Pattern Classification of a Civilian Turbofan's State Space for Real-Time Surrogate Modeling

Abstract

Modern civilian turbofans are complex and nonlinear systems, and they must get even more complex and nonlinear to meet the requirements for noise, emissions, and fuel burn in the future. The increase in the complexity and nonlinearity are due to more advanced component designs and more complex interactions between these components. Consequently, models must get more complex and nonlinear to be useful for design and development in the future. In particular, real-time models must capture all relevant nonlinearity and complexity with acceptable accuracy and execution time to be useful in important applications, such as control system development. For this purpose, several real-time modeling techniques, namely transfer function, piecewise linear, aero-thermodynamic, and surrogate models can be used. Among the real-time modeling techniques, surrogate models promise high computational speed in addition to capturing nonlinearity. However, this potential can only be realized in practice if a turbofan’s state space is sampled sufficiently and efficiently. Because the state space has functional dependencies, typical space filling sampling techniques face problems, such as sampling a significant number of infeasible points and sampling the feasible state space sparsely or incompletely. To overcome the problem due to the functional dependencies in the state space, this paper proposes sampling a civilian turbofan’s state space with Support Vector Machines (SVM) a nonlinear pattern classifier. Thus, the functional dependencies can be captured as a pattern and less infeasible points are sampled while capturing the feasible state space sufficiently and efficiently. SVM were initially trained with a relatively small set of feasible and infeasible points to estimate the boundary between feasible and infeasible regions in the state space. Thus, the remaining sampling points were chosen from the feasible state space to generate more accurate surrogate models for real-time applications without increasing the number of cases. For sampling and accuracy tests, a non-real-time civilian turbofan model with shaft dynamics was developed to be the truth model. The proposed sampling method was compared with space filling samplings which used 5% and 20% perturbations from the steady state at sea level static (SLS) condition. As a result, the reduction in the number of sampled infeasible points and better coverage of the feasible state space were shown. In this paper multilayer perceptron (MLP) with one hidden layer was chosen to demonstrate the accuracy of surrogate models created using the proposed sampling method because of its advantages over other surrogate modeling techniques and fair comparison with work in the literature. The MLPs trained on the data generated by the proposed sampling method were tested in capturing truth model’s small and large signal behavior with step inputs at SLS.