Chinese Journal of Aeronautics, (2024), 37(4): 93–120
Chinese Society of Aeronautics and Astronautics
& Beihang University
Chinese Journal of Aeronautics
cja@buaa.edu.cn
www.sciencedirect.com
REVIEW ARTICLE
Intelligent fault diagnosis methods toward gas
turbine: A review
Xiaofeng LIU a,*, Yingjie CHEN a, Liuqi XIONG a, Jianhua WANG b,
Chenshuang LUO a, Liming ZHANG a, Kehuan WANG a
a
b
School of Transportation Science and Engineering, Beihang University, Beijing 100191, China
Systems Engineering Research Institute, China State Shipbuilding Corporation, Beijing 100094, China
Received 27 April 2023; revised 7 June 2023; accepted 11 September 2023
Available online 28 September 2023
KEYWORDS
Fault diagnosis;
Health management;
Gas turbine;
Artificial intelligence;
Intelligent diagnosis method
Abstract Fault diagnosis plays a significant role in conducting condition-based maintenance and
health management for gas turbines (GTs) to improve reliability and reduce costs. Various diagnosis methods developed by modeling engine systems or certain components implement faults detection and diagnosis based on the measurement of systemic parameters deviations. However, these
conventional model-based methods are hindered by limitations of inability to handle the nonlinear
nature, measurement uncertainty, fault coupling and other implementing problems. Recently, the
development of artificial intelligence algorithms has provided an effective solution to the above
problems, triggering broad researches for data-driven fault diagnosis methods with better accuracy,
dynamic performance, and universality. This paper presents a systematic review of recently proposed intelligent fault diagnosis methods for GT engines, according to the classification of shallow
learning methods, deep learning methods and hybrid intelligent methods. Moreover, the principle of
typical algorithms, the evolution of enhanced methods, and the assessment of pros and cons are
summarized to conclude the present status and look forward to the future in the field of GT fault
diagnosis. Possible directions for development in method validation, information fusion, and interpretability of intelligent diagnosis methods are concluded in the end to provide insightful concepts
for scholars in related fields.
Ó 2023 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and
Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/
licenses/by-nc-nd/4.0/).
1. Introduction
* Corresponding author.
E-mail address: liuxf@buaa.edu.cn (X. LIU).
Peer review under responsibility of Editorial Committee of CJA.
Production and hosting by Elsevier
As one of the main sources of power for many industrial applications, gas turbines (GTs) play an important role in civil aircraft, commercial ships, motor vehicles, and electricity
productions. Availability and reliability are the two most desirable attributes of GTs to maintain constant operation of the
devices.1 However, due to the extreme working conditions of
high temperature and high pressure, the performance of GT
https://doi.org/10.1016/j.cja.2023.09.024
1000-9361 Ó 2023 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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X. LIU et al.
deteriorates gradually, accompanied with increased fuel consumption, polluting emissions, and insecurity risks.2,3 According to the Aviation Week’s 2021 fleet data projections, the
expense on engine maintenance, repair, and operating is about
to increase at the rate of 4.9% per year over the coming decade, reaching over $886 billion in 2030.4 In this context, a
proper and timely maintenance strategy based on accurate
fault diagnosis is an immediate need for GTs to ensure reliability and economize costs.
Generally, all the possible faults of the gas turbine can be
categorized as gas path faults, mechanical faults, sensor faults,
and auxiliary subsystems (such as electronic control system,
coupling unit, lubricating oil system, fuel system) faults. The
definitions and common faults of each type are summarized
in Table 1. Typically, any damage in a single component or
inconsistency in a set of components can increase machine
degradation. After 70 years of development and exploration,
various GT fault diagnosis methods have been developed
extensively, which can be generally divided into model-based
(MB) and data-driven (DD) methods. 5 MB methods are the
first-generation engine fault diagnosis methods, which are in
essence a mathematical procedure to model the whole engine
or certain components. Gas-path analysis (GPA) 6,7 and Kalman filter (KF) 8,9 are the two most representative MB methods. In GPA, the diagnostic problem is solved by the
establishment of mathematical relationship between the measurement parameters (such as temperature, pressure, rotor
speed, and fuel flow) and the unmeasurable performance
parameters (such as pressure ratio, flow capacity, and isentropic efficiency). According to this approach, practical experience and professional knowledge are needed to establish the
explicit mathematical and thermodynamic equations. The
thresholds of different fault types are determined by these
equations to judge whether the engine is working regularly.
However, due to the increasing nonlinearity and complexity
of engine systems, the inaccuracy and high time cost of mathematical modeling greatly hinder the development of traditional GPA methods. The introduction of KF in 196010
provides a solution for the above problem as a predictor–corrector technique. By using systematic model and observations
to estimate the real state of the system, KF methods show the
priority in precision when dealing with nonlinearity and uncertainty.11 KF methods can overcome two main limitations of
GPA, including the inability of underdetermined problem
due to the limited number of sensors and the poor robustness
Table 1
due to the measurement uncertainty.12 Optimizations and
modifications on KF have emerged endlessly to realize
onboard diagnosis in the whole flight envelope and in different
engine states.13,14 Later, the proposal of extended KF (EKF)
and unscented KF (UKF) by Simon15,16 extends the application of KF to nonlinear problem and achieved certain accomplishments.17–19 Although KF methods are widespread applied
to many actual systems, the selection of system matrix is an
experience-based prescription without systematic method
which causes uneven diagnostic accuracy. To remedy the
above defects, modified adaptive KF models optimized by
adaptively updating systemic matrix for higher numerical stability and accuracy have become an increasingly popular trend
and are successfully applied in many industrial programs.20–22
Furthermore, to solve the invalidation problem of EKF when
the parameters to be estimated are more than the measured
parameters, Liu et al.23 used model tuning parameter to optimize EKF and provided mathematical proof of convergence.
