## 5 Optimization for PCSH Wind Turbine Tower
### Optimization Results for the PCSH Wind Turbine Tower
#### 5.2.5 Computation Efficiency Comparison  
To verify the effectiveness of the proposed PUPSO algorithm for the optimization of the PCSH wind turbine tower, the comparison of computational times at different number of cycles between the PUPSO approach and the UPSO computation is shown in Table 11. When the cycle was 5, the computation time was saved by 49% and 38%, respectively. When the cycle was 10, the computation time was saved by 47% and 51%, respectively. It can be seen that by the use of the proposed PUPSO approach, the optimization computation efficiency was clearly enhanced.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Weight** & **Before Optimization** & **After Optimization** \\ \hline Steel segment (t) & 90 & 16 \\ PC segment (t) & 338 & 528 \\ Total (t) & 428 & 544 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Weight comparison of different tower.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Tower** & **Maximum Utilization Ratio** & **Before Optimization** & **After Optimization** \\ \hline \multirow{6}{*}{Steel segment} & Local buckling & 0.45 & 0.84 \\  & Overall stability & 0.40 & 0.52 \\  & Compressive load-carrying capacity & 0.53 & 0.76 \\  & Shear load-carrying capacity & 0.15 & 0.37 \\  & Torsion load-carrying capacity & 0.00075 & 0.0013 \\  & Combined load-carrying capacity & 0.29 & 0.67 \\  & Fatigue & 0.41 & 0.52 \\ \hline \multirow{6}{*}{PC segment} & Load-carrying capacity of windward side & 0.064 & 0.34 \\  & Load-carrying capacity of leeward side & 0.48 & 0.25 \\ \cline{1-1}  & Combined load-carrying capacity & 0.091 & 0.45 \\ \cline{1-1}  & Fatigue of windward side & 0.56 & 0.94 \\ \cline{1-1}  & Fatigue of leeward side & 0.21 & 0.48 \\ \cline{1-1}  & Fatigue of prestressing bar & 0.93 & 0.91 \\ \hline \hline \end{tabular}
\end{table}
Table 8: The maximum utilization ratio of PCSH tower before and after optimization.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Weight** & **Before Optimization** & **After Optimization** \\ \hline Steel segment (t) & 90 & 16 \\ PC segment (t) & 338 & 528 \\ Total (t) & 428 & 544 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Weight comparison of different tower.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Tower** & **Frequency (Hz)** \\ \hline Before optimization & 0.45 \\ After optimization & 0.56 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Natural frequency comparison of different tower.  
The comparison of computational time for PSO, UPSO, and PUPSO is shown in Table 12. The proposed PUPSO algorithm has better optimization abilities compared with the PSO and UPSO. As shown in Table 12, the computation time of the proposed PUPSO can be saved by 51% and 53% when compared with the PSO and UPSO, respectively. In conclusion, compared with the PSO and UPSO algorithm, the PUPSO algorithm can improve the optimization efficiency by 60-110%. The reason for the large difference in calculation efficiency is that computing time will be saved when a constraint violation occurs as the checking procedure is interrupted directly and employs the penalty term, as shown in Figure 3. Not only does the approach speed up the calculation efficiency but it also avoids premature convergence as much as possible.