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

  • Gabriela Belinato
  • Fabrício Alves de AlmeidaEmail author
  • Anderson Paulo de Paiva
  • José Henrique de Freitas Gomes
  • Pedro Paulo Balestrassi
  • Pedro Alexandre Rodrigues Carvalho Rosa
Original Article


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.


Laser beam machining Principal component analysis Normal boundary intersection Material removal rate Roughness 



The authors gratefully acknowledge the IDMEC/UL, Associated Laboratory for Energy, Transports and Aeronautics (LAETA), IST/University of Lisbon, the SMART2 program from ERASMUS MUNDUS, FAPEMIG, CAPES, CNPq and IFSULDEMINAS.

Supplementary material

366_2018_678_MOESM1_ESM.rar (732 kb)
Supplementary material 1 (RAR 732 KB)


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Gabriela Belinato
    • 1
    • 2
  • Fabrício Alves de Almeida
    • 1
    Email author
  • Anderson Paulo de Paiva
    • 1
  • José Henrique de Freitas Gomes
    • 1
  • Pedro Paulo Balestrassi
    • 1
  • Pedro Alexandre Rodrigues Carvalho Rosa
    • 3
  1. 1.Institute of Industrial Engineering and ManagementFederal University of ItajubáItajubáBrazil
  2. 2.IFSULDEMINAS Federal Institute of South Minas GeraisPouso AlegreBrazil
  3. 3.IDMEC Department of Mechanical Engineering, Technician Superior Institute of LisbonUniversity of LisbonLisbonPortugal

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