Modeling of the Complex Behavior through an Improved Response Surface Methodology

ABSTRACT

Response surface methodology has been applied in numerous studies using polynomial models despite some of them exhibit poor correlation coefficient $R^2$, which implies an incorrect optimization. In this work, a methodology for obtaining response surfaces when a small data set is available and its behavior is complex is presented. The methodology consists of four steps. First, the classic experimental design is used for obtaining a data set. Second, using the experimental results from a design of experiment, the classical kriging is employed for estimating properties at unsampled locations. Third, a response surface is obtained by training an artificial neural network using the kriging-estimated data set, and a hybrid algorithm based on differential evolution and backpropagation algorithms. The verification of the model is accomplished with the experimental data set. Fourth, the uncertainty quantification is utilized for studying the behavior of the response against uncertainties, which guarantee the robustness of the model developed. The methodology was applied to three cases, considering verification, validation, and uncertainty quantification. The results indicate that the proposed methodology is robust, and it provides more stable response surfaces than the approaches commonly used for polynomials and artificial neural networks. As a result, better optimal conditions are attained.

KEYWORDS:

• Response surface methodology
• classical kriging
• artificial neural networks
• uncertainty quantification
• hybrid algorithm

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Consejo Nacional de Innovación, Ciencia y Tecnología [Fondecyt 1171341 and PIA ACM 170005].