## 5 Modeling Design of LS-SVM Based on FOA and Simulation Test  
### Sampling Data  
As an example, a sample set from an actual pressure control system of chlorine in a salt industry plant (shown in Figure 3) is used to model the upstream pressure of the control valve. In order to maintain a normal production, the pressure of the chlorine pipeline should be maintained between 29-30 KPa. This is accomplished by a control valve. Its opening is adjusted according to the actual production situation to guarantee the needed upstream pressure. In the process of production, the temperature of chlorine changes little and the downstream pressure is influenced by the upstream pressure, opening and the flow rate. Consequently, in order to improve the computing speed, the simulation test uses the opening and the flow rate as the input data to predict the upstream pressure. The test results shown in _Section 5.2_ indicate that using the two independent variables can reach a satisfactory accuracy.  
A set of 600 data is sampled in the process of commissioning by the DCS every 20 s. Table 2 shows the descriptive statistical values of the indexes. The data set is divided averagely into five groups. Among them, four groups are used as training data and the other group is used to test the model.  
At present, in the area of parameter optimization, particle swarm optimization (PSO) algorithm is the most frequently studied and is widely applied, and the grid search method is the simplest algorithm. In this article, parameters of \(C\) and \(\sigma\) are also optimized by PSO and the grid search algorithm respectively. The scope of \(C\) is \([2^{-10},\,2^{10}]\) and that of \(\sigma\) is \([0,\,0.2]\). Without loss of generality, the iteration times of the two algorithms are set to be 50 and number of particle is 10, which are the same with FOA. Comparison of the convergence histories is shown in Figure 7 and the predicting performance indicators are listed in Table 4 in which _MSE_ are the mean square error, MAE are the mean absolute error.  
Figure 7 shows that FOA has faster convergence speed and equal optimal result compared with the other two algorithms. The test indicators in Table 4 further improve the above conclusion. All the three methods could give good LSSVM parameters with offering small MSE and MAE as shown in Table 4. They are equal in forecasting performance. However, from the time consuming point of view, FOA has a significant advantage. Therefore, FOA is more suitable for the online prediction of the pressure of control valve.  
The test data is sampled by the DCS of the plant. The validity of FOA is verified by comparing the predicted results with the actual data. The values of MSE and MAE respectively are \(2.474\times 10^{-3}\) and \(0.808\times 10^{-3}\) kPa. In addition, in order to further observe the optimization ability, simulation experiments based on PSO algorithm and the grid search method are carried out. With the prediction results comparison, the LS-SVM model based on FOA has equal performance in prediction accuracy. However, FOA has a significant advantage because it is less time consuming and is more suitable for the online prediction.  
This work is supported by the National Natural Science Foundation (NNSF) of China (No. 51175299), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20110131110042) and the Scientific Research Fund Project of Binzhou University (BZXYG1306).  
The idea for this research work is proposed by [PERSON], the MATLAB code and the paper writing are achieved by [PERSON].  
The authors declare no conflict of interest.