Both theoretical derivation and semi-physical experiments
proved the feasibility of the optimized EKF on gas path
diagnosis.
Recently, the development trends of engine systems
towards complexity, digitization and intellectualization have
brought new challenges to GT fault diagnosis technology.
The ever-increasing nonlinear nature, limited sensor mounting
positions, severity of simultaneous failures, and increased security requirements of GT systems make the common failings
existing in MB diagnosis methods more obvious. On the one
hand, in consideration of modeling the complex engine system,
professional technologies and engineering experience are
required to be possessed; in addition, the baseline model is
always limited to a certain engine type or a certain working
condition, causing the lack of transitivity and universality.
On the other hand, even the MB methods especially for nonlinearity problem, such as EKF and UKF, have a limited scope
for application, and the accuracy of manual modeling can
hardly meet the need for precise fault detection and prediction.
An overview of the deficiencies in MB diagnosis methods is
summarized in Fig. 1.
DD methods successfully remedy above inherent defects of
MB methods, which can automatically process operational
data to find the underlying regularity and create data-driven
models based on it for fault detection and classification.
Data-driven models can ignore engine individual difference
and lifecycle performance deterioration, endowed with higher
Possible faults in gas turbine.
Gas path fault
Mechanical faults
Sensor faults
Auxiliary subsystems faults
Damage or degradation of gas
path components, which causes the
deviation between actual state and
expected performance
Domestic object damage
Foreign object damage
Compressor/Turbine fouling
Compressor/Turbine erosion
Compressor/Turbine corrosion
Thermal distortion
Failure of mechanical parts such as
bearings, gears, and rotors, which
results in defects of vibration signals
in a specific frequency band
Rotor thermal bending
Shaft bent or bow
Angular misalignment
Crack and shaft rub
Bearing assembly looseness
Turbine disc fracture
Bias or failure of sensors,
which leads to inconsistency
in measured values of sensors
with actual parameters
Sensor hard fault
Sensor soft fault
Error or failure in the auxiliary
subsystems such as electronic
control system, coupling unit,
lubricating oil system.
Fuel control system fault
High voltage circuit fault
Low voltage circuit fault
Cooling and sealing fault
Ignition gas system fault
Coupling unit fault
Intelligent fault diagnosis methods toward gas turbine
Fig. 1
95
Deficiencies of MB diagnosis methods and advantages of AI-based diagnosis methods.
accuracy and universality. Commonly used DD methods
include expert system (ES), fuzzy logic (FL) and artificial intelligence (AI). Among all the DD methods, AI algorithms are
blessed with perfect ability of nonlinear approximation,
large-scale data processing, abstract information extraction
and have large room of development in robustness and realtime performance. As is demonstrated in Fig. 1, AI algorithms
can perfectly feed the need of GT fault diagnosis. Therefore,
the present review focuses on fault diagnosis based on AI models, which are generally categorized into intelligent fault diagnosis methods.
As shown in Fig. 2, the general procedures of AI-based
fault diagnosis for GT can be divided into two sections including model building and method implementation. Multiple
choices of different AI algorithms are existed when building
a diagnostic model. According to different data representation
hierarchy, intelligent diagnosis methods was divided into shallow learning (SL) based ones and deep learning (DL) based
ones. In the early stage of GT fault diagnosis, the most
frequently-used AI algorithms include back-propagation neural network (BPNN), extreme learning machine (ELM), and
support vector machine (SVM), which have been proved effective by abundant experiments.24,25 As natural networks keep
evolving in complexity and capability, the intelligent fault
diagnosis methods have also progressed in prediction accuracy
and real-time performance. However, the gradient diffusion
problem and explosive growth of parameters make it nearly
untrainable for generally shallow networks such as BPNN to
achieve deep architectures with more than five layers.26 The
training problem of multilayer networks remain unsolved until
Hinton and Salakhutdinov27 presented the concept of deep
learning in 2006.
Different from the simple superposition of hidden layers,
DL is considered as a novel algorithm framework for network
training by adopting weight sharing and local connection technology.28 In fault diagnosis, DL models have presented broad
prospects because of the automatic and advanced feature
extraction ability. Zhao et al.29 proposed a multi-branch
CNN model with an integrated cross-entropy for fault diagnosis of diesel engine system. Verified by the original operating
data collected by the TBD234 diesel engine test bench, the
proposed method achieved the minimum accuracy of 99%
for each fault mode while the accuracy of multilayer perceptron was only 77% on average. The underlying reason of
the excellent performance of the multi-branch CNN was then
revealed by an additional visualization experiment as the
extraction of effective fault features, which demonstrated the
performance variation between DL and multilayer network.
Typical DL algorithms include initially-presented DL model
called deep belief network (DBN), extensively-used convolutional neural network (CNN) and newly-developed recurrent
neural network (RNN). Relatively, networks which are commonly with a few layers such as BPNN, ELM and SVM are
categorized as SL models. However, due to the domain specificity of GT fault diagnosis, high cost of experiment and data
privacy aggravate the problem of data deficiencies. Low tolerance of error diagnosis obstructs the application of most single
intelligent diagnosis methods with inexplicability. Therefore,
the potential of hybrid intelligent methods for fault diagnosis
have been extensively investigated recently to improve the
diagnosis accuracy, the real-time performance, and the
interpretability.
