Polynomial Chaos Expansion-Based Uncertainty Model for Fast Assessment of Gas Turbine Aero-Engines Thrust Regulation: A Sparse Regression Approach

Uncertainties in gas turbine aero-engines are unavoidable among which manufacturing tolerance is a typical manifestation. Uncertainties from manufacturing tolerance directly influence the thrust regulation performance, which may lead to the technical risks of newly produced aero-engines. Moreover, classic sample-based uncertainty quantification approaches are usually computationally intensive. In this paper, to consider the uncertainties in the control design phase in advance, a polynomial chaos expansion-based uncertainty model (PCEUM) using a sparse regression method is proposed to get the accurate probability distribution of thrust regulation performance and other concerned engine variables at a decreased computational burden. In PCEUM, engine variables are initially expressed as linear combinations of several orthogonal polynomials, whose weighting coefficients are solved by a sparse-regression-based method, i.e. orthogonal matching pursuit (OMP). A nominal aero-thermal model for a large turbofan engine, whose maximum errors for key engine parameters are within 2.25% against NPSS data, serves as the basis of PCEUM. Meanwhile, two classic sample-based uncertainty quantification approaches, (i.e. Monte-Carlo simulations (MCS), Latin hypercube sampling (LHS)) and a least angle regression (LARS) based PCE are set as benchmarks. Numerical simulations using publicly available manufacturing tolerance statistics are conducted at take-off states for the tested engine on a desktop computer. Results show that the proposed PCEUM costs only 47.06s at the expense of 200 samples to obtain stable probability distributions for interested engine parameters, e.g. thrust, whose errors of mean and standard deviation compared with MCS at 100,000 samples are within 0.01% and 1%, respectively. While the computational burden of MCS, LHS, and LARS are 854.63s at 9,000 samples, 250.13s at 3,000 samples, and 54.16s at 200 samples at the same precision level, respectively. It means that compared to the latter three methods, PCEUM can save 94.5%, 81.2%, and 13.1% of the simulation time, respectively. Hence, the proposed model is verified regarding both the accuracy and speed for uncertainty assessment, which provides a promising solution for both conventional gas turbine engines and future aero-propulsion systems.