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12-12-2018 | Original Article

A multivariate normal boundary intersection PCA-based approach to reduce dimensionality in optimization problems for LBM process

Authors: Gabriela Belinato, Fabrício Alves de Almeida, Anderson Paulo de Paiva, José Henrique de Freitas Gomes, Pedro Paulo Balestrassi, Pedro Alexandre Rodrigues Carvalho Rosa

Published in: Engineering with Computers | Issue 4/2019

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Abstract

Laser beam machining (LBM) is a promising manufacturing process that exhibits several desirable quality characteristics. Given a large number of objective functions, the level of complexity increases in an optimization problem. Therefore, this study presents a multivariate application of the normal boundary intersection (NBI) method to reduce dimensionality in optimization problems of the LBM process. Such an approach is capable of exploring the entire solution space with only a small number of Pareto points, and generating equispaced frontiers based on the objective functions written in terms of principal component scores. Hence, a design of experiment with three input parameters and six quality characteristics was undertaken to appropriately model the process requirements applied to AISI 314S steel. The results indicate that the proposed methodology is capable of achieving optimal values for interest characteristics. In addition, this approach shows a reduction in computational effort of approximately 91.89% (from 259 to 21 subproblems) in obtaining the best solution for rough operation.

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Meijer J (2004) Laser beam machining (LBM), state of the art and new opportunities. J Mater Process Technol 149:2–17. https://doi.org/10.1016/j.jmatprotec.2004.02.003 CrossRef

Dubey AK, Yadava V (2008) Laser beam machining-A review. Int J Mach Tools Manuf 48:609–628. https://doi.org/10.1016/j.ijmachtools.2007.10.017 CrossRef

Gomes GF, de Almeida FA, da Silva Lopes Alexandrino P et al (2018) A multiobjective sensor placement optimization for SHM systems considering Fisher information matrix and mode shape interpolation. Eng Comput 10:1–17. https://doi.org/10.1007/s00366-018-0613-7

Saghatforoush A, Monjezi M, Shirani Faradonbeh R, Jahed Armaghani D (2016) Combination of neural network and ant colony optimization algorithms for prediction and optimization of flyrock and back-break induced by blasting. Eng Comput 32:255–266. https://doi.org/10.1007/s00366-015-0415-0 CrossRef

Chen XL, Fu JP, Yao JL, Gan JF (2018) Prediction of shear strength for squat RC walls using a hybrid ANN–PSO model. Eng Comput 34:367–383. https://doi.org/10.1007/s00366-017-0547-5 CrossRef

Gomes GF, de Almeida FA, da Cunha SS et al (2018) An estimate of the location of multiple delaminations on aeronautical CFRP plates using modal data inverse problem. Int J Adv Manuf Technol 99:1155. https://doi.org/10.1007/s00170-018-2502-z CrossRef

MiarNaeimi F, Azizyan G, Rashki M (2017) Multi-level cross entropy optimizer (MCEO): an evolutionary optimization algorithm for engineering problems. Eng Comput. https://doi.org/10.1007/s00366-017-0569-z

Gomes GF, da Cunha SS, Ancelotti AC (2018) A sunflower optimization (SFO) algorithm applied to damage identification on laminated composite plates. Eng Comput. https://doi.org/10.1007/s00366-018-0620-8

Dubey A, Yadava V (2008) Robust parameter design and multi-objective optimization of laser beam cutting for aluminium alloy sheet. Int J Adv Manuf Technol 38:268–277. https://doi.org/10.1007/s00170-007-1105-x CrossRef

10.

Kasman Ş, Etem Saklakoglu I (2012) Determination of process parameters in the laser micromilling application using Taguchi method: a case study for AISI H13 tool steel. Int J Adv Manuf Technol 58:201–209. https://doi.org/10.1007/s00170-011-3371-x CrossRef

11.

Ghosal A, Manna A (2013) Optics & laser technology response surface method based optimization of ytterbium fiber laser parameter during machining of Al/ Al₂O₃ -MMC. Opt Laser Technol 46:67–76. https://doi.org/10.1016/j.optlastec.2012.04.030 CrossRef

12.

Parandoush P, Hossain A (2014) A review of modeling and simulation of laser beam machining. Int J Mach Tools Manuf 85:135–145. https://doi.org/10.1016/j.ijmachtools.2014.05.008 CrossRef

13.

Li CH, Tsai MJ (2009) Multi-objective optimization of laser scribing for the isolation process of solar cell wafers using grey relational analysis. IEEE Int Symp Ind Electron 41:1154–1159. https://doi.org/10.1109/ISIE.2009.5218137

14.

