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

Abstract

Manufacturing tolerance uncertainties in gas turbine aero-engines are unavoidable, which adversely influence the thrust control performance of newly produced aero-engines. However, classic sample-based uncertainty quantification approaches are usually computationally intensive. In this paper, to consider the uncertainties in the thrust 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, interested engine parameters 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). Meanwhile, two classic sample-based uncertainty quantification approaches, (i.e., Monte Carlo simulations (MCS), Latin hypercube sampling (LHS)) and least angle regression (LARS) are set as benchmarks. Numerical simulations on a verified large turbofan engine model at the takeoff state on a desktop computer show that PCEUM costs only 47.06 s at 200 samples to obtain converged probability distributions for interested engine parameters whose errors of mean and standard deviation are within 0.01% and 1%, respectively, compared to MCS at 100,000 samples. Meanwhile, compared to the latter three methods, PCEUM saves 94.5%, 81.2%, and 13.1% of the simulation time, accordingly. Hence, both the accuracy and speed of the proposed model are guaranteed for the uncertainty assessment of thrust regulation, which provides a promising solution for both conventional and future aero-propulsion system.