# A Study on Aeroengine Conceptual Design Considering Multi-Mission Performance Reliability
## 5 Results and Discussion
### Optimization Solution  
APSO is also exploited to solve the optimal value of cycle parameters. Figure 10 plots the global best value at each iteration. The observation is that the fitness value is gradually stable after 60 generations through four drops. According to the result of MC simulation computing time mentioned above, it would cost approximately 4760 s for one particle to calculate its fitness value that is associated with reliability in four states. In each iteration of the optimization process, it is not difficult to estimate that computation time is at least 39.6 h if the practice population size is 30. So, it would spend nearly 165.3 days to complete one optimization calculation when the evolutionary generation is 100, which is totally unaffordable. This situation reveals the vital issue that MC-based probabilistic design is extremely difficult to implement so that only concentrates on MPP and ignores other working conditions. Nevertheless, it only spent 224.2 s to complete one optimization procedure based on the reliability prediction of ANN surrogate models, which dramatically improved the calculation efficiency with acceptable accuracy. The optimal solution of the design problem is summarized in Table 7. \begin{table}
\begin{tabular}{c c c c c} \hline  & \multicolumn{2}{c}{**MC (10\({}^{3}\) times)**} & **ANN** & **Pre-trained ANN** \\ \hline \multicolumn{2}{c}{**Computing Time (s)**} & **95,262.2** & **0.1274** & **0.1267** \\ \hline \multirow{3}{*}{Averageabsolute error} & R\({}_{\text{Fr},\text{TKO}}\) & \(\backslash\) & 0.0426 & 0.0149 \\  & R\({}_{\text{Fr},\text{SuA}}\) & \(\backslash\) & 0.0319 & 0.0134 \\  & R\({}_{\text{Fr},\text{SuC}}\) & \(\backslash\) & 0.0394 & 0.0254 \\  & R\({}_{\text{SFC},\text{SuC}}\) & \(\backslash\) & 0.0657 & 0.0173 \\ \hline \multirow{3}{*}{Maximumabsolute error} & R\({}_{\text{Fr},\text{TKO}}\) & \(\backslash\) & 0.0137 & 0.0542 \\  & R\({}_{\text{Fr},\text{SuA}}\) & \(\backslash\) & 0.0782 & 0.0471 \\  & R\({}_{\text{Fr},\text{SuC}}\) & \(\backslash\) & 0.109 & 0.0475 \\  & R\({}_{\text{SFC},\text{SuC}}\) & \(\backslash\) & 0.228 & 0.0592 \\ \hline \end{tabular}
\end{table} 
Table 6: Comparison of computing time and precision (20 testing samples). MC = Monte Carlo. Figure 10: Fitness curve in the APSO evolutionary processes. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{5}{c}{**Cycle Parameters**} \\ \cline{2-7}  & \(\pi_{\text{F}}\) & \(\pi_{\text{C}}\) & \(T_{\text{ET}}\) (K) & \(R_{BP}\) & \(W_{stat}\)(kg/s) & \(R_{\text{TW}}\) & **Fitness** \\ \hline Origin & 3.302 & 9.750 & 1715 & 0.7900 & 122.7 & 6.75 & / \\ Optimized & 3.525 & 10.305 & 1727.2 & 0.8484 & 129.8 & 7.42 & 0.0243 \\ \hline \end{tabular}
\end{table} 
Table 7: The optimal solution of cycle parameters. According to design boundary of cycle parameters and \(R_{TW}\) requirement, the APSO is certainly functioning as expected in terms of rejecting unfeasible solutions that violate constraints. Compared with the original cycle scheme, the cycle parameter values of optimal solution are increased in varying levels, which is consistent with the expectation of increasing performance redundancy. In MC verification process, we input the candidate cycle solution to MTF model and then set sample capacity of 2000 for all operating condition. Figure 11 visually compare the overall performance frequency histogram of candidate solution and the original cycle scheme. The first observation is that the performance output responses approximately obey normal distribution. Secondly, the candidate cycle solution significantly shifts the performance distribution in the direction of improved performance reliability, but not far away from the benchmark lines of all operating conditions of interest. Referring to the Formula (4), further statistics are carried out and the results are displayed in Table 8.  
The results demonstrated that optimized solution make all target performance reliability not less than 98%, which make a significant improvement over the original cycle scheme.