Based on the above analysis and the reference of previous
reviews,11,24 a generalized comparison of typical fault diagnosis methods is presented in Table 2 to facilitate the cognition of
necessity to review the intelligent fault diagnosis methods for
future development. It is worth noting that the hierarchy in
the table is an average evaluation of a certain type, while each
type of methods has multiple variants with flexible performance assessment depending on the circumstances.
In conclusion, DD fault diagnosis methods have compensated for the lack of accuracy and universality of traditional
MB methods, becoming a hotspot of current researches. By
virtue of high reliability, great efficiency, perfect adaptability,
and strong robustness, AI algorithms provide a solid theoretical support to further improve the accuracy and dynamic performance of fault diagnosis. This review puts high emphasis on
the efforts in intelligent fault diagnosis methods towards GT
engine system, not limited to a specific fault type. The rest of
this review is organized as displayed in Fig. 3. According to
the evolution in complexity and capability, intelligent fault
diagnosis methods are divided into shallow learning methods,
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Fig. 2
Table 2
Performance indicators of different optimized support vector machine models.
Methods
MB
methods
GPA
KF
DD
methods
Methods
MB
methods
ES
FL
AI
GPA
KF
DD
methods
Schematics of general AI-based GT fault diagnostic procedures.11
ES
FL
AI
LGPA
NLGPA
LKF
NLKF
SL
DL
LGPA
NLGPA
LKF
NLKF
SL
DL
Professional
knowledge
Data preprocessing
Nonlinear
processing
Robustness under
noise/bias
Underestimation
problem
Needed
Needed
Needed
Needed
Needed
Needed
Needless
Needless
Model complexity
Low
Medium
Fairly Low
Medium
High
High
High
Fairly High
Yes
Yes
Yes
Yes
Yes
Yes
Partial
No
Diagnosis accuracy
Low
Low
Low
Medium
Medium
Low
High
Fairly high
Not favorable
Yes
Not favorable
Yes
Yes
Yes
Yes
Yes
Real-time performance
Offline
Offline
Online
Online
Offline
Offline
Partial
Offline
Low
Low
High
High
High
High
High
High
Repeatability
High
High
High
High
Low
Low
Low
Medium
Not favorable
Not favorable
Partial
Partial
Yes
Yes
Yes
Yes
Interpretability
Yes
Yes
Yes
Yes
Yes
Yes
No
No
Note: LGPA for linear GPA, NLGPA for nonlinear GPA, LKF for linear KF, NLKF for nonlinear KF.
deep learning methods, and hybrid intelligent methods, with
more specific algorithm examples of each group. A comprehensive survey of these methods including their strengths and
weaknesses is presented hereafter. Furthermore, research
emphases for optimization are summarized to indicate the
enhanced directions for each algorithm. Finally, the above discussions are concluded and possible research directions are
provided to inspire more researches in the related fields.
Intelligent fault diagnosis methods toward gas turbine
Fig. 3
97
Structure of this review.
2. Shallow learning methods
As a new and interdisciplinary science, AI algorithms have
been widely used in various spheres such as data analysis, pattern recognition, intelligent healthcare, automatic engineering,
and human behavior analysis.30–33 Fueled by the everincreasing amount of machinery data and the rapid progress
of analytics techniques, AI-based methods bring a paradigm
shift to engine health management (EHM) by realizing fault
diagnosis through learning from historical and operational
data.34 Due to the excellent capacity to handle the nonlinear
nature and the measurement uncertainty, fault diagnosis methods based on neural networks including BPNN, ELM and
SVM outperform traditional MB methods in diagnosis efficiency and accuracy. As is summarized in Table 3,36–43 each
algorithm has its advantages and limitations, and is always
combined or hybridized with optimization methods to further
improve classification accuracy and reduce computational
time.35
2.1. Back-propagation neural network
BPNN is a multilayer feedforward neural network, which usually includes one input layer, single or multiple hidden layers,
and one output layer. As depicted in Fig. 4, the input layer
receives raw data, the output layer outputs the final result,
and every neuron of the previous layer is conjunct with all
the other neurons of the latter layer. Information is transmitted from neurons in the previous layers to that of the next layers by forward propagation, while BPNN learns by
backpropagating errors based on residual learning mechanism.44 Mathematical theory proves that a three-layer neural
network can approximate any nonlinear continuous function
with arbitrary precision,36 thus the multilayer BPNN is blessed
with powerful nonlinear mapping capability and is appropriate
to disposing nonlinear problems with complex internal mechanism of GT engine system.
However, due to the local learning gradient descent technique, BPNN is prone to local minimum problem. Therefore,
the calculation of systemic parameters including neutral
weights, threshold value, learning rate, and topology structure
is of great significance, the improper selection of which may
induce slow convergence and even network stagnancy of
BPNN.46,47.
