# Gaussian Process Model-Based Performance Uncertainty Quantification of a Typical Turboshaft Engine
## 4 Results and Discussion
### Sensitivity Analysis of the Turboshaft Engine Performance
Figure 7: **(a)** The mean values of sensitivity indices of six uncertain parameters for \(T_{45}\) versus sample size; **(b)** the standard deviations of sensitivity indices of six uncertain parameters for \(T_{45}\) versus sample size; **(c)** the mean values of sensitivity indices of six uncertain parameters for \(P_{e}\) versus sample size; **(d)** the standard deviations of sensitivity indices of six uncertain parameters for \(P_{e}\) versus sample size; **(e)** the mean values of sensitivity indices of six uncertain parameters for SFC versus sample size; **(f)** the standard deviations of sensitivity indices of six uncertain parameters for SFC versus sample size. The final sensitivity analysis results for the turboshaft engine performance are shown in Figure 8. It should be noted that the value of each sensitivity index is marked above the corresponding bar. The first-order sensitivity indices of six uncertain parameters nearly account for 100% of the total variabilities of the three PMs, more specifically, 99.48% of the total variability in \(P_{e}\), 99.38% of the total variability in \(T_{45}\), and 99.68% of the total variability in SFC. Only a very small proportion of total variability is attributed to the sum of high-order sensitivity indices. The results imply that the main effects of six uncertain parameters have much larger influence on the PMs than the interaction effects do. Recall that \(S_{1}\), \(S_{2}\), \(S_{3}\), \(S_{4}\), \(S_{5}\), and \(S_{6}\) denote the first-order sensitivity indices of flow capacity of the compressor (\(w_{com}\)), adiabatic efficiency of the compressor (\(\eta_{com}\)), flow capacity of the HPT (\(w_{HPT}\)), adiabatic efficiency of the HPT (\(\eta_{HPT}\)), flow capacity of the LPT (\(w_{LPT}\)), and adiabatic efficiency of the LPT (\(\eta_{LPT}\)), respectively. From Figure 8, it can be observed that the six parameters play different roles in the three PMs. For \(T_{45}\), \(\eta_{HPT}\) is the most important parameter, which accounts for 37.485% of the total variability in \(T_{45}\). In the meantime, \(\eta_{com}\), \(w_{HPT}\), and \(w_{LPT}\) are also important to \(T_{45}\) as their indices are all greater than 10%. In particular, \(w_{com}\) and \(\eta_{LPT}\) are found to have little effect on \(T_{45}\) due to their small indices (\(S_{i}\leq 1\%\)). For \(P_{e}\), \(w_{LPT}\) has the most important effect on \(P_{e}\) comparing to other parameters since it contributes the highest percentage (35.89%) of the total variability in \(P_{e}\). The rest of the parameters except \(\eta_{LPT}\) are all considered as important parameters for \(P_{e}\) since the sum of their indices are about 60% and each index exceeds 10%. By contrast, \(\eta_{LPT}\) is less important to \(P_{e}\). As for SFC, there are two most important parameters (\(w_{LPT}\) and \(\eta_{LPT}\)) due to their large indices. The remaining four parameters are relatively unimportant to SFC. It should be noticed that \(w_{HPT}\) has, particularly, almost no effect on SFC. Figure 8: (**a**) The first-order sensitivity indices of six uncertain parameters for \(T_{45}\); (**b**) the first-order sensitivity indices of six uncertain parameters for \(P_{e}\); (**c**) the first-order sensitivity indices of six uncertain parameters for SFC (the value above each boxplot represents corresponding the interquartile range).