validated method is adopted to improve the optimization efficiency for the determination of the Pareto front. The Pareto fronts of uncertain optimization and deterministic optimization are compared, and the results show that more reliable solutions can be achieved by the presented method.