Mathematical, fuzzy logic and artificial neural network modeling of extraction kinetics of essential oil from aerial parts of yarrow (Achillea millefolium L.) using ohmic-assisted hydrodistillation

The aim of present research was to predict the kinetics of essential oil extraction during ohmic-assisted hydrodistillation by three different modeling (nonlinear regression techniques (mathematical), artificial neural networks (ANN), and fuzzy logic) techniques to compare the accuracy of those models. Based on the results obtained the ANN was the best technique among all implemented models in predicting of extraction yield. Four mathematical models (first order, second order, adsorption and sigmoid models) describing essential oil extraction has been fitted to the extraction yield experimental data. Results indicated that first order model could satisfactorily describe the extraction kinetics of essential oil with correlation coefficient (R2) equal 0.988 and root mean square error (RMSE) equal 0.00014. Neural network with one and two hidden layers and 4–30 neurons were randomly selected and network power was estimated for predicting the extraction yield. ANNs with Feedforward–backpropagation structure, Levenberg–Marquardt training algorithm and 3-11-11-1 topology deserved the maximum R2 (0.999) and minimum RMSE (0.0004). Fuzzy logic tool in MATLAB with Mamdani model in the form of If–Then rules along with triangular membership function was used for predict the extraction yield. Despite the fact that fuzzy logic warranted lower fitting rates (R2 = 0.997) than that of ANN, it was a powerful technique for fitting of extraction yield experimental data.