For decades, researches have focused on searching for optimization algorithms to remedy the limitation of local overfitting and slow convergence of BPNN.37 By virtue of the
advantage of global search, genetic algorithm (GA) has
become the most widely used optimization algorithm to reconstruct the BPNN model with optimal weight and threshold
value.48 The GA-optimized BPNN model is greatly improved
in stability, generalization, and convergence rate, which is
widely used for fault diagnosis of automobile engines,49–52
high-pressure common rail system,53 aero-engines, and liquid
rocket engines.54,55 Ling and Niu51 observed by the compara-
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Table 3
BPNN
ELM
SVM
X. LIU et al.
Summary for fault diagnosis methods based shallow learning models.36–43
Advantages
Limitations
Optimization directions
Simple structure
Strong ability to handle nonlinear
problems36
Better generalization ability
Lower computation without iteratively tuning38
Capable for online learning38
Local minimum and slow convergence due to gradient
descent algorithm37
Overfitting problem
Performance fluctuation due to random hidden
nodes39
Incapable to deal with imbalance data40
Lack of theoretical justification for randomness38
Optimal set
parameters
Solid theoretical foundation
Distinct advantage under small
sample cases41,42
Strong robustness43
High computation and memories occupied on large
sample41
Poor at multi-class problems43
Fig. 4
of
system
The appropriate number of
hidden nodes
Optimal set of system
parameters
Remedy hard margin flaw
Optimal choice of kernel
function
Optimal set of system
parameters
General structure of back-propagation neural network.45
tive experiment that the absolute error of the primordial
BPNN algorithm was 0.5976, while that of the GAoptimized BPNN algorithm was 0.1027, showing a high level
of consistency with the 19.04% increased average accuracy in
the work of Liu and Zhang.52 The overall fault diagnosis correct rate of 98.3% in Xie et al.49 was also consistent with that
of Li et al.53. However, in practical applications, GA is limited
by the universal problem as a heuristic search algorithm, such
as premature convergence, long training time, and low search-
ing efficiency.54 To overcome the above problems, Xu et al.54
proposed a novel optimization algorithm by integrating the
concept of quantum computation into GA algorithm. The
improved quantum GA was used to optimize the structure of
BPNN from multiple spots and showed the improved accuracy
and efficiency when applied to fault detection.55
Similar to the GA algorithm, particle swarm optimization
(PSO) is a global optimal algorithm motivated by the simulation of simplified social behavior of animals, developed by
Intelligent fault diagnosis methods toward gas turbine
Kennedy and Eberhart56 in the late 1990s. PSO leaves out the
inheritance operation such as cross and variation, which is
much easier in implementation with fewer parameters to adjust
compared to GA algorithm. Experiments have shown a strong
ability of nonlinear fitness of PSO-optimized BPNN.37,57 In
engine fault diagnosis, Li58 compared three different fault
diagnosis methods respectively based on SVM, random forest,
and PSO-optimized BPNN. Fig. 5 and Fig. 6 respectively display the comparative results of the recognition performance
and the average time consumption of the above three diagnosis
models based on two kinds of database. They got 500 normal
data and 800 fault data samples from AVIC Civil Aircraft
Maintenance Co., Ltd. Before testing the field-collected data
with three algorithms, a preliminary verification was conducted on the artificial fault data created by adding interference to normal operating data. Both artificial and field data
showed that the PSO-optimized BPNN took the highest diagnosis accuracy as well as the least operation time among the
three. However, owing to the high complexity and coupling
of the engine system, the convergence of PSO becomes worse
and it is easy to make false judgment with only one population.
Therefore, a modified multi-swarm cooperative PSO
(MCPSO)59 turns out to be a better option for fault diagnosis.
Xiao et al.45 utilized a competitive MCPSO (COM-MCPSO)
to optimize the node weights and network topology of BPNN
and applied the optimized BPNN under five different fault
conditions. It proved the superiority of the optimized BPNN
in training speed, generalization ability, and recognition
accuracy.
99
Fig. 6 The average time consumption of three algorithms for
fault data identification.56
2.2. Extreme learning machine
Fig. 7
ELM is a single-hidden layer feedforward neural network with
one input layer, one hidden layer, and one output layer.60
Fig. 7 represents the typical architecture of ELM. Weights of
connection nodes between layers and threshold of the hidden
layer are set randomly with no need for adjustment after setting. Furthermore, the network weighs are generated by calculation rather than multiple iterations. Thus, ELM can reduce
computational complexity while enhancing generalization performance, overcoming the high training time consumption and
overfitting problem of conventional neural networks.38 Its
real-time capability provides a powerful solution for online
fault diagnosis for GTs.
Fig. 5
Typical architecture of extreme learning machine.39
Recent studies have proposed different optimization methods to further improve computational efficiency, including
optimal set of system parameters and appropriate number of
hidden nodes. ELM generates hidden nodes randomly by
employing all training samples to avoid performance fluctuations caused by randomly assigning weights.39 However, excessive nodes can lead to structural redundancy in turn, which
will jeopardize the real-time performance. Therefore, optimizing the number of hidden nodes to simplify network structure
is one of the most critical optimal objects. Yang et al.61 utilized
quantum behaved PSO (Q-PSO) to search for the optimal set
Recognition performance of three diagnosis models for artificial and real data set.56
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of network parameters and the number of hidden nodes
according to the root mean square error on validation data
set and the norm of output weights. Analogously, Pang et al.62
used the same approach to optimize the multi-hidden-layer
ELM. The effectiveness of the proposed optimizer was validated by the application on aero-engine for gas path component fault diagnosis.
