Nonlinear optimization strategy based on multivariate prediction capability ratios: Analytical schemes and model validation for duplex stainless steel end milling

Abstract Given the complex nature of their phenomena and interactions, industrial processes often have multiple variables of interest, usually grouped into critical-to-quality and critical-to-performance characteristics. These variables often have significant correlations, which make engineering problems multivariate. For this reason, Response Surface Methodology, coupled with multivariate techniques, has been widely used as a logical roadmap for modeling and optimization of the characteristics of interest. However, the variability and prediction capability of the numerical solutions obtained are almost always neglected, reducing the likelihood that numerical results are indeed compatible with observable process improvements. To fill this gap, this paper proposes a nonlinear multiobjective optimization strategy based on multivariate prediction capability ratios. For this, rotated Factor Analysis is used as the multivariate technique for grouping process characteristics and composing capability ratios, so that the prediction variance is taken as the natural variability of the process modeled and the expected value distances to the nadir solutions of the latent variables are taken as the allowed variability. Normal Boundary Intersection method, combined with Generalized Reduced Gradient algorithm, is used as the numerical scheme to maximize the prediction capability of Pareto optimal solutions. To illustrate the feasibility of the proposed strategy, we present a case study of end milling without cutting fluids of duplex stainless steel UNS S32205. Rotatable Central Composite Design, with three cutting parameters, was employed for data collection. Traditional multivariate and proposed approaches were compared. The results demonstrate that the proposed optimization strategy is able to provide solutions with satisfactory prediction capability for all variables analyzed, regardless of their convexities, optimization directions, and correlation structure. In addition, while critical-to-quality characteristics are more difficult to control, they have been favored by the proposed optimization regarding prediction capability, which was a desirable result.