Modeling the mean grain size of synthesized nanopowders produced by mechanical alloying

Gene expression programming (GEP) optimization tool has been utilized to predict the mean grain size of nanopowders synthesized by mechanical alloying. 86 data were collected from the literature, randomly divided into 65 and 21 sets and then, respectively, were trained and tested by 11 different GEP models. The differences between the models were in their linking functions (addition and multiplication) and sub expression trees (3, 4, 5, 6, 7 and 8). The method of calculation of the mean grain size, milling time, annealing temperature, produced phases after mechanical alloying, vial speed and ball to powder ratio were considered as input variables to predict mean grain size of nanopowders as output. The obtained results from training and testing of the different models showed that some of them are capable to predict mean grain size of the synthesized nanopowders in the considered range. However, the best results were obtained by using 7 sub expression trees addition as linking function. R2 value of the trained and tested suggested model showed this situation.