1. Introduction
Aero-engines are core machinery systems with complex structures, high levels of integration and poor working conditions, of which the reliable and efficient operations are crucial to the flight safety of aircraft. Prognostics and health management (PHM) is an effective maintenance technique to achieve safe and reliable operations of machines and systems, and plays a significant role in the operations of aero-engines [
1,
2,
3]. Incomplete statistics showed that failures of gas path components account for more than 90% of all engine failures, 60% of the aero-engine maintenance costs are spent on gas-path components [
4]. However, due to the unique manufacturing technologies and special materials of the aero-engine, it is difficult to maintain and replace the components of engines frequently [
5]. The PHM system is capable of determining whether a gas-path component has failed and deciding whether it needs to be repaired or replaced, thus can reduce routine maintenance costs and time. Fault diagnosis and remaining useful life (RUL) estimation are research emphases of PHM.
In general, PHM approaches can be categorized into model-based methods [
6,
7] and data-driven methods [
8,
9]. Model-based methods include physical models, structural analysis, contact analysis cumulative damage models, cyclic fatigue, and crack propagation models, etc., [
10]. Obviously, they need a detailed mathematical model of the aero-engine [
11]. In addition, their reliability decreases as the system nonlinearities, complexity, and modeling uncertainties increase. Data-driven methods can be roughly divided into two categories, namely machine learning algorithms and probability models, and they do not require deep knowledge of the engine mechanism, and mostly depend on real-time or collected historical data from the engine sensors and measurements, so they have attracted considerable attention and have been developed rapidly. Commonly used data-driven methods include artificial neural network (ANN), support vector machine (SVM), k-means clustering algorithm, Bayesian method, Markov model, Gaussian distribution, etc. [
12,
13,
14,
15,
16,
17,
18].
The operation and external conditions of aero-engine change over time and, therefore, the time-varying problems, have become the main challenge. Machine learning can be used for fault diagnosis, but it is not flexible enough to deal with time-varying problems and is difficult to update as data accumulates. The traditional ANN is also known as the black box model. Its construction process does not reflect the actual operation law of the engine. In addition, it has the limitations of weak generalization ability and difficulty in dealing with time-varying problems, etc. Chen et al. [
1] proposed a new deep learning method called deep belief network (DBN) for engine fault diagnosis. Compared with the traditional back propagation (BP) model, it has been greatly improved, but its essence is still ANN, which has the above-mentioned drawbacks. Compared with ANN, the probability model has unique advantages in dealing with time-varying problems due to its solid mathematical background. The Gaussian mixture model (GMM) is a typical probability model, which can fit the fault monitoring features (FMFs) of random distribution by a combination of a finite number of Gaussian components (GCs) [
19]. Avendaño Valencia et al. [
20] proposed a stochastic framework based on the Gaussian mixture random coefficient model for structural health state monitoring under time-varying conditions, and their results showed that GMM has great flexibility in dealing with time-varying and uncertain problems. Qiu et al. [
21] proposed an enhanced dynamic Gaussian mixture model-based damage monitoring method for aircraft structural health monitoring (SHM). Fang et al. [
22] proposed a probability modeling-based aircraft structural health monitoring framework under time-varying conditions.
However, the probability model is rarely used in aero-engine PHM systems, especially the GMM model. The difficulty of applying the probability model to aero-engines lies in the data of aero-engine contain noise, which is much more complex than those of other objects such as aircraft structural analysis [
23]. In addition, the biggest disadvantage of the traditional GMM model is that the initial values have a great influence on the result, and manual selection is required. At present, the most common improvement is to use the k-means clustering algorithm [
24], but it is still unable to achieve complete self-adaptation. A new method called adaptive density peaks clustering algorithm (ADPC) can solve these problems and realize adaptive initial clustering. Another difficulty in aero-engine fault diagnosis lies in the difficulty of obtaining a large amount of failure data for an engine. Most of the engine’s life cycle is in the non-failure state, and it is a gradual process for an engine from health to failure. Therefore, it is necessary to design a dynamic model that makes full use of the normal data and can be updated as the data accumulates.
RUL estimation is another focus in the PHM framework. Data-driven approaches are typical algorithms for RUL estimation. Soualhi et al. [
25] developed a data-driven approach for bearing RUL prediction using the Hilbert–Huang transform (HHT) and the SVM. Li et al. [
26] proposed a smooth transition auto-regression model combined with the Bayesian model to estimate the RUL. Listou et al. [
27] proposed a semi-supervised learning method for RUL prediction, which reduced the amount of marker training data. However, these methods also suffer from some deficiencies. For instance, the imperfection of expert knowledge may cause the handcrafted feature to fail to effectively reflect the engine degradation, and these methods do not propose a good solution mechanism for the utilization of historical data and current data. In addition, the prediction accuracy of these methods is not optimal.
In the construction of the PHM framework, Che et al. [
1] proposed a framework combining DBN and long short-term memory neural network (LSTM) methods. In his framework, fault diagnosis and RUL estimation are not deeply linked, and health indicators are not fully utilized in RUL estimation, which makes it necessary to mine information from engine sensor data again before RUL estimation, which is not the most efficient. Li et al. [
28] proposed a framework for deriving system requirements for PHM system development to provide a solution for predicting RUL. Similarly, the framework does not consider a technical route that combines fault diagnosis with RUL estimation.
Given the above, an aero-engine PHM framework based on GMM-ADPC algorithm and LSTM network is proposed in this study. In this study, a new GMM-ADPC algorithm is proposed to construct probability distribution space of engine data. Based on the GMM-ADPC algorithm, a dynamic probability (DP) model is proposed for modeling engine fault development. This model has a solid mathematical foundation and can make full use of engine life cycle data. And principal component analysis (PCA) is used to convert complex high-dimensional raw data into low-dimensional data. For the purpose of addressing the problems with the commonly used data-driven methods, the DP + LSTM model is introduced for RUL estimation. Here, the engine fault probability distribution data constructed by the DP model is used as the input of the LSTM network, which realizes the information transmission between the two modules, avoids sensor noise interference to a certain extent, and improves the stability and accuracy of the PHM framework.
The rest of this paper proceeds as follows.
Section 2 introduces the DP model and LSTM algorithms.
Section 3 details the architecture and the realization of the framework.
Section 4 provides the validation results of the framework in NASA’s dataset. Finally, the conclusion of this work is given in
Section 5.
5. Conclusions
In this study, a PHM framework combining the DP model and LSTM model is proposed for fault diagnosis and RUL estimation of aero-engine. Firstly, the DP model consisting of a baseline probability model and a monitoring probability model is constructed, in which the baseline probability model reflects the operating characteristics of the engine’s healthy state, and the monitoring probability model reflects the failure occurrence and evolution process of the engine. A GMM-ADPC algorithm is employed for modeling engine fault development, and the PCA method is adopted to reduce the dimension of the input data. Secondly, the probability difference measuring method is used to quantify the difference between the two probability models so as to obtain the fault detection indexes. Thirdly, the DP + LSTM model is introduced for a time series prediction of fault detection indexes, so as to estimate the RUL of the engine. Finally, the PHM framework is established by integrating the aforementioned models. The experimental results on the degradation datasets obtained by the C-MAPSS indicated that the proposed DP model can capture the process of engine failure well, and the DP + LSTM model can perform RUL estimation well. By comparing the results of the proposed method with some classical methods, it is shown that the proposed method has better stability and accuracy.
To sum up, the PHM framework proposed in this study can adequately realize the functions of fault diagnosis and RUL estimation.