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Multivariate Taguchi loss function optimization based on principal components analysis and normal boundary intersection

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Abstract

Optimization methods are widely used to improve industrial processes and enhance the quality characteristics of product, where process costs are directly linked. Given this assumption, this study aims to present a multivariate proposal of the Taguchi loss function, to model and optimize manufacturing processes, searching to establish values that prioritize quality and provide the minimum loss in view of the process costs. For this, design of experiments techniques will be used to model the process and the calculated loss functions. The strategy of principal components analysis is used to minimize the data dimension, considering the structure of variance–covariance. Then, the normal boundary intersection method is used to find the Pareto frontier. Based on the values, the method also proposes a total loss function equation, which is characterized as an approach to choose the optimal point based on the sum of the loss functions for the Pareto frontier through the process cost. To demonstrate the behavior of the method, the flux-cored arc welding of stainless-steel cladding process was applied. In view of the results, the method provided an optimal value at the Pareto frontier, contemplating an appropriate balance between minimal loss and higher quality, which were compared with other studies in the literature. The method also provided a reduction in computational effort of approximately 90% (from 210 to 21 subproblems), obtaining the best solution and contemplating the multivariate nature of the data.

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References

  1. Chatterjee S, Mahapatra SS, Bharadwaj V et al (2019) Prediction of quality characteristics of laser drilled holes using artificial intelligence techniques. Eng Comput. https://doi.org/10.1007/s00366-019-00878-y

    Article  Google Scholar 

  2. Gomes GF, de Almeida FA, de Lopes AP et al (2019) A multiobjective sensor placement optimization for SHM systems considering Fisher information matrix and mode shape interpolation. Eng Comput 35:519–535. https://doi.org/10.1007/s00366-018-0613-7

    Article  Google Scholar 

  3. Cicconi P, Castorani V, Germani M et al (2020) A multi-objective sequential method for manufacturing cost and structural optimization of modular steel towers. Eng Comput 36:475–497. https://doi.org/10.1007/s00366-019-00709-0

    Article  Google Scholar 

  4. Keshtiara M, Golabi S, Tarkesh Esfahani R (2019) Multi-objective optimization of stainless steel 304 tube laser forming process using GA. Eng Comput. https://doi.org/10.1007/s00366-019-00814-0

    Article  Google Scholar 

  5. Daroz Gaudêncio JH, de Almeida FA, Turrioni JB et al (2019) A multiobjective optimization model for machining quality in the AISI 12L14 steel turning process using fuzzy multivariate mean square error. Precis Eng 56:303–320. https://doi.org/10.1016/j.precisioneng.2019.01.001

    Article  Google Scholar 

  6. Thomas L (1999) The Taguchi loss function. Work Study 48:218–223. https://doi.org/10.1108/00438029910286477

    Article  Google Scholar 

  7. Taguchi G, Elsayed EATH (1989) Quality engineering in production systems. McGraw-Hill, New York

    Google Scholar 

  8. Wang B, Moayedi H, Nguyen H et al (2019) Feasibility of a novel predictive technique based on artificial neural network optimized with particle swarm optimization estimating pullout bearing capacity of helical piles. Eng Comput. https://doi.org/10.1007/s00366-019-00764-7

    Article  Google Scholar 

  9. Li E, Zhou J, Shi X et al (2020) Developing a hybrid model of salp swarm algorithm-based support vector machine to predict the strength of fiber-reinforced cemented paste backfill. Eng Comput. https://doi.org/10.1007/s00366-020-01014-x

    Article  Google Scholar 

  10. Ferreira Gomes G, Souza Chaves JA, de Almeida FA (2020) An inverse damage location problem applied to AS-350 rotor blades using bat optimization algorithm and multiaxial vibration data. Mech Syst Signal Process 145:106932. https://doi.org/10.1016/j.ymssp.2020.106932

    Article  Google Scholar 

  11. Gomes GF, de Almeida FA, Ancelotti AC, da Cunha SS (2020) Inverse structural damage identification problem in CFRP laminated plates using SFO algorithm based on strain fields. Eng Comput. https://doi.org/10.1007/s00366-020-01027-6

    Article  Google Scholar 

  12. Ribeiro Junior RF, de Almeida FA, Gomes GF (2020) Fault classification in three-phase motors based on vibration signal analysis and artificial neural networks. Neural Comput Appl. https://doi.org/10.1007/s00521-020-04868-w

