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

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Title: Modeling the uncertainty in response surface methodology through optimization and Monte Carlo simulation: An application in stamping process
Authors: Aneirson Francisco da Silva, Fernando Augusto Silva Marins, Erica Ximenes Dias, Jose Benedito da Silva Oliveira
Source: Materials & Design, Vol 173, Iss , Pp - (2019)
Publisher Information: Elsevier, 2019.
Publication Year: 2019
Collection: LCC:Materials of engineering and construction. Mechanics of materials
Subject Terms: Materials of engineering and construction. Mechanics of materials, TA401-492
More Details: 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. Keywords: Stamping process, Experimental problems, Response surface methodology, Uncertainty, Optimization via Monte Carlo simulation
Document Type: article
File Description: electronic resource
Language: English
ISSN: 0264-1275
Relation: http://www.sciencedirect.com/science/article/pii/S0264127519302138; https://doaj.org/toc/0264-1275
DOI: 10.1016/j.matdes.2019.107776
Access URL: https://doaj.org/article/a5aeb778c9cf45a099d802b827de758d
Accession Number: edsdoj.5aeb778c9cf45a099d802b827de758d
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  Data: <searchLink fieldCode="AR" term="%22Aneirson+Francisco+da+Silva%22">Aneirson Francisco da Silva</searchLink><br /><searchLink fieldCode="AR" term="%22Fernando+Augusto+Silva+Marins%22">Fernando Augusto Silva Marins</searchLink><br /><searchLink fieldCode="AR" term="%22Erica+Ximenes+Dias%22">Erica Ximenes Dias</searchLink><br /><searchLink fieldCode="AR" term="%22Jose+Benedito+da+Silva+Oliveira%22">Jose Benedito da Silva Oliveira</searchLink>
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  Data: Materials & Design, Vol 173, Iss , Pp - (2019)
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  Data: 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. Keywords: Stamping process, Experimental problems, Response surface methodology, Uncertainty, Optimization via Monte Carlo simulation
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