Global sensitivity analysis and multi-objective optimisation of loading path in tube hydroforming process based on metamodelling techniques

Tube hydroforming process is widely used in various industrial applications which consists of combining internal pressure and axial displacement to manufacture tubular parts. Inappropriate choice as small changes in such variables may affect the process stability and, in some cases, lead to failure. Consequently, loading path should be optimised to better control the process and to guarantee hydroformed parts with desired specifications. However, optimisation procedure requires several evaluations of the real models which induces a huge computational time. To cope with this limitation, we propose to compare two metamodelling techniques to solve the problem efficiently: the response surface method and the least squares support vector regression. To enhance the metamodels precision, optimal latin hypercube design is used to generate sampled points. It is obtained through iterative optimisation procedure based on a modified version of the simulated annealing algorithm by minimising simultaneously two optimality criterions. Then, multi-objective optimisation problem is formulated to search for the Pareto optimal solutions. Fuzzy classification is then applied to rank the non-dominated solutions which helps designers in the decision-making phase. Before optimising the process, a global sensitivity analysis is carried out using the variance-based method by coupling metamodels and Monte Carlo simulations in order to identify the relative importance of the design variables in terms of internal pressure and axial displacement on the variance of the responses of interest defined to control the process.