Modeling particle size in the dispersion polymerization of styrene using artificial neural network and genetic algorithm

Abstract

Artificial neural network (ANN) combined with genetic algorithm (GA) method was employed to predict the particle size and particle size distribution in the dispersion polymerization of styrene stabilized by polyvinyl pyrrolidone in ethanol. A D-optimal split-plot design was utilized to obtain the 70 required experiments using the Expert Design 9 software. The restricted maximum likelihood (REML) method was employed in order to model the effect of reaction parameters on the particle size and particle size distribution. A back propagation learning algorithm with adaptive learning rate was used to train the neural network. The number of neurons in each hidden layer of the network was determined by applying genetic algorithm. Two thirds of the experimental data were randomly used for network training, and the remaining data were utilized to determine the validity of the network. This procedure was repeated 100 times for cross-validation. The average R 2 for modeling the validation data set for the particle size and the particle size distribution were 0.95 and 0.92, respectively. The average R 2 for modeling the training data set for the particle size and the particle size distribution were 0.97 and 0.95, respectively. Although using all the experimental data for building the model in the REML method, the R 2 for modeling the particle size and particle size distribution were 0.92 and 0.89, respectively. It can be concluded that ANN is a more powerful tool for modeling the particle size and particle size distribution.