## 6 Conclusions  
The connection between the steel joint and the aluminum alloy pipe is the weak part of the aluminum alloy drill pipe and the main site of its failure. In actual operation, the interference connection between aluminum alloy rod body and steel joint is usually realized by thermal assembly. In this paper, the relationship among cooling water flow rate, initial heating temperature of steel joint and thermal deformation of steel joint in interference thermal assembly was studied and predicted based on a BP neural network algorithm. The thermal deformation of the steel joint was predicted. Furthermore, the magnitude of the interference fit of the steel joint was predicted as well, and the prediction results of the BP neural network were analyzed. A polynomial model, exponential model and Gaussian model based on the least square method were adopted to predict the sectional deformation in order to compare and analyze the prediction performance of the BP neural network. A polynomial model was used to predict the magnitude of the interference fit. Through a comparative analysis of SSE and MAE, it can be concluded that the BP neural network has good prediction accuracy. Conclusions from the paper could be summarized as follows:  
1. The higher the initial heating temperature of steel joint, the greater the influence of the cooling water flow rate on the temperature and thermal deformation of steel joints. 2. For the prediction model of thermal deformation in same section, when \(r\) = 74 mm, the prediction error was the largest. As the \(r\) increased or decreased, the prediction error decreased. 3. For the prediction model of the magnitude of interference fit and relevant factors, with the increase of heating temperature, the prediction error increased. When the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**T**} & \multicolumn{2}{c}{**BP**} & \multicolumn{2}{c}{**Polynomial**} \\ \cline{2-5}  & **SSE** & **MAE** & **SSE** & **MAE** \\ \hline
300 \({}^{\circ}\)C & 3.00E-04 & 8.80E-03 & 3.15E-02 & 8.14E-02 \\
400 \({}^{\circ}\)C & 3.13E-04 & 8.80E-03 & 1.00E-02 & 4.73E-02 \\
500 \({}^{\circ}\)C & 5.13E-04 & 1.02E-02 & 3.00E-02 & 7.81E-02 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison of accuracy of prediction models at different initial heating temperatures. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**v/m/s**} & \multicolumn{3}{c}{**RE**} & \multirow{2}{*}{**SSE**} & \multirow{2}{*}{**MAE**} \\ \cline{2-2} \cline{4-5}  & **T = 300 \({}^{\circ}\)C** & & & & \\ \hline
0.016 & 3.96E-03 & 7.64E-02 & 1.56E-01 & 3.03E-02 & 7.89E-02 \\
0.038 & \(-\)8.36E-02 & \(-\)5.66E-04 & 7.39E-02 & 1.25E-02 & 5.27E-02 \\
0.061 & \(-\)1.57E-01 & \(-\)6.49E-02 & \(-\)4.04E-03 & 2.88E-02 & 7.52E-02 \\ \hline SSE & 3.15E-02 & 1.00E-02 & 3.00E-02 & & \\ MAE & 8.14E-02 & 4.73E-02 & 7.81E-02 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The prediction model accuracy of the polynomial model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**v/m/s**} & \multicolumn{3}{c}{**BP**} & \multicolumn{2}{c}{**Polynomial**} \\ \cline{2-5}  & **SSE** & **MAE** & **SSE** & **MAE** \\ \hline
0.016 & 3.30E-04 & 8.42E-03 & 3.03E-02 & 7.89E-02 \\
0.038 & 9.22E-05 & 4.42E-03 & 1.25E-02 & 5.27E-02 \\
0.061 & 7.03E-04 & 1.42E-02 & 2.88E-02 & 7.52E-02 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of accuracy of prediction models at different water velocities. cooling water velocity was 0.038 m/s, the prediction accuracy was the highest. With the velocity increase or decrease, the prediction error increased. Especially when the velocity increased, the error's trend to increase was more obvious. 4. The polynomial model, exponential model and Gaussian model were, respectively, compared and analyzed with the BP neural network.