The analysis of liquid–liquid equilibria (LLE) of toluene + heptane + ionic liquid ternary mixture using intelligent models

Abstract

This paper is to verify the applicability of three intelligence methods including artificial neural network (ANN), support vector machine (SVM) and least square support vector machine (LSSVM) in forecasting the thermodynamic phase behavior of LLE for toluene/heptane/ionic liquid ternary systems. The shuffled complex evolution (SCE), particle swarm optimization (PSO) and genetic algorithm (GA) are 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 589 liquid–liquid equilibria (LLE) data, the comparison between the capability of applied intelligent models and NRTL thermodynamic model has also been made in giving the phase behavior of ternary system toluene/heptane/ionic liquid. The findings are indicative of a prefect agreement between the estimation from intelligent models and the experimental data. Comparison between these three investigated models reveals that the performance of SCE-LSSVM in prediction of LLE is somewhat better than other intelligent models (i.e., ANN and SVM) in prognosticating LLE behavior in those 40 studied ILs as the coefficient determination (R2) and root mean squared error (RMSE) are respectively 0.9895 and 0.0361 for test sets of data. This is likely due to the existence of structural risk minimization principle of LSSVM which is embodied in SVM algorithm and effectively minimizes upper bound of the generalization error, rather than minimizing the training error.