## 5 Results and Discussion
### Full-Heliostat Field Simulation Experiment  
The 3-dimensional display of the heliostat field receiver unfolded diagram is shown in Figure 16. A full-heliostat field simulation with a cloud movement path is presented in this section, and the clouds move according to the paths in Figure 17. The cloud positions at three different periods are selected chronologically to demonstrate the performance of the proposed method, where the aiming strategy of each heliostat field sector is obtained independently by IUPSO.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{2}{c}{**Mid-Line Cloud Path of Y-Axis**} \\ \cline{2-3}  & **Modified PSO** & **IUPSO** \\ \hline
**Mean Intercept ratio score** & 0.7525 & 0.9131 \\
**Mean Fitness Value** & 335.0197 & 394.9755 \\
**Optimization time per-period (/s)** & 0.52 & 0.15 \\
**Mean Optimization periods** & — & 87 \\
**Mean Optimization time (/s)** & — & 12.89 \\ \hline
**Parameters** & **Mid-Line Cloud Path of X-Axis** \\ \hline
**Mean Intercept ratio score** & 0.8028 & 0.8310 \\
**Mean Fitness Value** & 297.6034 & 387.6110 \\
**Optimization time per-period (/s)** & 0.66 & 0.31 \\
**Mean Optimization periods** & — & 82 \\
**Mean Optimization time (/s)** & — & 25.96 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Data analysis and comparison based on the mid-line cloud path of the Y-axis and X-axis.  
Figure 15: IUPSO versus Modified PSO performance improvement based on simulation data from 400 virtual reality heliostat fields. It can be seen that the fitness improvement of \(75.0\pm 4.5\) and power improvement of \(10.1\pm 2.0\) MW\(/\)m\({}^{2}\) are observed in the 400 sets of random dynamic sampling heliostat field simulations with different cloud moving paths, showing that IUPSO outperforms the Modified PSO algorithm for all cases.  
The velocity of the cloud in the case of full heliostat field experiments is 5 m/s, the radius of the cloud is 200 m, the azimuth angle is 180\({}^{\circ}\), and the elevation angle is 70\({}^{\circ}\). The flux map of the cylindrical receiver is unfolded to a flat surface according to Figure 17. The flux map of the three locations in the full heliostat optimized by IUPSO proposed in this paper is shown in Figures 17 and 18. All experiments were performed ten times; the data are reported in figures and tables as the mean values.  
From Figure 18a-c, the flux gap indicates the influence on the flux map caused by the obscuration of the heliostat field caused by clouds at different locations. The mean optimization time in location A is 15.36 s, in location B is 23.23 s, and location C is 18.53 s. The IUPSO effectively addresses the real-time aiming strategy for the full heliostat field. The results show it is equally effective for the sector heliostat aiming strategy optimization algorithm. Additionally, the IUPSO's average optimization time in the three scenes is shorter than the heliostat field sampling period, indicating its capability for real-time aiming strategy optimization.  
Figure 16: A diagram of the 3D display of the heliostat field receiver unfolded.  
Figure 17: A 3D display of the heliostat field receiver for a full heliostat field.