A multi-objective robust evolutionary optimization approach applied to the multivariate helical milling process of super duplex steel

Abstract

This work presents an approach for multivariate modeling and multi-objective robust evolutionary optimization for processes presenting as inputs control and noise variables and as outputs a set of correlated responses regarding process performance and product quality. Factor analysis is applied to obtain a transformed output set that is uncorrelated and retains most part of the information of the original outputs. Models that are robust regarding noise variables relating this transformed output set with the control variables are obtained through robust parameter design. Response models in the function of process and noise variables are obtained through the least squares method. Mean and variance models as a function of process variables are obtained through error propagation. Robust mean square error models are obtained to model the bias and variance of each latent variable. Finally, multi-objective evolutionary optimization is performed. Three evolutionary algorithms were applied and compared through hypervolume. The approach is applied in the helical milling of super duplex stainless steel UNS S32760. Tool overhang length, hole depth, and lubri-cooling flow rate were set as noise factors. Cutting forces were monitored, while roughness and roundness were measured to evaluate process performance and product quality. The three factors, obtained to represent the six outputs, guaranteed dimensionality reduction and minimized the redundancy in output space. The mean square error models obtained to these three factors as a function of control variables minimize both bias and variance regarding noise factors. The AGE-MOEA multi-objective evolutionary algorithm obtained the best performance considering the hypervolume. Some solutions with high trade-off were selected through pseudo-weights to aid the decision-making.