## 5 Conclusions  
Reliable temperature information is necessary for many industrial processes. A temperature field reconstruction method based on proper orthogonal decomposition is proposed in this study. Both the simulation results and experimental results show that the proposed method is feasible and reliable. The main findings of this study can be summarized as follows:  
1. In simulation tests and experimental tests, the proposed method can rapidly reconstruct the temperature field with limited measurement data. It can dramatically reduce computation complexity and measurement cost. It also has good adaptability and can apply to real-time applications. 2. The dataset which is used to generate the POD basis vector plays a very important role in the proposed method. All the methods used in this study are based on it. When using CFD results to set up the dataset, sampling a wide range of boundary conditions which can cover most of working conditions in the flow field is of vital importance. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Position** & **Optimal** & **Random 1** & **Random 2** & **Random 3** \\ \hline
1 & 955.46 & 958.24 & 957.88 & 956.29 \\
2 & 1028.13 & 1026.36 & 1025.46 & 1027.54 \\
3 & 1012.98 & 1013.56 & 1017.76 & 1015.22 \\
4 & 1420.86 & 1424.92 & 1425.73 & 1424.18 \\
5 & 1119.37 & 1118.58 & 1126.75 & 1124.71 \\
6 & 1191.33 & 1186.57 & 1186.58 & 1185.99 \\
7 & 1112.33 & 1111.47 & 1107.12 & 1109.26 \\
8 & 1332.85 & 1330.16 & 1330.65 & 1332.44 \\
9 & 1174.38 & 1173.99 & 1177.79 & 1175.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Temperature values (K) for test reconstruction result. \begin{table}
\begin{tabular}{c c} \hline \hline
**Sensor Placement** & **Error** \\ \hline Optimal placement & 1.77 \\ Random placement 1 & 2.23 \\ Random placement 2 & 7.76 \\ Random placement 3 & 22.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Reconstruction errors (%) for 9 positions. \begin{table}
\begin{tabular}{c c} \hline \hline
**Sensor Placement** & **Error** \\ \hline Optimal placement & 1.94 \\ Random placement 1 & 8.43 \\ Random placement 2 & 3.68 \\ Random placement 3 & 16.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Reconstruction errors (%) for 85 positions. POD basis vectors can be extracted from a high-dimensional experience dataset. The first few basis vectors carry most of the useful information. With the use of a large number of basis vectors, too much useless information is introduced to the reconstruction process, and the reconstruction result is much more sensitive to the noise. Thus, it is necessary to obtain a balance between reconstruction accuracy and noise sensitivity. \"Energy\", which was mentioned in Section 3.3.1, can be used in finding the balance point. In the experience of this study, the vectors which contain \"energy\" lower than 0.1% are more sensitive to noise, so avoiding using these vectors will be better. 4. The proposed method needs little measurement data to yield an acceptable reconstruction result. The sensor number has some effect on the reconstruction result: the greater the number of sensors used, the better result. However, this effect decreases when the number of sensors increases to a certain threshold. Therefore, the balance between measurement cost and reconstruction accuracy requires the appropriate numbers of sensors. 5. When only a few sensors are used for reconstruction, sensor placement has a great influence on reconstruction accuracy. The sensor placement optimization algorithm was also tested in this study. The results show that optimal placement can yield a much more accurate result than random placement. The optimal sensor placement algorithm in this paper may not obtain the best solution, but it is more adaptable in different conditions and less sensitive to noise. 6. Noise has a great effect on the reconstruction error. However, the proposed method can also yield an acceptable reconstruction result in the presence of noise, and this effect tends to decrease when using a large number of sensors.