    Article  Google Scholar 

  13. Yu Z, Shi X, Zhou J et al (2020) Prediction of blast-induced rock movement during bench blasting: use of gray wolf optimizer and support vector regression. Nat Resour Res 29:843–865. https://doi.org/10.1007/s11053-019-09593-3

    Article  Google Scholar 

  14. Belinato G, de Almeida FA, de Paiva AP et al (2019) A multivariate normal boundary intersection PCA-based approach to reduce dimensionality in optimization problems for LBM process. Eng Comput 35:1533–1544. https://doi.org/10.1007/s00366-018-0678-3

    Article  Google Scholar 

  15. Almeida FA, Leite RR, Gomes GF et al (2020) Multivariate data quality assessment based on rotated factor scores and confidence ellipsoids. Decis Support Syst 129:113173. https://doi.org/10.1016/j.dss.2019.113173

    Article  Google Scholar 

  16. Nhu V-H, Samui P, Kumar D et al (2019) Advanced soft computing techniques for predicting soil compression coefficient in engineering project: a comparative study. Eng Comput. https://doi.org/10.1007/s00366-019-00772-7

    Article  Google Scholar 

  17. de Almeida FA, Miranda Filho J, Amorim LF et al (2020) Enhancement of discriminatory power by ellipsoidal functions for substation clustering in voltage sag studies. Electr Power Syst Res 185:106368. https://doi.org/10.1016/j.epsr.2020.106368

    Article  Google Scholar 

  18. Shirani Faradonbeh R, Taheri A (2019) Long-term prediction of rockburst hazard in deep underground openings using three robust data mining techniques. Eng Comput 35:659–675. https://doi.org/10.1007/s00366-018-0624-4

    Article  Google Scholar 

  19. Marques PV, Modenesi PJ, Bracarense AQ (2017) Soldagem: fundamentos e tecnologia, 4th edn. Elsevier, Rio de Janeiro

    Google Scholar 

  20. Torres AF, Rocha FB, Almeida FA et al (2020) Multivariate stochastic optimization approach applied in a flux-cored arc welding process. IEEE Access 8:61267–61276. https://doi.org/10.1109/ACCESS.2020.2983566

    Article  Google Scholar 

  21. Choi D, Lee H, Cho S-K et al (2020) Microstructure and charpy impact properties of FCAW and SAW heat affected zones of 100 mm thick steel plate for offshore platforms. Met Mater Int 26:867–881. https://doi.org/10.1007/s12540-020-00626-8

    Article  Google Scholar 

  22. Cheng F, Zhang S, Di X et al (2017) Arc characteristic and metal transfer of pulse current horizontal flux-cored arc welding. Trans Tianjin Univ 23:101–109. https://doi.org/10.1007/s12209-017-0039-0

    Article  Google Scholar 

  23. Gomes JHF, Paiva AP, Costa SC et al (2013) Weighted Multivariate Mean Square Error for processes optimization: a case study on flux-cored arc welding for stainless steel claddings. Eur J Oper Res 226:522–535. https://doi.org/10.1016/j.ejor.2012.11.042

    Article  Google Scholar 

  24. Senthilkumar B, Kannan T, Madesh R (2017) Optimization of flux-cored arc welding process parameters by using genetic algorithm. Int J Adv Manuf Technol 93:35–41. https://doi.org/10.1007/s00170-015-7636-7

    Article  Google Scholar 

  25. Ordoobadi SM (2013) Application of AHP and Taguchi loss functions in evaluation of advanced manufacturing technologies. Int J Adv Manuf Technol 67:2593–2605. https://doi.org/10.1007/s00170-012-4676-0

    Article  Google Scholar 

  26. Myers RH, Montgomery DC, Anderson-Cook CM (2016) Response surface methodology: process and product optimization using designed experiments, 4th edn. Wiley, New York

    MATH  Google Scholar 

  27. Echempati R, Fox A (2013) Integrated metal forming and vibration analysis of sheet metal parts. Eng Comput 29:307–318. https://doi.org/10.1007/s00366-012-0273-y

