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

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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 xi and dependent variables ys 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 element (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.

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Authors and Affiliations

  1. Department of Production, São Paulo State University, Av. Ariberto Pereira da Cunha, 333, Portal das Colinas, Guaratinguetá, São Paulo, CEP 12516-410, Brazil

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

Authors
  1. Aneirson Francisco da Silva
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  2. Fernando Augusto Silva Marins
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  3. Jose Benedito da Silva Oliveira
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  4. Erica Ximenes Dias
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Correspondence to Aneirson Francisco da Silva.

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Ethics approval

This paper does not use data, which requires ethical approval, since all studies are done in a computational way. However, the main contribution of this article is to propose a new procedure that considers the insertion of uncertainties in the coefficients of the empirical functions in RSM with multiple responses, in practical experimental problems. It was possible to determine that RSM combined finite elements with Optimization via Monte Carlo Simulation (OvMCS) outperforms the use of (deterministic) optimization, using the generalized reduced gradient (GRG) algorithm, which is traditionally employed in RSM applications. Therefore, this paper does not directly involve people or biological information.

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Author contribution

The author Aneirson Silva was responsible for writing the article as well as programming in VBA-excel for the optimization multiobjectives problems and, also, for the statistical modeling of the data.

The author José Benedito was responsible for the writing of the article as well as the modeling and simulation by finite elements.

The author Fernando Marins was responsible for writing the article as well as for the final correction of the paper.

The author Erica Ximenes was responsible for writing the article and statistical and mechanical analysis.

Consent to participate and consent to publish

All authors are aware of their participation and also regarding the publication of this paper.

Prof. Aneirson Francisco da Silva

Prof. Fernando Augusto Silva Marins

Phd. Erica Ximenes Dias

Msc. José Benedito da Silva Oliveira

Competitive interests

I am submitting the article Multiple Response Optimization and Finite Element Method combined with Optimization via Monte Carlo Simulation in a stamping process under uncertainty. The main contribution of this article is to propose a new procedure that considers the insertion of uncertainties in the coefficients of the empirical functions in RSM with multiple answers, in practical experimental problems. This innovative procedure provides managers with useful information that will facilitate their work in seeking improvements in the analyzed printing process.

The main competitive interests are linked to companies that produce automotive components, since this system proposes an innovative way to analyze and improve stamping process problems.

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da Silva, A.F., Marins, F.A.S., da Silva Oliveira, J.B. et al. Multi-objective optimization and finite element method combined with optimization via Monte Carlo simulation in a stamping process under uncertainty. Int J Adv Manuf Technol 117, 305–327 (2021). https://doi.org/10.1007/s00170-021-07644-9

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