# Gaussian Process Model-Based Performance Uncertainty Quantification of a Typical Turboshaft Engine
## 4 Results and Discussion
### Engine Performance Baseline and Uncertain Parameters  
This paper focuses on the uninstalled, sea level static performance of the turboshaft engine. The maximum power is chosen as the design point of the engine. The ambient conditions, operating conditions, and control variables at the design point are summarized in Table 2. The thermodynamic cycle for the design point is calculated through the design point module. A set of desired values of the thermodynamic parameters is determined. Some important parameters serve as references to calculate the off-design point performance, such as component performance, throat area of the nozzle, mechanical efficiency and so on. The design point performance is treated as the performance baseline of the engine. Three key performance metrics (PMs) are analyzed in this study, including the output power (denoted as \(P_{e}\)), the SFC, and the total temperature at the outlet of the HPT (denoted as \(T_{45}\)). Due to confidentiality concerns, the design values of parameters and the performance baseline are not presented in this paper. It is noticed that the values of the PMs shown in this paper are the ratios of the actual PMs to their baseline values. Based on the results of design point calculation and given the values of control variables, the PMs at any other operating points can be calculated using the off-design point module. In this study, the off-design module is used to establish the GPMs for the three PMs.  
In this paper, the effects of flow capacity and adiabatic efficiency of the rotational component are investigated. This is due to the fact that the deviations of the component performance often lead to significant variations of the three PMs [37; 38]. Table 3 gives a detailed description of the uncertain parameters. The variation range (from low level to high level) over which each of the six uncertain parameters can be varied in this study is also summarized in Table 3. It should be noted that the ranges represent relative deviations from their design values.  
The range (\(-0.02\) to \(0.02\)) is adequate for the performance uncertainty quantification purpose since the anticipated variability in the actual component performance is strictly controlled. In addition, the six uncertain parameters are all assumed to follow truncated Gaussian distributions around their design values. The distributions are truncated by the range \([\mu-3\sigma,\mu+3\sigma]\), where, \(\mu\) and \(\sigma\) are the mean value and standard deviation of the Gaussian distribution, respectively. This means that the actual component performance falls into the range \([\mu-3\sigma,\mu+3\sigma]\) with a probability of 99.73%. It makes sense that the variation of the component performance is restricted within a certain range in practice.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Ambient temperature & 288.15 & K \\ Ambient pressure & 101,325 & Pa \\ Height & 0 & km \\ Mach number & 0 & – \\ Relative spool speed of HPR (control variable) & 0.97 & – \\ Relative spool speed of LPT (control variable) & 1 & – \\ \hline \hline \end{tabular}
\end{table}
Table 2: The ambient conditions, working conditions, and control variables.