Teixidor D, Ferrer I, Ciurana J, Özel T (2013) Optimization of process parameters for pulsed laser milling of micro-channels on AISI H13 tool steel. Robot Comput Integr Manuf 29:209–218CrossRef

15.

Childs THC, Hauser C, Badrossamay M (2004) Mapping and modelling single scan track formation in direct metal selective laser melting. CIRP Ann Manuf Technol 53:191–194. https://doi.org/10.1016/S0007-8506(07)60676-3 CrossRef

16.

Childs THC, Hauser C, Badrossamay M (2005) Selective laser sintering (melting) of stainless and tool steel powders: experiments and modelling. Proc Inst Mech Eng Part B J Eng Manuf 219:339–357CrossRef

17.

Pandey AK, Dubey AK (2012) Taguchi based fuzzy logic optimization of multiple quality characteristics in laser cutting of Duralumin sheet. Opt Lasers Eng 50:328–335. https://doi.org/10.1016/j.optlaseng.2011.11.005 CrossRef

18.

Mistry V, James S (2017) Finite element analysis and simulation of liquid-assisted laser beam machining process. Int J Adv Manuf Technol 2325–2331. https://doi.org/10.1007/s00170-017-1009-3

19.

Darwish S, Ahmed N, Alahmari AM, Mufti NA (2017) A study of micro-channel size and spatter dispersion for laser beam micro-milling. Mater Manuf Process 32:171–184. https://doi.org/10.1080/10426914.2016.1176188 CrossRef

20.

Darwish S, Ahmed N, Alahmari AM, Mufti NA (2016) A comparison of laser beam machining of micro-channels under dry and wet mediums. Int J Adv Manuf Technol 83:1539–1555. https://doi.org/10.1007/s00170-015-7658-1 CrossRef

21.

Pan LK, Wang CC, Wei SL, Sher HF (2007) Optimizing multiple quality characteristics via Taguchi method-based Grey analysis. J Mater Process Technol 182:107–116. https://doi.org/10.1016/j.jmatprotec.2006.07.015 CrossRef

22.

Schweier M, Heins JF, Haubold MW, Zaeh MF (2013) Spatter formation in laser welding with beam oscillation. Phys Procedia 41:20–30. https://doi.org/10.1016/j.phpro.2013.03.047 CrossRef

23.

Rao RV, Kalyankar VD (2014) Optimization of modern machining processes using advanced optimization techniques: a review. Int J Adv Manuf Technol 73:1159–1188. https://doi.org/10.1007/s00170-014-5894-4 CrossRef

24.

Almeida FA de, Gomes GF, De Paula VR et al (2018) A weighted mean square error approach to the robust optimization of the surface roughness in an AISI 12L14 free-machining steel-Turning process. Stroj Vestnik/J Mech Eng 64:147–156. https://doi.org/10.5545/sv-jme.2017.4901

25.

Yu X, Zhang S, Johnson E (2003) A discrete post-processing method for structural optimization. Eng Comput 19:213–220. https://doi.org/10.1007/s00366-003-0259-x CrossRef

26.

Almeida FA, Gomes GF, Sabioni RC, Gomes JHF, Paula VR, Paiva AP et al (2018) A gage study applied in shear test to indentify variation causes from a resistance spot welding measurement system. Stroj Vestnik/J Mech Eng 63:621–631

27.

Fabiano Luis N, Tayana Incerti P, Pedro Paulo B et al (2017) Multivariate normal boundary intersection based on rotated factor scores: a multiobjective optimization method for methyl orange treatment. J Clean Prod 143:413–439CrossRef

28.

Manjoth S, Keshavamurthy R, Kumar GSP (2016) Optimization and analysis of laser beam machining parameters for Al7075-TiB < inf> 2</inf> in-situ composite. IOP Conf Ser Mater Sci Eng 149:12013. https://doi.org/10.1088/1757-899X/149/1/012013 CrossRef

29.

Ahmed N, Alahmari AM, Darwish S, Khan AA (2016) Experimental investigation of micro-channels produced in aluminum alloy (AA 2024) through laser machining. Appl Phys A 122:948. https://doi.org/10.1007/s00339-016-0463-3 CrossRef

30.

Umer U, Mohammed MK, Al-Ahmari A (2017) Multi-response optimization of machining parameters in micro milling of alumina ceramics using Nd:YAG laser. Meas J Int Meas Confed 95:181–192. https://doi.org/10.1016/j.measurement.2016.10.004 CrossRef

31.

Prakash C, Kansal HK, Pabla BS, Puri S (2016) Multi-objective optimization of powder mixed electric discharge machining parame- ters for fabrication of biocompatible layer on β -Ti alloy using NSGA-II coupled with Taguchi based response surface methodology †. J Mech Sci Technol 30:4195–4204. https://doi.org/10.1007/s12206-016-0831-0 CrossRef

32.

