Automatic modeling of a gas turbine using genetic programming: An experimental study
Graphical abstract
Introduction
Gas turbines (GTs) are one of the key elements in the electrical power industry since they transform mechanical power into the desired electrical output. In particular, GTs are widely used in so-called Open Cycle Plants and Combined Cycle Plants. They are considered to be high-risk units since they operate at high speed, temperature and pressure, conditions that impose strict control requirements. The control system executes the startup and shutdown sequences, controls speed, power and temperature, while also performing functions related to safety and protection. Startup and shutdown sequences consist of a series of complex events where each step has to be satisfactorily completed before continuing to the next. Moreover, in central power generation it is of utmost importance to ensure high levels of availability and reliability of the generating units, particularly due to the high costs associated to system failure or an interruption in the availability of electrical power. Therefore, condition monitoring of GTs within power plants is highly desirable to guarantee the long-term safety of the units and their efficient operation [1].
For instance, a condition monitoring system can be connected in parallel to the control system for the early detection of potential abnormalities. This can allow supervisors to perform an orderly shutdown of the unit, thus avoiding unexpected stops or failures of a greater magnitude [1]. An important element of such a monitoring system is the model that is used to describe or predict the behavior of the unit. If the models are sufficiently accurate, they can be used to detect unwanted deviations from what is considered to be normal behavior. Indeed, many different physical models of GTs have been developed in the past [2]. These models capture the dynamics of the turbine, but their precision can significantly vary based on the specific unit that is used. In practice, it is not always possible to have complete mathematical models that describe all of the turbine behaviors accurately. Therefore, another alternative is to develop statistical or computational models that might provide a more accurate characterization of the behavior of such units.
Several authors have developed dynamic mathematical and computational models, as well as specialized test equipment for GTs [3]. The modeling of GTs for diagnostics and prognostics has been carried out with a variety of techniques, which can be categorized into two major groups: physics-based methods and data-driven methods. The physics-based methods are limited to the cases where failure mechanisms can be quantified [3], and require specialized personnel to aid in the modeling process as well as a detailed description of the particular system to be modeled with specific technical information from the manufacturer of the equipment, which are often not available. The data-driven methods attempt to derive the models directly from recorded system data without digging into the physics of the system, using tools derived from artificial intelligence, machine learning, statistical analysis and computational intelligence [3]. For instance, a popular approach is to use neural networks [4], [5].
This work proposes the use of genetic programming (GP) [6], [7], [8] to model a Mitsubishi single shaft Turbo-Generator, Model MS6001, with a 30 MW generation capacity. GP is a data-driven approach, a form of evolutionary algorithm (EA) [8] intended for automatic program or model induction. GP has recently gained popularity given its ability to generate syntactic models in a wide variety of problem domains [9], in many cases outperforming more common machine learning paradigms [10], [11], [12], [13] while using very little in the way of prior knowledge. While EAs have been used before in GT systems, they are mostly used for optimizing or improving system efficiency using previously derived models [14]. To the extent of our knowledge, this is the first work to address the GT modeling problem directly using a GP approach. Moreover, this work compares recent proposals in GP literature, including the fairly recent geometric semantic GP (GSGP) [15], [16] and improved variants of standard GP [17], [18]. The experimental work compares several variants of these methods, particularly emphasizing algorithms that combine the global search process provided by the basic GP paradigm with greedy local search operators. Such combinations have been shown to improve algorithm convergence and predictive accuracy [19], while also reducing model size and complexity [17], [18]. Comparisons are also made with seven non-GP modeling methods, showing that GP search outperforms all other methods in terms of predictive accuracy and model size, particularly on the most difficult modeling task.
The remainder of this paper proceeds as follows. Section 2 describes the power generation process of GTs in general and the particular unit studied in this work, describing how data was collected to apply the data-driven approach. Section 3 provides a general overview of GP, focusing on the specialized variants employed in this work and developed by the authors. The experimental work and results are presented in Section 4. Finally, conclusions and future work are outlined in Section 5.
Section snippets
Gas turbine operation and case study
This section provides a brief introduction to GTs and how they are used for power generation, as well as a detailed description of how the dataset used in this study was extracted.
Genetic programming
GP is part of the larger research area known as evolutionary computation, which deals with the development of global search and optimization algorithms that are designed based on some of the core principles of neo-Darwinian evolutionary theory [6], [7], [8]. However, the GP paradigm distinguishes itself from other EAs in several key respects. GP is intended to solve problems that can be broadly defined as automatic program induction, using a supervised learning methodology. In other words, the
Experiments
This work focuses on applying GP to model a GT unit using a data-driven approach following a supervised learning formulation. Therefore, we will use the datasets described in Section 2 to pose two symbolic regression problems and solve them with the variants of GP described in Section 3. Hereafter, we will refer to the problem of modeling the fuel flow of the GT unit as the Fuel problem, and the problem of modeling the exhaust gas temperature as the Temperature problem.
Five different algorithms
Conclusions and future work
This paper addresses the problem of modeling key aspects of a GT power system, namely the fuel flow of the system and the temperature of the exhaust gas. Both variables are critical to the proper functioning and performance of the GT power generator. In particular, this paper describes a data-driven approach to generate the models using GP, a paradigm of evolutionary computation for automatic program induction. Recent state-of-the-art variants of GP are tested. These variants integrate a
Acknowledgements
This research was partially supported by CONACYT Basic Science Research Project No. 178323, TecNM (México) Research Project 5621.15-P, as well as by FP7-Marie Curie-IRSES 2013 European Commission program with project ACoBSEC with contract No. 612689. Third and fourth authors are supported by CONACYT doctoral scholarships, Nos. 294213 and 302526, respectively. The authors also thank Ing. Sergio Ruíz González (Superintendente General) and Ing. Genero Mena Ramírez (Supervisor de Instrumentación y
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