# Gaussian Process Model-Based Performance Uncertainty Quantification of a Typical Turboshaft Engine
## 5 Conclusions  
The demand for quantifying the uncertainty of engine performance in the preliminary design is increasing due to the expectation of reliable engine performance design. In this paper, a GPM-based uncertainty quantification method is proposed to quantify the effect of component performance uncertainty on the overall performance of a turboshaft engine. Six uncertain parameters related to the component performance and three PMs of the engine are determined. To significantly reduce the number of running the time-consuming simulation model, three GPMs that reflect the functional relationships between six uncertain parameters and three PMs are constructed. The validation shows that the GPMs are of high accuracy. LHS is utilized to propagate the uncertainty to the engine performance and provide the statistical information of the engine performance. The GPM-based LHS is validated to perform better than the most frequently used simulation-based MCS. In addition, based on the GPMs, the variance-based sensitivity analysis is employed to recognize the main contributors to the engine performance uncertainty. According to the first-order sensitivity index, the important uncertain parameters for three PMs are determined with the criterion \(S_{i}\geq 10\%\), which is very useful for the engine designers. To obtain reliable and robust results, both approximation and sampling errors are investigated in this study. Some useful results are summarized as follows:  
1. A strong correlation (with a correlation efficiency of 60%) between the flow capacity and adiabatic efficiency of compressor only has a small influence on the standard deviation of the turboshaft engine performance. Specifically, the standard deviation of \(P_{e}\) decreases by around 6.6-8.7% as the standard deviation of uncertain parameters varies from 0.002 to 0.004. Likewise, a reduction of 2.3-4.2% is observed for \(T_{45}\), but an increase of 3.0-3.7% for SFC. With an assumption of independent parameters, the maximum \(T_{45}\), minimum \(P_{e}\), and maximum SFC deviate 1.3%, 2.2%, and 0.84% from their nominal design values in the unfavorable direction when the standard deviations of uncertain parameters are equal to 0.002. The deviations almost double as the standard deviations increase to 0.004.
2. The first-order sensitivity indices of six uncertain parameters almost 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.
3. The important parameters for \(T_{45}\) are \(\eta_{com}\), \(w_{HPT}\), \(\eta_{HPT}\), and \(w_{LPT}\). All the uncertain parameters other than \(\eta_{LPT}\) are the important parameters for \(P_{e}\). Only \(w_{LPT}\) and \(\eta_{LPT}\) are the important parameters for SFC. In particular, \(w_{LPT}\) is important to all the three PMs of the turboshaft engine.  
Conceptualization, X.L., H.T. and X.Z.; methodology, X.L.; software, X.L.; validation, X.L. and X.Z.; formal analysis, X.L.; investigation, X.L. and X.Z.; resources, X.L. and X.Z.; data curation, X.L.; writing--original draft preparation, X.L.; writing--review and editing, H.T. and M.C.; visualization, X.L.; supervision, H.T. and M.C.; project administration, H.T. and M.C.; funding acquisition, H.T. and M.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China, grant number 51776010 and 91860205.  
Not applicable.