Modeling and prediction of the preparation of hydroxyapatite with sol-gel method by using support vector regression

A novel modeling approach, support vector regression (SVR) combined with particle swarm optimization (PSO), was employed to construct mathematical model for prediction of the purity and average particle size of hydroxyapatite (HA) based on five synthesis process factors, including the P₂O₅ content, Ca(NO₃)₂·4H₂O content, aging time, synthesis temperature, and holding time. The accuracy and reliability of the constructed SVR model are validated through the mean absolute percentage error of the leave-one-out cross validation. Then the SVR model is applied to optimize the process parameters. The maximum purity of HA is found to be 98.06% predicted by the SVR model under the optimal synthesis parameters, i.e., the P₂O₅ content is 1.98 mol/L, Ca(NO₃)₂·4H₂O content is 2.68mol/L, aging time is 17.68h, synthesis temperature is 818.93°C, and holding time is 3.17h. These studies suggest that SVR is an effective and practical methodology to assist the design of experiment, and is helpful to increase the yield and control the average particle size of the synthesized HA via rational process parameters.