# Distributed Kernel Extreme Learning Machines for Aircraft Engine Failure Diagnostics
## 1 Introduction  
Aircraft engine is a mission-critical mechanical system [1] with complicated structure and poor operating conditions [2], and its stable and reliable operation is of great importance to the flight safety [3]. During its whole service life, the performance of the aircraft engine degrades gradually due to fouling [4] and corrosion [5] of blades, and the increase of tip clearance [6]. In addition, foreign or inner object damage [7] may cause sharp felling of performance. In reverse, decline of the performance would result in thrust loss of the aircraft engine, and then the fuel is required to guarantee the required thrust of the aircraft engine [8]. Thus the operating point would be closer to the surge margin and the exhaust gas temperature (EGT) would increase. Consequently, the reliability would be jeopardized by the former case and the service life would be jeopardized by the latter case. For the purpose of improving the reliability and reducing the maintenance cost, the condition-based maintenance (CBM) system is adopted to facilitate the mission scheduling [9]. Fault diagnostics and prognostics constitute two typical portions of the CBM system. Diagnostics is to detect the fault and then carry out the identification and isolation [10], and the main purpose of prognostics is to predict the aircraft engine performance after the degradation and failure [11]. Quantifiable evaluation of aircraft engine degradation is the core to the CBM system. In terms of the economic endurance, effective health assessment and reliable performance prediction are conducive to effectively cut down flight costsand improve the reliability and availability [12]. In addition, by utilizing the performance prediction technology reasonably, the aircraft engine can be restored to healthy state before failures, and thus catastrophic accidents can be avoided. The existing diagnostic methods for aircraft engine mainly include the model-based method [13; 14] and the data-driven method [15; 16]. For the model-based approach, mathematical models are usually required to assess the internal characteristics of the aircraft engine failure. However, the failure mechanism of the aircraft engine is usually extremely complex, and it is hard to establish a volumetric dynamic or thermodynamics model that can predict the health state and is applicable to the whole working condition range [17] with high reliability. In the last few years, with the fast evolution of machine learning methods and the continuous accumulation of flight cycle data, the data-driven methods have attracted more and more attention in the field of diagnostics for aircraft engine [18]. In addition, some successful developments of aircraft engine CBM system are based on data-driven methods, and a great deal of practical cases have verified that the data-driven method can improve the accuracy of engine fault diagnosis and performance prediction without additional need for internal understanding of aircraft engine [19; 20]. Common data-driven methods mainly include artificial neural networks (ANNs) [21; 22], support vector machine (SVM) [23] and statistical feature analysis [24], etc. The nonlinear mapping capabilities of neural networks are excellent, and thus the application in fault diagnosis and performance prediction for aircraft engine is developed rapidly. The general structure of neural network usually involves input layer, hidden layer and output layer [25]. The training method based on gradient is widely used in the iterative adjustment of network structure parameters, thus in the practical application, the slow learning speed is a common problem of neural networks [26]. In order to improve the training speed, extreme learning machine (ELM) is proposed to train the single hidden layer feed-forward neural networks (SLFNs), which is one of the most popular networks. Different from the traditional ANNs, ELM randomly assigns the network parameter, and then the output weight is determined analytically [27].