Comparison of neuro-fuzzy network and response surface methodology pertaining to the viscosity of polymer solutions

Abstract

Abstract This study has utilized the response surface methodology (RSM) and adaptive neuro-fuzzy inference system (ANFIS) approaches for the modeling of polymer solution viscosity. In the absence of reports in the previous study on applying these two approaches, the main objective of this study has been to compare the performance of these methods toward the viscosity modeling of a polymer solution. By utilizing RSM technique, the effects of three independent parameters including shear rate, polymer concentration, and sodium chloride concentration on viscosity of polymer solution were examined. The RSM results showed that all the parameters were not equally important in the polymer solution viscosity. Moreover, analysis of variance (ANOVA) was also carried out and indicated that there was no evidence of lack of fit in the RSM model. As a second approach for polymer solution viscosity modeling, ANFIS was utilized with two rules constructed based on the first-order Sugeno fuzzy approach and trained by back propagation neural networks algorithm. High coefficient of determination (R 2) values ( >99%) showed that the prediction ability of both the ANFIS and RSM models was good enough for the response when the interpolation ability of the models was considered. In order to evaluate the extrapolation abilities of the two developed models, two data sets lying beyond the originally considered data were also taken into account. The results showed that their extrapolation predictive ability was poor. The reason could simply be the inherent behavior of the polymeric solution, i.e., the correlational structure seen in the sample used in the training step did not continue outside the sample space.

Keywords

• HPAM
• Adaptive neuro-fuzzy inference system (ANFIS)
• Polymer solution viscosity
• Response surface methodology (RSM)