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Weighted principal component analysis combined with Taguchi’s signal-to-noise ratio to the multiobjective optimization of dry end milling process: a comparative study

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Abstract

The weighted principal component analysis (WPCA) method is a mathematical programming technique developed to optimize multiple correlated characteristics, considering the most significant principal components scores, weighted by their respective eigenvalues. This method has obtained noteworthy results, given that it reduces the data set and still considers the correlation between the responses. However, when multiple correlated characteristics also have conflicting objectives, maximizing or minimizing the WPCA can favor some variables and harm others. This paper proposes a hybrid approach able to standardize the optimization objectives of the original responses, reduce dimensions, and, at the same time, eliminate the correlation between the multiple responses. This approach, called Weighted Principal Component Analysis combined with Taguchi’s Signal-to-noise ratio (or WPCA-SNR), is based on Taghuchi’s signal-to-noise ratio and Principal Component Analysis weighted by their respective eigenvalues. Since most of the manufacturing processes present multiple correlated characteristics and conflicting objectives, a case study based in six quality characteristics of the dry end milling process of the AISI 1045 steel is here presented to illustrate the comparative performance of two approaches, WPCA and WPCA-SNR. Theoretical and experimental results indicate that the WPCA-SNR method has evidenced acceptable solutions for both objectives, indicating feasibility of the multiobjective optimization technique applied to this process. In this case, fz = 0.08 mm/tooth, ap = 1.62 mm, Vc = 331 m/min, and ae = 15.49 mm are the optimal parameters for minimizing roughness and maximizing material removal rate, simultaneously.

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Acknowledgments

The authors would like to thank the National Counsel of Technological and Scientific Development (CNPq), the Higher Education Personnel Improvement Coordination (CAPES), the Foundation for Research Support of the State of Minas Gerais (FAPEMIG), and Foundation for Research Support of the State of Minas Gerais (IFSULDEMINAS).

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Authors and Affiliations

  1. Institute of Production Engineering and Management, Federal University of Itajubá, Bps Avenue 1303, Itajubá, Minas Gerais, 37500-188, Brazil

    Danielle M. D. Costa, Gabriela Belinato, Tarcísio G. Brito, Anderson P. Paiva, João R. Ferreira & Pedro P. Balestrassi

  2. Instituto Federal do Sul de Minas – Campus Pouso Alegre, Avenida Maria da Conceição Santos 900, Parque Real, Pouso Alegre, Minas Gerais, 37550-000, Brazil

    Danielle M. D. Costa, Gabriela Belinato & João R. Ferreira

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  1. Danielle M. D. Costa
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  2. Gabriela Belinato
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  3. Tarcísio G. Brito
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  4. Anderson P. Paiva
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  5. João R. Ferreira
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  6. Pedro P. Balestrassi
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Correspondence to Danielle M. D. Costa.

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Technical Editor: Márcio Bacci da Silva.

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Costa, D.M.D., Belinato, G., Brito, T.G. et al. Weighted principal component analysis combined with Taguchi’s signal-to-noise ratio to the multiobjective optimization of dry end milling process: a comparative study. J Braz. Soc. Mech. Sci. Eng. 39, 1663–1681 (2017). https://doi.org/10.1007/s40430-016-0614-7

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