# Gaussian Process Model-Based Performance Uncertainty Quantification of a Typical Turboshaft Engine
## 1 Introduction  
As a typical thermodynamic system, the gas turbine engine has been widely used to provide propulsion or power to various aircrafts, for example, to provide propulsion to civil airliners and power to helicopters. The operation of the engine is primarily based on the principle of the thermodynamic cycle [1, 2]. A cycle generally consists of a sequence of thermodynamic processes, involving the transfer of work and heat. Taking a single-spool turbojet engine as an example, its ideal cycle is mainly comprised of an isentropic compression process, an isobaric heating process, and an isentropic expansion process. In practice, these processes can be implemented through three mechanical components of the engine, namely, the compressor, the combustor, and the turbine. Since the engine performance depends largely on the cycle, it is an important fundamental task for engine designers to complete the overall performance design of engine using thermodynamic cycle calculation in the preliminary design stage. The task yields the final decisions of the component performance and other essential thermodynamic parameters. However, even with a well-controlled manufacturing process, geometric differences between individual engines are unavoidable due to the natural presence of manufacturing deviation. For instance, the produced blade profiles always deviate somewhat from their nominal values [3, 4]. In terms of the production engine, the geometries are randomly distributed within given tolerances, causing a performance scatter in the engine production [5]. The performance scatter often leads to a limited understanding of the performancelevel of the production engine. If the effect of the manufacturing uncertainty is ignored, there may be a high risk of design failure when a new engine is designed. Therefore, it is essential to investigate the effects of uncertain variables on the engine performance in the early design stage as the decisions must be made to some crucial design parameters at this stage. In the context of the overall performance design of the engine, a number of studies have been reported to investigate the influence of uncertain variables on the engine performance [6; 7; 8; 9; 10; 11]. [PERSON] et al. [6] performed uncertainty analysis for an advanced adaptive cycle engine by coupling Monte Carlo sampling (MCS) with linear models. The authors quantified the effects of uncertain flow capacity and adiabatic efficiency of rotating components on the engine performance. [PERSON] et al. [7] directly employed MCS to explore the impact of the uncertainty in component performance on the overall performance of a turboshaft engine. [PERSON] et al. [8] quantified the effect of component performance uncertainty on a turbofan engine using an artificial neural network-based MCS. [PERSON] et al. [9] also integrated the artificial neural network and the MCS to quantify the impact of efficiencies of the fan and high-pressure compressor on the performance of a turbofan engine. [PERSON] et al. [10] proposed a polynomial response surface-based MCS to investigate the effects of uncertain aerothermoelastic deformations on the performance of a scramjet engine. [PERSON] et al. [11] applied MCS to propagate the effects of uncertain deformations of forebody, splitter, and cowl to the performance of an advanced turbine-based combined cycle engine. It can be found that most studies are focused on using the probabilistic methods to perform uncertainty analysis in the literature of uncertainty quantification of engine performance. MCS is the most commonly used method. Generally, MCS is commonly used as the baseline reference due to its advantage of simplicity and accuracy [12]. The results of MCS do not depend on the number of input variables, but highly rely on the number of samples. Therefore, MCS becomes computationally intensive to ensure the accuracy of the results. When it comes to the time-consuming simulation models, MCS may not be applicable due to the computational burden.