Kernel-based ELM (K-ELM) combines ELM with kernel
functions to achieve better generalization capability with less
systemic parameters to regulate. However, the improvement
in classification performance is at the expense of sparsity,
which contributes to the linear growth in model scale when
the sample size increases. Merely optimizing the hidden nodes
number at the beginning of network construction can hardly
meet the need for K-ELM. Therefore, researches adopt a novel
approach to resolve redundancy by pruning the relatively
insignificant nodes of the network. To quantify the degree of
importance of the nodes, You et al.63 chose samples that contribute more to the output to constitute a kernel dictionary in
place of the whole training set, while Li and Zhao39 introduced
a special norm to reformulate the dual optimization problem
of K-ELM and neglected redundant nodes with small weights.
Both methods simplified the model structure by pruning the
relatively insignificant nodes, thus highly reducing the computational complexity. Li and Zhao39 further collected 11,488
simulation data across the whole flight envelope to test the performance of K-ELM with sparse structure. The proportion of
training samples were specially set as 5% to restore the real
diagnosis scenario of aero-engine where fault data is difficult
to obtain. The proposed method was proved capable especially
for monitoring system with limited onboard storage but relatively high real-time performance requirements.
In addition to optimizing the ELM by compacting its structure, good dynamic performance of the network is of equal
importance to meet instantaneity requirement for online detection of GTs. On the one hand, online fault diagnosis always
faces the dilemma that sequentially input data usually contains
a time-varying validity and the inoperative data can impair the
Fig. 8
subsequent training effect significantly. Thus, Liang et al.64
proposed an online sequential ELM (OS-ELM) by incorporating online learning algorithm with ELM to handle the sequential data in a chunk-by-chunk learning pattern. And to further
improve the time efficiency of the onboard fault diagnosis
based on ELM, Lu et al.65 optimized the OS-ELM with the
introduction of memory principle to better fit the timing characteristics of input data. The comparison experiments showed
a decrease in false alarm rate of proposed method for seven
different fault modes of aircraft engine system after taking
timeliness characteristic into consideration. On the other hand,
to improve the adaptivity and robustness of ELM, Lu at al.66
innovatively developed a restricted Boltzmann (RB) strategy
to learn topological parameters in different layers and then
to recursively tune the weights between input neurons and hidden neurons of ELM. As presented in Fig. 8, the topological
architecture of proposed RB-based ELM (RB-ELM) can be
divided in two parts, where the RB strategy practically acts
as a feature extractor to map the input dataset into hidden feature space. The proposed RB-ELM was applied to gas path
fault diagnosis for a turbofan engine under three different
noise levels. The experimental results in Fig. 9 proved that
the proposed model had better accuracy and stability compared with conventional ELM model.
Hard margin flaw is another common problem of ELM
that can lead to inconsistency between its constraint condition
and decision function as a result of the omission of sample
while training.67 This problem could be overcome by setting
a soft target margin for each training sample, which was
known as a soft ELM (S-ELM) in the study of Zhao et al.68.
This method was then applied to one-class ELM (OC-ELM)
by Zhao and Huang67 and its improvement in robustness
and accuracy showed more suitable in the low signal-to-noise
ratio fault detection conditions. In particular, Zhao and
Chen69 introduced the idea of transfer learning to transplant
the learned knowledge in related fields into target field for auxiliary training, to tackle the data deficiency and expiration
when applying ELM to GT fault diagnosis.
Topological architecture of proposed RB-ELM algorithm.66
Intelligent fault diagnosis methods toward gas turbine
Fig. 9
Classification accuracy of fault diagnosis of RB-ELM.66
2.3. Support vector machine
As the most representative technology in statistical learning
theory, SVM has become exceedingly popular in nonlinear
classification, function approximation, pattern recognition,
and other domains, getting rid of the inherent problems in
training pattern of constructing neural networks from the perspective of bionics. As shown in Fig. 10, the basic principle of
SVM is to search for an optimal separating hyperplane with
maximum spacing between different sample types70. The major
advantage of SVM is the classification ability under an inadequate database. Specifically speaking, most DD methods
highly depend on the large quantity of training data, while
the fault database always suffers from incompleteness and is
Fig. 10
101
Basic principle of support vector machine70
usually not allowed to share because of commercial security.
Under the circumstances, SVMs provide an ideal solution for
fault diagnosis as they distinctively afford balanced predictive
performance when sample sizes are limited, and their relative
simplicity can lower the risks of overfitting even dealing with
high-dimensional data.
As one of the earlier data-driven methods, SVM was originally adopted to classify the residuals automatically for fault
diagnosis.71 First, a data set needs to be built by collecting
the difference between the actual state of GT and the estimated
healthy condition data. Then SVM is trained and detects faults
of different modes, without exploration for physical properties
of GT system. In a comparison experiment of traditional
machine learning and deep learning classification algorithms
conducted by Wang et al.41, SVM was proved to have a higher
accuracy of 0.86 under a small sample COREL1000 dataset,
compared with 0.83 of CNN. The same conclusion was
reached in study of Yu et al.42 by using different AI algorithms
for wind turbine fault diagnosis. As shown in Fig. 11, the diagnostic performance of SVM was proved to distinctly exceed
most of artificial neural networks such as BPNN, probabilistic
neural network (PNN) and generalized regression neural network (GRNN), especially when the fault dataset was deficient
and unprocessed.
