## 5 Optimization for PCSH Wind Turbine Tower
### Optimization Results for the PCSH Wind Turbine Tower
#### 5.2.2 Utilization Ratio Comparison  
In order to evaluate the utilization of both concrete and steel material of the optimized PCSH wind turbine tower and the effectiveness of the approach, the material utilization ratio as the ratio of the actual to maximum allowable performance values is determined. Figure 8 shows the maximum constraint activity of all cases for the optimized design. According to Figure 8, it can be seen that all utilization rates are less than one but greater than zero and local buckling for the steel section and fatigue damage for the concrete section are prominent. Therefore, no constraint was violated and the safety of the structure is ensured. The utilization rate at the upper part of the steel segment is less than that at the lower part of the steel segment due to the fact that \(D_{st}^{1}\) is not optimized and is determined by the wind turbine and that the thickness of the steel section is constant along the height direction. The maximum utilization rate of the concrete segment is close to one along with the height, which means that the optimal result is close to the global optimal solution.  
The maximum utilization ratio of the PCSH tower before and after optimization are listed in Table 8. According to Table 8, the utilization ratio of steel and concrete has been enhanced significantly. That both maximum utilization ratios of prestressing bars are close to one means the prestressing bars are fully used. The change of prestressed reinforcement is mainly due to the change of structural internal forces caused by the change of structural dimensions. The maximum utilization ratio for the load-carrying capacity of the PC segment at windward side is below zero, which means that the windward side of the tower is compressed rather than tensioned under the impact of prestress. The maximum utilization rate of the optimized PCSH wind turbine tower is close to one, which illustrated the effectiveness of the PUPSO algorithm.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Tower** & **Variable** & **Before Optimization** & **After Optimization** \\ \hline \multirow{10}{*}{Steel tube segment} & Segment & 3 & 1 \\  & \(t_{s}^{1}\) (mm) & 14 & 10 \\  & \(D_{st}^{1}\) (mm) & 2686 & 2686 \\  & \(D_{st}^{1}\) (mm) & 3485 & 3296 \\  & \(H_{s}^{1}\) (mm) & 21,500 & 22,000 \\  & \(t_{s}^{2}\) (mm) & 18 & - \\ Steel tube segment & \(D_{st}^{1}\) (mm) & 3485 & - \\  & \(D_{sb}^{1}\) (mm) & 4046 & - \\  & \(H_{s}^{2}\) (mm) & 20,000 & - \\  & \(D_{st}^{3}\) (mm) & 4046 & - \\  & \(D_{sb}^{3}\) (mm) & 4400 & - \\  & \(H_{s}^{3}\) (mm) & 20,000 & - \\ \hline \multirow{10}{*}{PC segment} & \(t_{ct}\) (mm) & 500 & 270 \\  & \(t_{cb}\) (mm) & 500 & 285 \\  & \(H_{c}\) (mm) & 16,000 & 55,500 \\ \cline{1-1}  & \(D_{ct}\) (mm) & 4878 & 3549 \\ \cline{1-1}  & \(D_{cb}\) (mm) & 6900 & 5800 \\ \cline{1-1}  & Prestressed duct number & 36 & 36 \\ \cline{1-1}  & Prestressed reinforcement & \(8\Phi^{5}1\times 7\) (\(d=15.2\) mm) & \(7\Phi^{5}1\times 7\) (\(d=12.7\) mm) \\ \cline{1-1}  & Prestressed reinforcement area (mm\({}^{2}\)) & 40,320 & 24,872 \\ \hline \end{tabular}
\end{table}
Table 7: PCSH tower dimension before and after optimization.