Modeling the uncertainty in response surface methodology through optimization and Monte Carlo simulation: An application in stamping process

Author(s)

da Silva, Aneirson Francisco ; Silva Marins, Fernando Augusto ; Dias, Erica Ximenes ; da Silva Oliveira, Jose Benedito

• Document type: Journal article
• Source: MATERIALS & DESIGN; v. 173, p. 13-pg., 2019-07-05.

Abstract

Among the most frequently used experimental design techniques is the response surface methodology (RSM), which uses an approximation of the real objective function, in the form of an empirical quadratic function. RSM allows the identification of the relations between independent variables (or factors) and a (dependent) response variable. The main contribution of this article is to propose a new procedure that considers the insertion of uncertainties in the coefficients of this empirical function, which is what generally occurs, in practical experimental problems. The new procedure was applied to a real case related to a stamping process in an automotive company, and the results were compared to those obtained by applying classic RSM. The advantages offered by this innovative procedure are presented and discussed, including the statistical validation of the results. The proposed procedure reduces, and sometimes eliminates, the need for additional confirmatory experiments in the laboratory, and allows getting a better adjustment of the factor values and the optimized response variable value compared to the results calculated by classic RSM. It was possible to determine that the proposed procedure outperforms the use of (deterministic) optimization, using the generalized reduced gradient (GRG) algorithm, which is traditionally employed in RSM applications. (C) 2019 Published by Elsevier Ltd. (AU)

• FAPESP's process: 18/06858-0 - Optimization via Monte Carlo simulation combined with the response surface method: a proposal for insertion of uncertainty in optimization of experimental problems
• Grantee: Aneirson Francisco da Silva
• Support Opportunities: Regular Research Grants
• FAPESP's process: 18/14433-0 - Application of the multi-objective optimization under uncertainty for paper waste Reclycing systems
• Grantee: Fernando Augusto Silva Marins
• Support Opportunities: Regular Research Grants