Linear separability of input data is the prerequisites for
conventional linear SVM. However, in view of the complexity
and randomness of fault data, kernel functions are needed to
map the input data to high dimensional feature space for linear
classification. Fig. 12 depicts the transforming mechanism of
kernel function. Linear kernels,72 radial basis function (RBF)
or gaussian kernels,73,74 and polynomial kernels75 are the most
widely studied types in recent years. Extensive researches have
indicated that linear kernels are computationally efficient but
with limited applications; RBF kernels are local feature sensitive but with weak generalization capability; polynomial kernels, inversely, is blessed with strong generalization ability
102
X. LIU et al.
Fig. 11
Comparison of different diagnostic approaches on small sample of source data.42
Fig. 12
Transforming mechanism of kernel function.70
while have difficulty in local feature extraction.70 A summary
for the advantages and limitations of different kernel functions
are shown in Table 4. It can be concluded that SVM based on
a single kernel has its advantages and disadvantages. Therefore, multi-kernels SVM76,77 and mixed-kernels SVM78 have
been developed to aggregate multiple merits of different kernel
types, representing good prospects for future development of
SVM.
No matter which kernel is applied, the selection of kernel
function parameters of SVM is an important factor affecting
the accuracy of classification. As is mentioned above, the
heuristic global optimization capability of PSO can effectively
avoid long training time and slow convergence speed of the
neutral networks. Therefore, PSO is also widely applied to
parameters optimization of SVM and is proved effective to
increase the diagnostic accuracy of common fault modes of
engine system.79,80 Apart from common optimization algorithms such as GA and PSO, Wumaier et al.81 optimized
SVM model with a newly proposed sparrow search algorithm
(SSA) to search for an optimal set of penalty factor and kernel
function parameter. Field data were collected continuously for
a whole year via supervisory control and data acquisition
(SCADA) systems of a wind farm. A random forest was used
for dimension reduction and 29 feature quantities of higher
importance were extracted for SVM models to train. Comparison experiment results of different optimized SVM models for
wind turbine fault diagnosis are shown in Fig. 13 and Table 5,
illustrated by evaluation index including confusion matrices,
Intelligent fault diagnosis methods toward gas turbine
Table 4
103
Summary for commonly used kernel functions.
Linear
kernels
RBF
kernels
Polynomial
kernels
Mathematical formula
Advantages
Limitation
C
Simplest without parameters to tune.
The value of the constant C is of a
wide range.
The effect of linear kernel is equal to algorithms without a kernel function.
The optimal value of C is tried by
experiments.
Improper parameter easily results in overfitting problem.
Low computing efficiency.
Multiple parameters to adjust.
It fails to handle new/unknown data and has
a high testing error.
kx x k2
K xi ; xj ¼ exp i2r2 j r
represents standard deviation
d
K xi ; xj ¼ xi ; xj d P 1 is
manually selected parameter
Fig. 13
Simple with only one parameter.
The decision boundary can be
flexible.
It has strong generalization ability to
fit training data.
The power of number can be subjectively set based on demand.
Confusion matrices of different optimized SVM models.81
precision, recall, F1-score and accuracy. It can be found that
the SSA-optimized SVM model ranked the first in convergence
speed and diagnosis accuracy among conventional SVM, GA-
optimized SVM and PSO-optimized SVM models. The accuracy of 99.2% proved the effectiveness of SSA-optimized
SVM in fault diagnosis task of industrial applications.
104
Table 5
X. LIU et al.
Performance indicators of different optimized SVM models.81
Evaluation metrics
Diagnosis model
SVM
GA-SVM
PSO-SVM
SSA-SVM
Precision (%)
Recall (%)
F1-score (%)
Accuracy (%)
93.98
96.23
98.03
99.20
92.50
95.50
97.78
99.16
92.36
95.48
97.76
99.15
92.50
95.60
97.80
99.20
Due to the harsh working condition of engine system, the
measurement signals usually contain nonstationary, nonlinearity, and complexity properties, which may damage the accuracy of classification. Therefore, preprocessing is necessary
for feature enhancement of input data. The implementation
of dimension reduction methodology provides an effective
method for better fault diagnosis. This technology includes
methods such as linear discriminant analysis,82 principal component analysis (PCA)83,84 and other popular learning methods.85 PCA can convert multidimensional correlated variable
into low-dimensional independent eigenvector, thus accelerating fault diagnosis tasks.86 However, Liu et al.87 pointed out
that performing linear methods on nonlinear data may leave
out the distribution rules between the data and yield poor features results. To better capture nonlinear features when reducing the dimension, Bai et al.88 utilized stacked sparse
autoencoder (SSAE) to realize high-dimension data feature
extraction before applying SVM for fault diagnosis of a diesel
engine. The SSAE can remove the nonlinear correlation in the
high-dimension data while retaining the original features in the
low-dimension output data for SVM training. The successful
application of the proposed method in preset fault experiments
have inspired a deeper exploration for the fusion of data preprocessing technique with shallow learning fault diagnosis
methods.
The application details of SL methods for GT fault diagnosis are summarized in Table 639,42,45,49,58,61-63,66,80,81,88,89.
3. Deep learning methods
Data representation hierarchy is the standard of the taxonomy
of shallow learning and deep learning.26 In contrast to SL, DL
can learn more complex feature hierarchies of high-level data
representations through multiple layers of nonlinear information processing. An adequate investigation of recently published researches reflects an implementation habit that
shallow models are always accompanied by data preprocessing methods for dimension reduction or feature
enhancement. Although the gap of feature processing ability
between SL and DL has been partly compensated with the
advancement of data pre-processing methods and optimization
algorithms, it should be mentioned that the need for professional knowledge and time cost still exist during the selection
of optimal methods and efforts to match each other. Also, feature extraction and intelligent diagnosis in the optimized shallow models are treated separately, which fails to improve the
performance of classifiers essentially. In contrast, the end-toend feature learning module of DL models can integrate data
preprocessing and modes classification as a whole, eliminating
the error of manual feature extraction. In this context, DL
methods can result in better abstractions of the original data
for subsequent classifications with higher accuracy and robustness, which have become the mainstream among intelligent
diagnosis methods.
