## 4 Composite Optimization
### Sensitivity Analysis
\begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline \multicolumn{10}{l}{**Sensitivity Analysis**} \\ \hline
**Scenario (1), Variables (1) and (14)** & & & & & & & & & & & \\ Variable & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\ \multicolumn{10}{l}{value:} \\ F.C. & 0.45213 & 0.46342 & 0.47516 & 0.48733 & 0.49999 & 0.51318 & 0.52693 & 0.54141 & 0.56038 \\ \multicolumn{10}{l}{values:} \\ T.R. & 49,156.96 & 39,410.42 & 38,860.61 & 37,512.19 & 36,410.64 & 34,841.99 & 33,512.3 & 32,201.97 & 30,891.85 \\
**Scenario (2), Variables (2) and (13)** & & & & & & & & \\ Variable & 3 & 2 & 1 & & & & & & \\ \multicolumn{10}{l}{value:} \\ F.C. & 0.45213 & 0.46027 & 0.46805 & & & & & & & \\ T.R. & 49,156.96 & 40,881.4 & 40,024.01 & & & & & & \\ Variable & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\ \multicolumn{10}{l}{value:} \\ F.C. & 0.45213 & 0.46318 & 0.47461 & 0.48638 & 0.49852 & 0.51105 & 0.52342 \\ \multicolumn{10}{l}{values:} \\ T.R. & 49,156.96 & 40,249.55 & 38,925.65 & 37,610.95 & 36,306.87 & 35,014.01 & 33,523.15 \\ \multicolumn{10}{l}{**Scenario (4), Variables (4) and (10)**} \\ Variable & 3 & 2 & 1 & & & & & \\ F.C. & 0.45213 & 0.46044 & 0.46897 & & & & & \\ T.R. & 49,156.96 & 40,817.99 & 40,046.45 & & & & & \\ \multicolumn{10}{l}{**Scenario (5), Variables (5) and (9)**} \\ Variable & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\ F.C. & 0.45213 & 0.46365 & 0.47475 & 0.48662 & 0.49886 & 0.5115 & 0.52453 \\ \multicolumn{10}{l}{values:} \\ T.R. & 49,156.96 & 40,273.86 & 38,974.2 & 37,686.07 & 36,408.65 & 35,143.21 & 33,887.97 \\ \multicolumn{10}{l}{**Scenario (6), Variables (6) and (9)**} \\ Variable & 3 & 2 & 1 & & & & & \\ F.C. & 0.45213 & 0.45961 & 0.46729 & & & & & \\ T.R. & 49,156.96 & 41,226.91 & 39,956.85 & & & & & \\ \multicolumn{10}{l}{(Nm/deg):} \\ \multicolumn{10}{l}{**Scenario (7), Variables (7) and (8)**} \\ Variable & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\ \multicolumn{10}{l}{value:} \\ F.C. & 0.45213 & 0.46389 & 0.47617 & 0.48897 & 0.50236 & 0.51643 & 0.53131 \\ \multicolumn{10}{l}{values:} \\ T.R. & 49,156.96 & 40,290.09 & 39,007.65 & 37,737.27 & 36,479.04 & 35,232.36 & 34,013.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Sensitivity analysis results. standard deviation (\(\sigma\)) were derived to quantify the magnitude, direction, and variability of each variable's influence. Results indicate that Scenario (1) and Scenario (7) exhibit the highest sensitivity, with \(\mu*\) values of approximately 0.0135 and 0.0134, respectively, suggesting that the variables involved in these scenarios have the greatest impact on performance, identifying key variables for targeted optimization. Lower sensitivity was observed in Scenarios (2), (4), and (6), with \(\mu*\) values below 0.0085. The relatively low standard deviations across scenarios imply mostly linear effects with limited interaction. Within the sensitivity analysis that was performed, the impact on torsional rigidity was also measured. Scenarios with fewer variable levels (e.g., Scenario 2 and Scenario 6) exhibited larger magnitudes of elementary effects, indicating a more pronounced impact of individual variable perturbations on the output. Conversely, scenarios with more extensive variable levels (e.g., Scenario 1 and Scenario 3) demonstrate comparatively smaller mean absolute elementary effects, suggesting a more gradual influence of variable changes. The mean absolute values of the elementary effects (\(\mu*\)) provide a robust measure of the average sensitivity, while the standard deviations (\(\sigma\)) reflect the heterogeneity and potential nonlinearity in the response. Also, elevated standard deviations in scenarios such as Scenario 2 and Scenario 5 denote the presence of complex interactions or nonlinear effects within the system. In summary, variables (2), (13), (5), and (9) are the most influential on torsional rigidity, as confirmed by the experiments and sensitivity metrics, denoting a connection between the monocoque panels' resistance to bending and the torsional rigidity exhibited by the structure.