Nonlinear identification of aircraft gas-turbine dynamics
Introduction
Engine condition monitoring is a vital and urgent issue in aircraft-in-service use and flight safety. Unplanned maintenance and repair expenses follow unexpected faults of equipment. In order to be able to develop further on a fault detection and isolation system for gas-turbine engines, a first step required is the development of an accurate model describing the engine under normal, not faulty, conditions. Previous research in this topic show that the engine dynamics vary with the operating point considered. One possibility to deal with this type of systems is the identification of a global nonlinear model that can cope with the entire range of working conditions. An alternative is the use of local models, by decomposing the entire operational range of the system into a number of possibly overlapping regions, and identifying models for each region. These models are then combined in some way to yield a global model. Another approach involves the use of information units, describing the nonlinear process behaviour at specified operating points, and at their neighbourhoods. All these approaches are discussed in this paper. One major difficulty in the use of these models is the determination of their structure. In this paper, the use of multiobjective genetic programming for the determination of suitable model structures is also addressed.
In Section 2, gas-turbine engines are introduced, and the main findings of previous works using classical linear system identification techniques are reported. Section 3 classifies nonlinear model structures. Section 4 introduces NARMAX and NARX models, and discusses the use of multiobjective genetic programming for determining the model structure which describes the dynamic behaviour of the nonlinear system under investigation. A special emphasis will be given to the introduction of the validation stage of the identification procedure in the multiobjective tool. Section 5 reports the use of different types of neural models for gas-turbine identification, focusing on B-spline neural networks, and describing how multiobjective genetic programming can be employed for designing this type of networks. Conclusions and guidelines for future work are given in Section 6.
Section snippets
Gas-turbine engines
A gas turbine is made up of three basic components: a compressor, a combustion chamber and a turbine. Air is drawn into the engine by the compressor, which compresses it and delivers it to the combustion chamber. There, the air is mixed with the fuel and the mixture ignited, producing a rise of temperature and therefore an expansion of the gases. These are expelled through the engine nozzle, but first pass through the turbine, designed to extract energy to keep the compressor rotating [10].
The
Nonlinear models
Isermann et al. [14] classify neural networks for nonlinear system identification into two categories: (i) using external dynamics (static models), or (ii) using internal dynamics (dynamic models). Static model implementations, such as that depicted in Fig. 4, consists of an “approximator” (which may be a neural network), whose output, yn(k), is a function of the plant inputs, up(k−1)⋯up(k−nu), and the approximator outputs, yn(k−1),…,yn(k−ny), where ny and nu are the associated maximum lags.
Neural network models
Due to the intensive research performed in the last decade, neural networks are now established models for nonlinear system identification. We shall here investigate the use of multilayer perceptrons (MLPs) [20], radial basis function networks (RBFs) [6], and B-spline networks [7] for gas-turbine identification.
Three different operating points were considered: 53.8%, 75.45% and 88.7% NH. For each operating point, the training process employed 4000 training samples, corresponding to 1 signal
Conclusions
Different nonlinear model structures have been applied for the identification of the Rolls Royce Spey MK 202 dynamics. Among the neural network models considered, the B-spline neural network proved to be the one delivering the best results. For determining the model structure, for both NARMAX and B-spline models, genetic programming has been found to be a powerful tool, lending itself very naturally to the simultaneous optimisation of multiple objectives, related with model performance, model
Acknowledgements
This work was done under the support of INTAS 2000-757 grant. The authors wish to acknowledge Rolls-Royce plc. (specially Dr. D. Hill) and DERA (Pyestock) for their cooperation and support for the provision of the engine data.
Carlos Fonseca received his Licenciatura in Electronic and Telecommunications Engineering from the University of Aveiro, Portugal, in 1991, having been awarded the Prize “Eng. José Ferreira Pinto Basto” by Alcatel, Portugal, “in appreciation of the classification achieved in this degree”. He obtained the degree of Ph.D. at the University of Sheffield, UK, in 1995, for research into multiobjective genetic algorithms. He was a Research Associate in the Department of Automatic Control and Systems
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Carlos Fonseca received his Licenciatura in Electronic and Telecommunications Engineering from the University of Aveiro, Portugal, in 1991, having been awarded the Prize “Eng. José Ferreira Pinto Basto” by Alcatel, Portugal, “in appreciation of the classification achieved in this degree”. He obtained the degree of Ph.D. at the University of Sheffield, UK, in 1995, for research into multiobjective genetic algorithms. He was a Research Associate in the Department of Automatic Control and Systems Engineering at the University of Sheffield from 1994 until he joined the University of Algarve, Portugal, as an Invited Lecturer in 1997. He was appointed Lecturer in 1998, and is currently the Vice-Coordinator of the Centre for Intelligent Systems of the University of Algarve. He has been a member of the IFAC Technical Committee on Optimal Control since 1996, and a member of the EvoNet Management Board since 2001. His main research interests are evolutionary multiobjective optimization and its applications to control and systems engineering.
César Teixeira is an undergraduate student of the Centre for Intelligent Systems at the University of Algarve. He is at the moment working in the project “Application of Soft-Computing Techniques to Hydroponic Greenhouse Environmental Control of Vegetable Production”. His research interests lie in control systems, evolutionary computing and Neural Networks.
Peter Fleming is Professor of Industrial Systems and Control at the University of Sheffield and Director of the Rolls-Royce University Technology Centre for Control and Systems Engineering. He is Vice-President of the International Federation of Automatic Control and the Editor of International Journal of Systems Science. His research interests in control systems, optimisation and evolutionary computing have led to close links with industries in sectors such as aerospace, power generation, food processing, pharmaceuticals and manufacturing.
Katya Rodrı́guez-Vázquez was born in Mexico in 1970. She received a Computing Engineering degree from the National University of Mexico in 1994. She received Ph.D. degree in 1999 from the University of Sheffield, UK. She is currently a Research Associate at the Institute of Applied Mathematics and System Engineering Institute, National University of Mexico. She has published a number of papers in international journals and conference and has been member of the Program Committee for conference related to Evolutionary Computation field. Her research interests include evolutionary computation, multi-objective optimisation, parallel computing and optimisation.
Antonio Ruano was born in 1959 in Espinho, Portugal. He received the First Degree in Electronic and Telecommunications Engineering from the University of Aveiro, Portugal, in 1982, the M.Sc. in Electrothecnic Engineering from the University of Coimbra, Portugal, in 1989, and the Ph.D. degree in Electronic Engineering from the University of Wales in 1992. In 1992 he joined the Department of Systems Engineering and Computing of the Faculty of Sciences & Technology of the Universidade do Algarve, where in 1996 he became Assistant Professor of Automatic Control. His main research interests are neural control (both theoretical issues and applications), environmental control and parallel processing techniques applied to real-time control. He has over 100 research publications, he is Associate Editor for Automatica, he is a member of the Editorial Board of International Journal of Systems Science, and serves as reviewer for other journals and international Conferences.