Expert and gray box modeling of high pressure liquid carbon dioxide extraction of Pimpinella anisum L. seed

In this study, a neuro-fuzzy model has been developed to predict the mass of extract in the process of supercritical fluid extraction of Pimpinella anisum L. seed. In this case first, an adaptive neuro-fuzzy inference system (ANFIS) technique was trained with the recorded data from kinetic experiments at pressures of 8, 10, 14 and 18 MPa and constant temperature of 303.15 K. The performance of this proposed model was validated with experimental data and excellent predictions with root mean square error (RMSE) of 0.0235 were observed.In the next step of study, mass transfer coefficient in terms of Sherwood number was estimated by a neuro-fuzzy network. The estimated mass transfer coefficient was embedded in mathematical model. The proposed gray box (hybrid) model was validated with the experimental data and RMSE of 0.0523 proved that equipping mathematical model with neuro-fuzzy network has significantly improved performance of the model. Then, neuro-fuzzy and gray box models were compared with previously published artificial neural network and mathematical models. It was found that ANFIS model has the best performance compared to all modeling techniques.Finally, extrapolation ability of ANFIS, white box, and gray box models were studied. The mass of extracted was predicted up to 300 min (beyond the training range). It was observed that again ANFIS model is the best model for extrapolation purposes.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Neuro-fuzzy models are more accurate than neural network and white box modeling. ► Neuro-fuzzy model has good extrapolation capability. ► Gray box model is more accurate than mathematical and neural network models.