Session: 05-04 Fault Detection, Optimization & Uncertainty

Paper Number: 121246

121246 - 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 prevalent during the production and in-service stage, including manufacturing tolerance and degradation. These uncertainties inevitably influence the thrust regulation performance under the current industrial controller with an indirect thrust control mode, which is due to the lack of available on-board thrust measurements. To mitigate technical risks due to these uncertainties, it is imperative to meticulously account for the uncertainties in the control design phase. However, the computational burden to quantify these uncertainties using purely sample-based Monte-Carlo simulations (MCS) is usually considerable, because repeated sampling phenomena are very severe from pseudo-random sampling properties. Moreover, for advanced engine configurations with more gas path components, e.g. geared inter-cooled turbofan engines, current research reveals that MCS needs over 10 hours on a desktop computer.

In this paper, a Polynomial Chaos Expansions-based uncertainty model (PCEUM) for thrust regulation assessment is proposed to get accurate probability distribution for engines’ interested controlled variables at a decreased computational burden. The parameters of PCEUM are solved by a regression approach of sparse-sampling method, which utilizes limited samples to obtain a faithful output distribution of the engine at a reduced simulation time.

As a model basis for PCEUM, a nominal aero-thermal model for a large civil turbofan engine, which is to simulate the ideal/average performance of the new engine, was established and verified against NPSS publicly available data. The engine is a two-shaft, separate flow, fixed-nozzle turbofan for large transport airplanes. Actual physical aero-thermal mechanisms, including the specific heat capacity of gas at constant pressure, bleed, and cooling effects, are carefully considered in the nominal aero-thermal model. The air/gas thermal properties due to the drastic temperature change along the gas path is fitted by the function of the specific heat capacity, enthalpy, and specific entropy at constant pressure. Additionally, the cooling effects in high-pressure turbine are modelled by energy conservation equations based on the mixing of the cooling air from high-pressure compressor and the main gas from high-pressure turbine. Simulations from idle to take-off thrust at sea-level static conditions on the nominal aero-thermal engine model show that key engine performance parameters, e.g., fan flow capacity, thrust, turbine entry temperature, and specific fuel consumption, are all within 3.1% errors, compared to the NPSS data. Hence, the nominal aero-thermal engine model is validated.

To simulate the uncertainty effects from manufacture tolerance, the nominal aero-thermal engine model is then extended with the health parameters of gas path components using representative uncertainty statistics. The uncertainty in gas path components could be modelled by scaling their nominal maps using these health parameters. Uncertainty simulations are performed by holding a constant low-pressure shaft speed (N1) to simulate the N1 thrust control mode. This is based on the fact that the current industrial controller usually owns a Proportional-Integral structure in the thrust regulation loop for steady-state zero-error thrust command tracking. Hence, it is plausible to run an open-loop uncertainty engine model at a constant N1 command when the model is converged at  steady states, which could describe the engine performance regulated by an industrial controller.

Simulation comparisons are conducted at the take-off thrust setting on a desktop computer between the proposed model and two purely sample-based benchmark methods, i.e. MCS and stratified Latin Hypercube Sampling (LHS). Results show that PCEUM only needs 99.4s to get the estimated mean and standard deviation for key engine performance parameters, including thrust, fan inlet flow, and turbine entry temperature, with only 200 samples. However, LHS requires 407s at the cost of 1000 samples and MCS needs 3424s under 8000 samples for a stable distribution for the concerned engine parameters, respectively. It means that more than 97.1% and 75.6% of the computational time decrease is achieved by PCEUM, compared to MCS and LHS accordingly.

Hence, the effectiveness of the proposed model is confirmed. It can be applied in the fast assessment for thrust control of traditional gas turbines and future ultra-high bypass ratio engines.

Presenting Author: Shijia Li Research Institute of Aero-Engines, Beihang University

Presenting Author Biography: Mr. Shijia Li is a PhD candidate in advanced modelling and control for aircraft gas turbine engine.

Authors:

Shijia Li Research Institute of Aero-Engines, Beihang University
Zhiyuan Wei Research Institute of Aero-Engines, Beihang University
Shuguang Zhang Beihang University
Zhaohui Cen Propulsion and Space Research Center, Technology Innovation Institute
Elias Tsoutsanis Propulsion and Space Research Center, Technology Innovation Institute