# Optimization of the Battery Pack Heat Dissipation Structure of a Battery-Type Loader
## 5 Combined Parameter Optimization
### Model Establishment  
As RBF neural networks can approximate arbitrary nonlinear functions and can deal with the intrinsic unresolved regularities of systems, we used an RBF neural network to establish a prediction model between the structural parameters and battery pack temperature. An RBF neural network is a three-layer neural network which includes an input layer, an implicit layer, and an output layer; where the transformation from the input space to the implicit layer space is non-linear; and where the transformation from the implicit layer space to the output layer spatial transformation is linear [27], as detailed in Figure 20.  
The output of an RBF neural network [23] can be given as:  
\[y_{j}=\sum_{i=1}^{h}w_{ij}\exp\left(-\frac{1}{2\sigma^{2}}\
orm{x_{p}-c_{i}}^{ 2}\right)\,j=1,2,\cdots,n\,i=1,2,\cdots,h, \tag{3}\]  
where \(n\) is the number of samples or classifications of the output and \(w_{\bar{i}\bar{j}}\) is the weight between the \(i\)th implied layer node to the \(j\)th output layer node.  
The neural network training sample was established according to the \(n\times 10\) principle and should be uniformly distributed within the range of the independent variables. Considering that the number of levels in this experiment was relatively large, a uniform experimental design table was adopted to establish the RBF neural network training sample.  
Figure 19: Temperature change curves for the battery pack: (**a**) the maximum temperature change curve; (**b**) the average temperature change curve; and (**c**) the temperature difference curve.  
According to the previous single-factor study, when the heat dissipation performance of the battery pack is relatively good, the air outlet location of the battery pack is on both sides and the gap width of the partition is 10 mm. Therefore, the optimization variables to be studied in this paper were the remaining three factors; that is, air outlet width, deflector location, and deflector angle. According to previous research and the actual situation of this case, the optimization variables and their levels were determined, as shown in Table 3.  
According to the \(n\times 10\) principle, at least 30 samples were required to train the neural network. Therefore, a uniform experimental design with three factors and 31 levels was selected; that is, the U\({}_{31}\) (31\({}^{12}\)) table  
As we included three optimization variables in the study, it can be seen from the experimental table that columns 1, 4, and 8 were selected for the experimental arrangement, which was converted into the corresponding structural parameters while the other parameters were kept unchanged. Then, ANSYS numerical simulation was used for calculation. For this paper, the MATLAB software was used for the writing and running of the RBF neural network, where the newrb function was used to construct the RBF neural network topology, as shown in Equation (4):  
\[\text{net}=\text{newrb}(\text{P},\text{T},\text{GOAL},\text{SPREAD},\text{MN},\text{DF}), \tag{4}\]  
where P is the input vector, T is the output vector, GOAL is the mean square error (which takes the value of 0.001), SPREAD is the RBF function distribution density (which takes the value of 2), MN is the maximum number of neurons, and DF is the display frequency of the training process. The data from the experimental arrangement were input into the main RBF neural network program in MATLAB for training. To verify the reliability of the neural network training, the rand function of MATLAB was used to randomly generate five sets of structural parameters, and the predicted values generated by the neural network were compared with the simulation calculation values, as shown in Table 6.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c  
The error analysis showed that the maximum error in the maximum temperature was 3.2%, the maximum error in the average temperature was 3.1%, and the maximum error in the temperature difference was 5.4%, all of which are within the scope of engineering permission.