3.1. Deep belief network
The initial proposal of DBN model with a pre-training and
fine-tuning learning algorithm by Hinton27 in 2006 has become
the main framework of DL techniques. A DBN model employs
a hierarchical structure of several restricted Boltzmann machines (RBMs), as shown in Fig. 14.90 RBMs are connected in
series where the hidden layer of the previous RBM acts as
the visible layer of the successive one. DBN is trained with a
layer-by-layer unsupervised learning algorithm, with every
RBM trained independently to achieve optimal feature vector
mapping. The backpropagation algorithm is used to continuously fine-tuning the entire DBN model for global optimality.
Guo et al.91 applied DBN to engine system fault classification and established a reasonable simulation experiment to
analyzed the performance. The results showed that even without artificial feature extraction, the accuracy of DBN-based
diagnosis methods can reach 96.6%, which was higher than
SL methods such as BPNN and SVM. Meanwhile, a contrast
test group was set by applying PCA and relevance analysis for
feature extraction. Compared with the original classifiers,
BPNN and SVM showed a sharp rise in accuracy while performance of DBN surprisingly fell. Researchers attributed the
reason of degradation to the information loss because of artificial feature extraction. The comparison results perfectly
proved the effectiveness of DL models in automatic feature
extraction. Xu et al.92 designed orthogonal tests to optimize
the hyper-parameters of DBN including the number of hidden
layer nodes and learning rate. The optimized DBN model was
used to detect gas path faults of a turbofan engine model. The
same conclusion was reached by comparing DBN with BPNN
and SVM, as shown in Fig. 15, which demonstrates the superiority of the DBN model in fault diagnosis.
Although few studies have been published on the application for GT fault diagnosis, DBNs have shown great success
in other engineering fields for fault diagnosis, for example,
fault diagnosis systems of the deep-sea human occupied vehicle,93 industrial robots,94 fuel cell stacks95 and other universal
bearing systems.96 These experiments have proved the feasibility of DBN-based methods and provide a reference for GT
fault diagnosis. Additionally, the information fusion strategy
of multi-sensor health diagnosis methodology93 to match the
multilayer structure of the DBN model also indicates promising prospects for the application on GT engine systems.
Intelligent fault diagnosis methods toward gas turbine
Table 6
105
Applications of shallow learning methods for GT fault diagnosis.
Technique
Database
Application
Diagnosis effect
GA optimized BPNN49
Real-time operating data on the built test
platform of South Korea Hyundai fault test
vehicle
Fault data from AVIC Civil Aircraft
Maintenance Co., Ltd. and simulation
experiment of Airbus 340–300 (engine type:
CFM56-5C)
Real-time operating data of Weichai WP6
engine based on CAN bus
Simulated component fault data based on
fault injection technique of a two-shaft
turbine fan engine
Simulated component fault data based on
fault injection technique of a two-shaft
turbine fan engine
Fault diagnosis by mixed-using
engine’s sensors data flow and
exhaust emissions information
Fault diagnosis based on filed
data with larger dispersion
degree in data characteristics
Accuracy of 98.33%
Fault detection between ’00 and
’10 digital data of diesel engines
Single and multiple fault
diagnosis with fewer input
parameters
Efficient and robust fault
diagnosis in need of enough
and adequate engine
performance data
Fault diagnosis of an aircraft
turbofan engine with high
accuracy and real-time
performance
Fault diagnosis of a dual-shaft
turbofan engine
Accuracy of 94.84%
Low-dimension engineering
problem like engine gas path
fault diagnosis in flight
envelope
Effective fault diagnosis of
wind power when the sample
size is insufficient
Better diagnostic stability
and accuracy at most
operations compared to
original ELM
Preprocessed datasets
improve the classification
accuracy of ELM with zero
error
Accuracy of 98.8%
PSO optimized BPNN58
COM-MCPSO optimized
BPNN45
Q-PSO optimized ELM61
Q-PSO optimized multihidden-layer ELM62
Recursive reduced K-ELM63
Simulated data by injecting 10 component
fault patterns to the areo-engine model
Group reduced K-ELM39
Simulated component fault data of 5 modes
across the whole flight envelope based on
fault injection technique
Simulated fault data based on fault injection
technique of turbofan engine at three flight
operations
RB-ELM for fault
recognition combined with
Relief-F fault feature
extraction66
ELM fault diagnosis method
based on virtual expansion
and spherical mapping
model42
PSO optimized SVM80
SSA-optimized SVM81
SSAE for data dimension
reduction combined with
optimized SVM for fault
diagnosis88
Simulation data from a fault simulation
experiment platform for the drive system of a
wind turbine in Ref. 89
Simulated control system fault data based on
fault injection methods of 5 fault states with
80 sets of data in each state
SCADA data consisting of 61 features of a
wind farm in Inner Mongolia for 365
consecutive days
Collecting data on a built data acquisition
system under 6 preset failure modes of diesel
engine
3.2. Convolutional neural network
The DBN-based fault diagnosis methods can eliminate the step
of dimension reduction, however, signal preprocessing is still
needed.97 Novel fault diagnosis schemes based on CNN, which
integrate feature extraction and fault classification without the
need for exploring the intrinsic mechanism of industrial system, can avoid information loss caused by data preprocessing.98 The concept of CNN was initially proposed by Lecun
et al.99 in 1998. Typical CNN usually includes input layer, convolution layers, pooling layers, fully connected layer, and output layer, as illustrated in Fig. 16. The input layer can
preprocess the raw data for normalization and whitening.
