Multi-objective optimization and finite element method combined with optimization via Monte Carlo simulation in a stamping process under uncertainty

Abstract

The Response Surface Methodology (RSM), which uses a quadratic empirical function as an approximation to the original function and allows the identification of relationships between independent variables x i and dependent variables y s associated with multiple responses, stands out. The main contribution of the present study is to propose an innovative procedure for the optimization of experimental problems with multiple responses, which considers the insertion of uncertainties in the coefficients of the obtained empirical functions in order to adequately represent real situations. This new procedure, which combines RSM with the Finite Elements (FE) method and the Monte Carlo Simulation Optimization (OvMCS), was applied to a real stamping process of a Brazilian multinational automotive company. For RSM with multiple responses, were compared the results obtained using the agglutination methods: Compromise Programming, Desirability Function (DF), and the Modified Desirability Function (MDF). The functions were optimized by applying the Generalized Reduced Gradient (GRG) algorithm, which is a classic procedure widely adopted in this type of experimental problem, without the uncertainty in the coefficients of independent factors. The advantages offered by this innovative procedure are presented and discussed, as well as the statistical validation of its results. It can be highlighted, for example, that the proposed procedure reduces, and sometimes eliminates, the need for additional confirmation experiments, as well as a better adjustment of factor values and response variable values when comparing to the results of RSM with classic multiple responses. The new proposed procedure added relevant and useful information to the managers responsible for the studied stamping process. Moreover, the proposed procedure facilitates the improvement of the process, with lower associated costs.