# Reactor Temperature Prediction Method Based on CPSO-RBF-BP Neural Network
## 3 Analysis of Predicted Reactor Temperature  
### Selection of Data  
The temperature data of a chemical company in Hengdian, Zhejiang Province, China, is used as the usual production reaction temperature of the reactor in this research. Figure 6 shows the trend of temperature data. A total of 400 sets of real-time temperature data of the reactor's normal production are gathered, with the first 300 sets utilized as training samples and the last 100 sets used as prediction samples. Figure 7 depicts the reactor of the enterprise site's production reaction. The temperature data is formed from the temperature sensor in this kettle and sent to the control cabinet in Figure 8; the reactor's internal temperature range is 7 to 30 degrees Celsius; the temperature data is collected from the control cabinet seen in Figure 8; and Table 1 displays the reactor temperature data. It can be seen from the trend that samples 0-100 are the temperature of the reactor when there is no charging at the beginning, samples 100-200 belong to the reaction heating stage of the material, and samples 200-400 belong to the stage when the material begins to release heat.  
Figure 6: Temperature data trend diagram.  
Figure 7: Enterprise site reactor.  
\[RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(\delta_{i}-o_{i})^{2}} \tag{8}\]  
\[R^{2}=\sum_{i=1}^{N}(T_{i}-O_{i})^{2}/\sum_{i=1}^{N}\left(O_{i}-O_{\text{avg}} \right)^{2} \tag{9}\]  
Figures 9-11 show a direct comparison of the predicted and measured temperatures of the reactor by the combined optimization models of various neural networks and CPSO-RBF-BP neural networks. It can be seen that the single BP neural network model has a significant deviation from the expected displacement trend. The expected change trend of the CPSO-RBF-BP neural network prediction model matched the measured value. The CPSO-RBF-BP model was the nearest to the measured value in a comparison of four combinatorial optimization models. Figures 12 and 13 depict the network error shift and fitting curve of the CPSO-RBF-BP model during training. It can be seen that the CPSO-RBF-BP network model outperforms the BP, RBF-BP, and PSO-RBF-BP networks in terms of error efficiency. Only a few spots are outside the fitting curve, and the fitting coefficient is 0.9966. Table 2 provides a comparison of various predicted values. According to the experimental data, the BP error is big, the RBF-BP combined neural network error is moderate, and the CPSO-RBF-BP error is considerably lower than the other two types of prediction. Table 3 displays the mean absolute error, root means square error, and coefficient of determination of predicted reactor temperature values for various combination optimization models. The mean absolute error of the CPSO-RBF-BP model is 0.114, the root mean square error is 0.173, and the coefficient of determination is 0.9966. It has better prediction accuracy when compared to the other three prediction models, proving the model's superiority and effectiveness. The experimental findings indicate that when compared to the BP, RBF-BP, and PSO-RBF-BP neural network models, the prediction model optimized by the RBF-BP neural network using the chaotic particle swarm optimization algorithm can better reflect the trend of reactor temperature and is more practicable.  
Figure 11: Prediction results of CPSO-RBF-BP neural network model.  
Figure 10: RBF-BP neural network model.