    Article  Google Scholar 

  28. Simpson TW, Poplinski JD, Koch PN, Allen JK (2001) Metamodels for computer-based engineering design: survey and recommendations. Eng Comput 17:129–150. https://doi.org/10.1007/PL00007198

    Article  MATH  Google Scholar 

  29. Antony J (2000) Multi-response optimization in industrial experiments using Taguchi’s quality loss function and principal component analysis. Qual Reliab Eng Int 16:3–8. https://doi.org/10.1002/(SICI)1099-1638(200001/02)16:1%3c3:AID-QRE276%3e3.0.CO;2-W

    Article  Google Scholar 

  30. Johnson RA, Wichern D (2007) Applied multivariate statistical analysis, 6th edn. Prentice-Hall, New Jersey

    MATH  Google Scholar 

  31. Gu F, Hall P, Miles NJ (2016) Performance evaluation for composites based on recycled polypropylene using principal component analysis and cluster analysis. J Clean Prod 115:343–353. https://doi.org/10.1016/j.jclepro.2015.12.062

    Article  Google Scholar 

  32. Salah B, Zoheir M, Slimane Z, Jurgen B (2015) Inferential sensor-based adaptive principal components analysis of mould bath level for breakout defect detection and evaluation in continuous casting. Appl Soft Comput 34:120–128. https://doi.org/10.1016/j.asoc.2015.04.042

    Article  Google Scholar 

  33. de Almeida FA, Gomes GF, Gaudêncio JHD et al (2019) A new multivariate approach based on weighted factor scores and confidence ellipses to precision evaluation of textured fiber bobbins measurement system. Precis Eng 60:520–534. https://doi.org/10.1016/j.precisioneng.2019.09.010

    Article  Google Scholar 

  34. Das I, Dennis JE (1998) Normal-boundary intersection: a new method for generating the pareto surface in nonlinear multicriteria optimization problems. SIAM J Optim 8:631–657. https://doi.org/10.1137/S1052623496307510

    Article  MathSciNet  MATH  Google Scholar 

  35. Ahmadi A, Moghimi H, Nezhad AE et al (2015) Multi-objective economic emission dispatch considering combined heat and power by normal boundary intersection method. Electr Power Syst Res 129:32–43. https://doi.org/10.1016/j.epsr.2015.07.011

    Article  Google Scholar 

  36. Izadbakhsh M, Gandomkar M, Rezvani A, Ahmadi A (2015) Short-term resource scheduling of a renewable energy based micro grid. Renew Energy 75:598–606. https://doi.org/10.1016/j.renene.2014.10.043

    Article  Google Scholar 

  37. Mavalizadeh H, Ahmadi A (2014) Hybrid expansion planning considering security and emission by augmented epsilon-constraint method. Int J Electr Power Energy Syst 61:90–100. https://doi.org/10.1016/j.ijepes.2014.03.004

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to express their gratitude to Prof. M.Sc. Alexandre Fonseca Torres, CAPES, FAPEMIG (Grant number APQ-00385-18) and CNPq (project number 303586/2015-0 and 409318/2017-5) for their support in this research.

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Authors and Affiliations

  1. Institute of Industrial Engineering and Management, Federal University of Itajubá, Itajubá, Brazil

    Fabrício Alves de Almeida, Anderson Paulo de Paiva & José Henrique de Freitas Gomes

  2. Department of Economics, Faculty of Economic Sciences Southern Minas, Itajubá, Brazil

    Fabrício Alves de Almeida

  3. Institute of Integrated Engineering, Federal University of Itajubá, Itabira, Brazil

    Ana Carolina Oliveira Santos

  4. Mechanical Engineering Institute, Federal University of Itajubá, Itajubá, Brazil

    Guilherme Ferreira Gomes

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  1. Fabrício Alves de Almeida
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  2. Ana Carolina Oliveira Santos
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  4. Guilherme Ferreira Gomes
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  5. José Henrique de Freitas Gomes
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Correspondence to Fabrício Alves de Almeida.

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de Almeida, F.A., Santos, A.C.O., de Paiva, A.P. et al. Multivariate Taguchi loss function optimization based on principal components analysis and normal boundary intersection. Engineering with Computers 38, 1627–1643 (2022). https://doi.org/10.1007/s00366-020-01122-8

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  • DOI: https://doi.org/10.1007/s00366-020-01122-8

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