# Gaussian Process Model-Based Performance Uncertainty Quantification of a Typical Turboshaft Engine
## 1 Introduction
To solve this problem, several studies built surrogate models to replace the time-consuming physical simulation model [6; 8; 9; 10]. However, the surrogate model inevitably leads to approximation error since it cannot perfectly substitute the simulation model. The approximation error should be explained when employing surrogate models in the uncertainty analysis. In addition, the non-probabilistic methods are employed to perform uncertainty analysis of engine performance in only a few studies. [PERSON] et al. [13] applied an interval analysis method based on Taylor series expansion to analyze the effect of component performance uncertainty on an adaptive cycle engine. The interval analysis methods are often used in the problems where the precise statistical information of uncertain variables cannot be obtained. However, the probabilistic methods have advantages over the non-probabilistic methods in accuracy and precision [14]. Moreover, the probabilistic methods can provide some statistics, e.g., the mean and the standard deviation, about the uncertain variables. This information is very useful for engine designers to better understand and reduce the engine performance uncertainty. Therefore, this paper concentrates on the development of the probabilistic method. The overall performance of the engine is generally simulated by a nonlinear component-level model. The model incorporates the calculation of thermodynamic processes and the match of various thermodynamic parameters and component performance. A set of appropriate values can be determined through an iterative process when introducing several physical constraints. The constraints are usually associated with the aerodynamic and mechanic connections in the engine. To perform uncertainty quantification with such a model, an improved uncertainty quantification method is developed to significantly reduce the computational burden. Firstly, a more efficient sampling method, called Latin hypercube sampling (LHS), is proposed to perform uncertainty quantification. Compared with MCS, LHS improves the sampling strategy to achieve a significant reduction in sample size but equally accurate result [15]. In general, LHS is a kind of stratified sampling, and the key is to stratify the probability distributions of input variables. Due to this feature,LHS can uniformly distribute the sample points in the parameter space, leading to a faster convergence than MCS [16]. Moreover, the Gaussian process model (GPM) is used to substitute the performance simulation model of the engine. In general, GPMs are widely used as surrogate models to substitute ex-pensive simulation models [17; 18; 19]. A GPM represents a prior for the input-output relation of a simulator. When the training data are obtained, usually by the space-filling design, the prior Gaussian process (GP) can be updated using the data. Thus, a posterior GP can be established for prediction. The GPM is a nonlinear interpolation model. Due to the inherent nature of the GPM, the prediction error at any new point can be directly derived. Thus, it is feasible to fit the overall performance simulation model and convenient to evaluate the effect of approximation error on the predicted results. A combination of GPM and LHS, i.e., the GPM-based LHS, has advantages over the traditional simulation-based MCS in the rate of convergence and the robustness of the uncertainty quantification results. In addition, the GPM-based LHS can quantify the effect of approximation error on the uncertainty quantification results thanks to the feature of the GPM. In this paper, the proposed GPM-based LHS method is adopted to investigate the overall performance uncertainty of a typical turboshaft engine. According to the relevant literature, the uncertainty regarding the component performance is taken into account in this study.