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A multivariate robust parameter optimization approach based on Principal Component Analysis with combined arrays

Abstract

Today’s modern industries have found a wide array of applications for optimization methods based on modeling with robust parameter designs (RPD). Methods of carrying out RPD have thus multiplied. However, little attention has been given to the multiobjective optimization of correlated multiple responses using response surface with combined arrays. Considering this gap, this paper presents a multiobjective hybrid approach combining response surface methodology (RSM) with Principal Component Analysis (PCA) to study a multi-response dataset with an embedded noise factor, using a DOE combined array. How this approach differs from the most common approaches to RPD is that it derives the mean and variance equations using the propagation of error principle (POE). This comes from a control-noise response surface equation written with the most significant principal component scores that can be used to replace the original correlated dataset. Besides the dimensional reduction, this multiobjective programming approach has the benefit of considering the correlation among the multiple responses while generating convex Pareto frontiers to mean square error (MSE) functions. To demonstrate the proposal, we used a bivariate case of AISI 52100 hardened steel turning employing wiper mixed ceramic tools. Theoretical and experimental results are convergent and confirm the adequacy of our proposal.

 

Keywords

  • Multiple objective programming;
  • Robust Parameter Design (RPD);
  • Multivariate Mean Square Error (MMSE);
  • Principal Component Analysis (PCA)

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