Costa DMD, Belinato G, Brito TG et al (2016) 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 Brazilian Soc Mech Sci Eng. https://doi.org/10.1007/s40430-016-0614-7

33.

Almeida FA, De Paula TI, Leite RR, Gomes GF, Gomes JHF, Paiva APBP (2018) A multivariate GR&R approach to variability evaluation of measuring instruments in resistance spot welding process. J Manuf Process 36:465–479. https://doi.org/10.1016/j.jmapro.2018.10.030 CrossRef

34.

Montgomery DC (2016) Design and analysis of experiments, 9th edn. Wiley, New York

35.

Myers RH, Montgomery DC, Anderson-Cook CM (2009) Response surface methodology, 3rd ed. Taylor & Francis, RoutledgeMATH

36.

Singh D, Rao PV (2007) A surface roughness prediction model for hard turning process. Int J Adv Manuf Technol 32:1115–1124CrossRef

37.

Skrypnyk R, Nielsen JCO, Ekh M, Pålsson BA (2018) Metamodelling of wheel–rail normal contact in railway crossings with elasto-plastic material behaviour. Eng Comput. https://doi.org/10.1007/s00366-018-0589-3

38.

Amaral FF, Almeida FA, Costa SC, Leme RCPA (2018) Application of the response surface methodology for optimization of the resistance spot welding process in AISI 1006 galvanized steel. Soldag Inspeção 32:129–142CrossRef

39.

Camposeco-Negrete C (2015) Optimization of cutting parameters using response surface method for minimizing energy consumption and maximizing cutting quality in turning of AISI 6061 T6 aluminum. J Clean Prod 91:109–117CrossRef

40.

Asiltürk I, Neşeli S, Ince MA (2016) Optimisation of parameters affecting surface roughness of Co28Cr6Mo medical material during CNC lathe machining by using the Taguchi and RSM methods. Measurement 78:120–128CrossRef

41.

Cukor G, Jurković Z, Sekulić M (2011) Rotatable central composite design of experiments versus Taguchi method in the optimization of turning. Metalurgija 50:17–20

42.

Al-Ahmari AMA (2007) Predictive machinability models for a selected hard material in turning operations. J Mater Process Technol 190:305–311CrossRef

43.

Noordin MY, Venkatesh VC, Sharif S et al (2004) Application of response surface methodology in describing the performance of coated carbide tools when turning AISI 1045 steel. J Mater Process Technol 145:46–58CrossRef

44.

Johnson RA, Wichern DW (2007) Applied multivariate statistical analysis, 6th edn. Prentice Hall, New JerseyMATH

45.

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 MathSciNetCrossRefMATH

46.

Brito TG, Paiva AP, Ferreira JR et al (2014) A normal boundary intersection approach to multiresponse robust optimization of the surface roughness in end milling process with combined arrays. Precis Eng 38:628–638. https://doi.org/10.1016/j.precisioneng.2014.02.013 CrossRef

47.

Lopes LGD, Brito TG, Paiva AP et al (2016) Robust parameter optimization based on multivariate normal boundary intersection. Comput Ind Eng 93:55–66. https://doi.org/10.1016/j.cie.2015.12.023 CrossRef

48.

Abdollah A, Hadi M, Ali Esmaeel N et al (2015) Multi-objective economic emission dispatch considering combined heat and power by normal boundary intersection method..2015.07.011. Electr Power Syst Res 129:32–43CrossRef

49.

Gomes JHF, Paiva a P, 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 CrossRef

50.

Gaudêncio JHD, Almeida FA, Sabioni RC, Turrioni JB, Paiva AP, Campos PHS (2018) Fuzzy multivariate mean square error in equispaced pareto frontiers considering manufacturing process optimization problems. Eng Comput. https://doi.org/10.1007/s00366-018-0660-0

51.

Rocha LCS, De Paiva AP, Balestrassi PP et al (2015) Entropy-based weighting for multiobjective optimization: an application on vertical turning. Math Probl Eng. https://doi.org/10.1155/2015/608325

52.

Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423MathSciNetCrossRefMATH

Title: A multivariate normal boundary intersection PCA-based approach to reduce dimensionality in optimization problems for LBM process
Authors: Gabriela Belinato
Fabrício Alves de Almeida
Anderson Paulo de Paiva
José Henrique de Freitas Gomes
Pedro Paulo Balestrassi
Pedro Alexandre Rodrigues Carvalho Rosa
Publication date: 12-12-2018
Publisher: Springer London
Published in: Engineering with Computers / Issue 4/2019
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI: https://doi.org/10.1007/s00366-018-0678-3

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