
Prediction capability of Pareto optimal solutions: A multi-criteria optimization strategy based on model capability ratios
2019; Elsevier BV; Volume: 59; Linguagem: Inglês
10.1016/j.precisioneng.2019.06.008
ISSN1873-2372
AutoresLucas Guedes de Oliveira, Anderson Paulo de Paiva, Paulo Henrique da Silva Campos, Emerson José de Paiva, Pedro Paulo Balestrassi,
Tópico(s)Manufacturing Process and Optimization
ResumoResponse 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. 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, we present a case study of the turning without cutting fluids of AISI H13 steel with wiper CC650 tool. The results have supported that the proposed approach was able to find a set of optimal solutions with satisfactory prediction capabilities for both responses of interest (tool life T and surface roughness Ra), for a case with reduced number of center points, a saddle-shaped function for T and a convex function for Ra, with conflicting objectives. Although it was a response more difficult to control, the optimization benefited more Ra, which was a desired result. Finally, we also provide the sample sizes to detect differences between Pareto optimal solutions, allowing the decision maker to find distinguishable solutions at given levels of risk.
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