The Development of Intelligent Models for Liquid–Liquid Equilibria (LLE) Phase Behavior of Thiophene/Alkane/Ionic Liquid Ternary System

This paper develops three models based on artificial neural network (ANN), support vector machine (SVM) and least square support vector machine (LSSVM) algorithm for phase behavior of thiophene/alkane/ionic liquid ternary system. The shuffled complex evolution (SCE) was employed to acquire the optimal magnitudes of hyper parameters (σ2 and γ) which are embedded parts of SVM and LSSVM models, and the trial and error was employed to obtain the optimal numbers of neuron and layers for ANN intelligent model. Gathering and using 618 LLE data, the comparison between the optimized version of applied intelligent models in giving the LLE was also made. The findings are indicative of a prefect agreement between the estimation from intelligent models and the experimental data. The finding also reveals that the performance of SVM in prediction of solubility is somewhat better than other intelligent models (i.e., ANN and SVM) as coefficient determination (R2) and root mean squared error (RMSE) are respectively 0.9961 and 0.0447 for test sets of data. This is likely due to the existence of structural risk minimization principle of SVM which is embodied in SVM algorithm and effectively minimizes upper bound of the generalization error, rather than minimizing the training error.