Least squares support vector machine (LSSVM) based on structural risk minimization

which is a simplified version of standard support vector machine (SVM)

is easy to be trained and has good modeling performance.The model precision of LSSVM is decided by its hyper parameters

while it is difficult to find the optimal hyper parameters of LSSVM via grid search and cross validation method.Based on the fast leave one out (LOO) method selecting hyper parameters of LSSVM

with the LOO prediction error on the entire training sample being the object of optimization

the gradient-based optimal algorithm was proposed in this paper to find the optimal hyper parameters of LSSVM.The LSSVM model whose hyper parameters found in this way is called G-LSSVM.To validate the performance of G-LSSVM

a citric acid fermentation process was taken as the benchmarking problem.The result showed that the modeling was time-economized and stable;while both the fitting and predicting performance of G-LSSVM were superior to standard SVM and artificial neural network whose hyper parameters and net structure are chosen by trial.G-LSSVM is recommended to model the chemical engineering process with high non-linearity and small size training sample whose mechanism is not clear.