Hybrid PSO–SVM-based method for forecasting of the remaining useful life for aircraft engines and evaluation of its reliability
Introduction
Reliability analysis is the technical framework for the study of the system failure and quantification of its probability [1], [2]. Dependability, or reliability, describes the ability of a system or component to function under stated conditions for a specified period of time [3]. The safe and reliable operation of engineering systems such as aircraft engines is of great significance for modern energy plants, production quality, preservation of human health and life, etc [1], [2], [3], [4]. Indeed, reliability is theoretically defined as the probability of failure, the frequency of failures, or in terms of availability, a probability derived from reliability and maintainability. Maintainability, the ease with which a machine can be maintained, may be defined as a part of reliability engineering. Reliability plays a key role in cost-effectiveness of systems [4], [5].
To fix ideas, an aircraft engine is the component of the propulsion system for an aircraft that generates mechanical power. Aircraft engines are almost always either lightweight piston engines or gas turbines. The gas turbine engine is a heat engine that uses air as working fluid to provide thrust. In order to be able to do this, the air passing through the engine has to be accelerated. To obtain this increase, the pressure energy is first of all increased, followed by the addition of heat energy, before final conversion back to kinetic energy in the form of a high velocity jet efflux [6], [7]. A gas turbine engine is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. The moving part of the turbine is called rotor, which is a shaft or drum with blades attached [8], [9], [10]. Gas turbines are used to power aircraft, trains, ships, electrical generators, or even main battle tanks.
The engine diagram in Fig. 1 shows the main elements of the engine model. Additionally, Fig. 2 shows the flowchart corresponding to the simulation with its modules.
The maintenance process covers not only the work required to maintain the engine and its systems in airworthy conditions from one flight to another but also the work required to return the engine to airworthy condition in those operations in which it is required to remove it from the aircraft. Since the last decade of the previous century, predictive maintenance is a key element in any integrated maintenance system such as an aircraft engine or gas turbine. It allows to obtain a precise description of the status of the engine. In the present research the concept of remaining useful life (RUL) is defined as the number of remaining time units that the equipment has before it reaches the limit for a safe operation [12], [13].
In the last decade the importance of the statistical approach to the concept of RUL has grown. The statistical approach is a convenient method as the RUL of any device can be considered as a random variable [14] that depends on some variables that are proper of each equipment such as its age, the operation environment and the operation conditions. Although some studies have tried to predict the RUL based on time series [15], [16], nowadays it is considered to be more useful to use models based on the values of those variables that are monitored during the operation of the equipment [17], [18]. The present research also uses this approach.
The objective of this study is to evaluate the application of support vector machines (SVMs) in combination with the particle swarm optimization (PSO) technique for the calculation of a predictive model of the RUL for aircraft engines. SVM models are based on the machine learning theory and are a new class of models that can be used for predicting values from very different fields [19], [20], [21], [22]. SVMs are a set of related supervised learning methods used for classification and regression, and possess the well-known ability of being universal approximators of any multivariate function to any desired degree of accuracy. The machine learning theory and structural risk minimization are the theoretical foundations for the learning algorithms of SVMs [22], [23]. In order to carry out the optimization mechanism corresponding to the kernel optimal hyperparameters setting in the SVM training, the particle swarm optimization (PSO) technique was used here with success. The PSO technique is a population-based search algorithm based on the simulation of the bird flocking. As other evolutionary computation algorithms, PSO generates a new population of solutions to the problem in each iteration. The new members of the population incorporate information or are constructed from one or more members of the previous population depending on their fitness and thus, PSO exploits the model of social sharing of information [24], [25]. For example, there are very recent and interesting applications of the PSO technique such as the evolution of cooperation among selfish individuals in the stochastic strategy spatial prisoner’s dilemma game [26] and then reviewed in another later reference [27]. For the above-mentioned purpose, an hybrid PSO optimized SVM (PSO–SVM) model [28], [29] were used as automated learning tools, training them in order to predict remaining useful life from other parameters. According to previous researches, the SVM technique has been proved to be an effective tool to predict natural parameters, being successfully used in a wide range of fields: forest modeling [30], solar radiation estimation [31], [32], prediction of the air quality [33], study of water properties [34], identification of the preferential attachment in big data [35], state-of-charge estimation for battery management system [36], forecasting electricity consumption [37] and so on.
In summary, the present study is structured as follows: first, the materials, methods and dataset used are explained; second, the results of the hybrid PSO–SVM-based model trained are presented and discussed; and finally, the main conclusions of this research work are drawn.
Section snippets
Experimental dataset
The present research uses data corresponding to an aircraft engine of 90,000 lb thrust class. The data includes working conditions with heights from sea conditions to 40,000 ft and temperatures from −51 °C to 39 °C. The above data was obtained through a software application known as MAPSS (modular aero-propulsion system simulation) [38]. This is a simulation environment for aeronautical turbines which allows access to a range of monitoring parameters controlling the operating state of the system
Analysis of results and discussion
As it was explained before, the total number of predicting variables used to build the hybrid PSO–SVM model was 14. The output predicted variable was the remaining useful life.
SVM techniques are strongly dependent on the SVM hyperparameters: the regularization factor C (see Eqs. (4), (6)); the hyperparameterthat defines the ε-insensitive tube (allowable error); and σ that represents the kernel parameter if a radial basis function (RBF) is chosen. There exist a vast body of literature regarding
Conclusions
The proposed hybrid model accurately predicts the RUL of the turbines. Furthermore, the model performed requires no knowledge of the previous status of the aircraft engine, as it only requires information of the current situation of the same data. This model provides the advantage of system robustness against possible failures in the memory registers. As a future line of research, the authors propose the performance of models taking into account the values of the input variables at earlier time
Acknowledgements
The authors wish to acknowledge the computational support provided by the Department of Mathematics at University of Oviedo. Additionally, this paper has been funded by the Government of the Principality of Asturias through funds from the Programme of Science, Technology and Innovation (PCTI) of Asturias, co-financed by 80% within the priority Focus 1 of the Operational Programme FEDER of the Principality of Asturias 2007–2013 (Research project FC-11-PC10-19). Finally, we would like to thank
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