Capacidade de previsão de soluções pareto ótimas

Abstract

Response Surface Methodology is an effective framework for performing modelling and optimization of industrial processes. The Central Composite Design is the most popular experimental design for response surface analyses given its good statistical properties, such as decreasing prediction variance in the design center, where it is expected to find the stationary points of the regression models. However, the common practice of reducing center points in response surface studies may damage this property. Moreover, stationary and optimum points are rarely the same in manufacturing processes, for several reasons, such as saddle-shaped models, convexity incompatible with optimization direction, conflicting responses, and distinct convexities. This means that even when the number of center points is appropriate, the optimal solutions will lie in regions with larger prediction variance. Considering that, in this paper, we advocate that the prediction variance should also be considered into multiobjective optimization problems. To do this, we propose a multi-criteria optimization strategy based on capability ratios, wherein (1) the prediction variance is taken as the natural variability of the model and (2) the differences of expected values to nadir solutions are taken as the allowed variability. Factor Analysis with rotated scores is adopted for the grouping of correlated variables. Normal Boundary Intersection method is formulated for performing the optimization of capability ratios and obtaining the Pareto frontiers. To illustrate the feasibility of the proposed approach, two case studies are presented: (1) the turning of AISI H13 steel with wiper CC650 tool and (2) the end milling of the UNS S32205 duplex stainless steel, both processes without cutting fluids. The results have supported that the proposed approach was able to find a set of optimal solutions with satisfactory prediction capabilities for all responses of interest. In the first case, this occurred even with a reduced number of center points, a saddle-shaped function and a convex function, with conflicting objectives. In the second case, similar results were observed for six correlated responses, with conflicting objectives and rotated factors modeled by saddles.