# Reactor Temperature Prediction Method Based on CPSO-RBF-BP Neural Network
## 2 RBF-BP Combined Neural Network Model
### RBF-BP Neural Network  
Because of their superior nonlinear prediction capability, robustness, and fault tolerance, RBF-BP neural networks are frequently used for nonlinear prediction. RBF-BP is a double-implicit neural network system composed of RBF and BP subnets that take advantage of the advantages of both neural networks. In terms of sample prediction ability, BP neural networks outperform RBF neural networks [21; 22]. The combined network can also compensate for the BP neural network's flaws, which are locally optimal solutions and  
Figure 1: RBF neural network structure.  
slow convergence [23]. Figure 3 shows the RBF-BP hybrid neural network's structure and network mechanism. The output of the RBF neural network acts as the input layer of the BP neural network, and this layer can also serve as the hybrid neural network's connection layer. The output layer of the hybrid neural network is the output layer of the BP neural network. Setting up the connection layer allows them to quickly and effectively reinforce their connection, which improves the nonlinear mapping's ability to fit.  
The mixed neural network algorithm consists of two processes: forwards propagation, which propagates the error between the network and the desired output layer by layer, and  
Figure 3: RBF-BP hybrid neural network model structure.  
Figure 2: BP neural network idea.  
backward propagation, which propagates the error between the network and the desired output from the output to the input layer, and calculates the weights according to a certain rule. The difference between the real output and the intended output can be reduced by repeated forwards and backward propagation to meet the specifications.  
The overall RBF-BP neural network is completed by the following six steps.  
Step 1: Initialize the weights and thresholds of each layer to (0, 1) and configure settings including the maximum number of iterations, the desired minimal error, and the learning rate.  
Step 2: Assign a Gaussian basis function with the following form to the transfer function of the implied layer of the RBF subnetwork.  
\[\varphi_{j}(x)=exp\left[-\frac{\left(x-c_{j}\right)^{2}}{\sigma^{2j}}\right] \text{, }j=1,2,\ldots,N \tag{1}\]  
\(j\) is the number of nodes, \(\varphi\) is the node output, \(x\) is the sample vector, \(c\) is the center of the Gaussian basis function, and \(\sigma\) is the width of the basis function.  
Step 3: Assign a sigmoid-type function to the BP hidden layer's transfer function.  
\[F(y)=1/\left(1+e^{-y}\right) \tag{2}\]  
Its output function is \(v(t)=F[\Sigma_{j=1}^{N_{2}}\beta_{2,t}(j)u(j)]\), where \(N_{2}\) represents the number of nodes in layer 2 hidden layer.  
Step 4: Compute the layer output node m.  
Step 5: Calculate the output layer SSE error sum of squares.  
\[SSE=\Sigma_{o=1}^{N_{3}}[T_{o}-Y(o)]^{2} \tag{3}\]  
\(T_{o}\) represents the desired output value.  
Step 6: Modify the individual thresholds and weights.  
\[\beta_{i,o}=\beta_{i,o}+\alpha Y(o)[1-Y(o)][T_{o}-Y(o)]\cdot Y(o) \tag{4}\]  
\[\theta_{o}=\theta_{o}+\alpha Y(o)[1-Y(o)][T_{o}-Y(o)] \tag{5}\]  
The procedure converges and training is completed when the training error of the merged neural network is less than the target error. When the number of training iterations exceeds the maximum number selected and the target error is not met, the algorithm returns to step 2 and executes the procedure until the entire process converges.