## 6 Conclusions  
In the present paper, based on PCA and QR decomposition, a 3D field reconstruction method combining optimal sensor placement is proposed, which can accurately reconstruct the 3D velocity field and pressure field with limited sensor data. A PCA-based reconstruction algorithm can quickly and accurately obtain 3D velocity and pressure distribution, while QR pivoting is efficient in greatly reducing the number of sensors and improving the prediction accuracy. A simulation and an experiment were performed to verify the practicability of the algorithms. The major findings are as follows:  
Figure 29: Reconstruction errors with a different number of sensors. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Location** & **Verification Points** & **CFD** & **Error** & **QR Pivoting** & **Error** & **Random 10** & **Error** & **Random 15** & **Error** \\ \hline
1 & 7.07 & 7.24 & 2.33 & 7.28 & 3.03 & 7.82 & 10.64 & 7.57 & 7.01 \\
2 & 6.81 & 8.28 & 21.63 & 6.73 & 1.14 & 6.99 & 2.61 & 7.09 & 4.15 \\
3 & 7.89 & 8.45 & 7.03 & 7.37 & 6.65 & 8.02 & 1.63 & 7.74 & 2.01 \\
4 & 6.62 & 7.09 & 7.13 & 7.12 & 7.59 & 7.58 & 14.60 & 7.47 & 12.87 \\
5 & 7.15 & 8.05 & 12.64 & 7.10 & 0.74 & 7.57 & 5.81 & 7.46 & 4.35 \\
6 & 7.30 & 8.61 & 17.95 & 7.40 & 1.30 & 7.84 & 7.37 & 7.65 & 4.81 \\
7 & 7.13 & 7.69 & 7.82 & 7.00 & 1.94 & 7.31 & 2.52 & 7.36 & 3.24 \\
8 & 6.94 & 7.59 & 9.42 & 7.27 & 4.87 & 7.76 & 11.83 & 7.60 & 9.52 \\
9 & 8.54 & 8.08 & 5.40 & 7.08 & 17.14 & 7.54 & 11.77 & 7.46 & 12.68 \\
10 & 6.94 & 7.09 & 2.10 & 7.18 & 3.42 & 7.67 & 10.46 & 7.46 & 7.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Measured value (m/s), CFD value (m/s), reconstructed value (m/s) and error (%) of each location. In the simulation, the reconstruction errors of the uniform inlet are 0.21% and 6.46%, respectively, while the maximum reconstruction errors including wind shear effect are 1.21% and 6.41%, respectively, which indicates that the reconstruction algorithm based on PCA and sparse sensing can accurately and quickly obtain the distribution characteristics of the velocity and pressure of a 3D wind field. 2. The effects of the number of basis vectors, measurement noise, number of sensors and placement on the reconstruction results were systematically investigated. The results show that an excessive increase of the number of basis vectors will result in reconstruction errors being more sensitive to noise level. 3. Reconstruction accuracy can be significantly influenced by the arrangement of sensors when sensor costs are restricted (e.g., less than 20), especially for the pressure field, where the difference between the maximum and minimum reconstruction errors is even 20 times. 4. Matrix QR pivoting was integrated into the reconstruction algorithm to determine the optimal sensor placement, and its performance was validated by the simulation. The results indicate that QR pivoting-based sensor placement can achieve better reconstruction performance than random measurements, which reduces costs associated with the purchase, placement and maintenance of sensors. 5. Optimized sensor placement characteristics indicate that better reconstruction results can be obtained by placing the sensor in areas with large gradients of velocity and pressure, where reconstruction errors are also typically larger. 6. A wind tunnel experiment of velocity field reconstruction was performed to verify the practicability of the optimized reconstruction method based on QR pivoting, and the results indicate that a reasonably high accuracy 3D wind field can be obtained with only 10 sensors (the error of most points is less than 5% and the minimum error is only 0.74%). In this work, we have demonstrated the practical implementation of an algorithm combining PCA and QR pivoting on a 3D wind field by a simulation and a wind tunnel experiment.