The preprocessed data are then passed to the convolution layer
for convolution operations with convolution kernels to obtain
the corresponding characteristics. The activation layer, also
called the nonlinear layer, can perform nonlinear transforma-
Control system fault diagnosis
of the German 3 W piston
engine with small samples
Troubleshooting wind turbines
Effective engine fault diagnosis
when employing fewer sensors
and eigenvalues
Accuracy of 98.3%
The highest accuracy in most
cases compared with original
ELM and BPNN
Less training time than DBN
and high accuracy of 98.3%
Average recognition rate of
94.03%
Better real-time performance
with maintaining accuracy
Accuracy of 99.2%
Accuracy of 100% under
optimal sensors set
tion on the output of each convolution layer to accelerate the
convergence of the network. A pooling layer is commonly
added after a batch normalization layer in the CNN architecture to reduce the number of systemic parameters. In the fully
connected layer, all the local features are combined into a global one with a final score of each category. Through a backpropagation learning algorithm, the CNN model can
automatically grab the feature from input data and adaptively
learn the spatial hierarchies of features to realize highprecision classification.
Present researches mostly apply CNNs to learn features
from two-dimensional images, solving the problems in image
processing and pattern recognition areas. However, these
widely used two-dimensional CNNs (2D CNNs) fail to identify
one-dimensional sensor data directly, which is the most commonly used data format in industrial fields. To implement
2D CNNs in fault diagnosis, Zhang et al.100 proposed a
106
X. LIU et al.
Fig. 14
Hierarchical structure of deep belief network.90
Fig. 15 Comparison of the prediction results of DBN with SL
models.92
Fig. 16
method of converting raw signals into two-dimensional images
and then used CNN model to extract the feature from the converted images, eliminating the impact of specialized knowledge
on the feature extraction process. Fig. 17 presents the complete
flow scheme for the above framework. Similarly, to convert the
one dimensional problem in signal processing into a two
dimensional image recognition task, Guo et al.101 used the
continuous wavelet transform (WT) to abstract characteristics
from seven common health condition signals to form scalograms, followed by a CNN model for feature extraction. The
proposed method can extract essential time–frequency features
and reached a diagnosis accuracy of 97% on a certain aircraft
engine. With the growing volume of industrial data and
increasingly strict requirement for real-time performance, these
data conversion methods have been phased out because of
high computing time and resources footprint.102,103 Onedimensional CNN (1D CNN) with lower model complexity
General architecture of convolutional neural network.
Intelligent fault diagnosis methods toward gas turbine
Fig. 17
107
Process of use 2D CNN for fault diagnosis.100
and better dynamic property has been proposed to process signal data directly, which has been proved effective and efficient
in fault diagnosis domain.104–108 Fig. 18 exhibits an example of
the full architecture of one-dimensional convolutional long
short-term memory network (LSTM),104 which is the combination of CNN with LSTM model. 1D CNN extracts feature
of input vibration data through the 1D convolution in each
segment. As shown in the subgraph named temporal convention, based on weight sharing technique, the convolution kernel slides across the entire input sequence Xðx1 ; x2 ; x3 ; :::; xn Þ
with a fixed step to achieve all feature vectors of the i-th layer
Fðfi1 ; fi2 ; fi3 ; :::; fiðn2Þ Þ. By stacking the basic network structure of conventional layer and polling layer, abundant and
complex features can be extracted for fault diagnosis. Combined with adaptive dropout and RNN technology, the proposed model reached an accuracy of 99.08% for engine
diagnosis under multi-factor operation conditions. Besides,
this DL method was also proved to have strong generalizability when implemented to different type of engines, showing the
potential to be used as initializer for similar tasks of transfer
learning.
On account of the extreme and volatile working environments, the performance of GT system fluctuates a lot. Differ-
ent fault modes turn to occur simultaneously with strong
coupling among each other, bringing great challenges for reliable fault diagnosis of GTs. Pacheco et al.109 used multiple
Bayesian processes to search for a best set of architecture
parameters and hyperparameters of CNN which can minimize
the loss function related to their transferability between different machines under different operating conditions, thus
improving the hybrid fault diagnosis capability of the unitary
model. An integrated CNN model proposed by Du et al.110
used multiple convolution kernels of different sizes to fully
extract redundant analytical information between sensors,
realizing detection of multiple faults in complex engine sensor
system. Similar to the ensemble learning idea of random forest
(RF), Wang et al.111 built a random CNN (RCNN) model
with several individual CNNs extracting discriminative features of vibration signals individually, as shown in Fig. 19.
The final diagnosis is a fusion of all individual CNNs based
on a combinational rule. Datasets were collected from a 4 S
high-speed diesel engine under 5 different working conditions
to verify the effectiveness. To offer a fairer comparison
between RCNN and commonly-used shallow classifiers such
as SVM, BPNN and RF, a representative and effective dimensionality reduction method of t-distributed stochastic neighbor
108
X. LIU et al.
Fig. 18
Full architecture of one-dimensional convolutional long short-term network.104
Fig. 19
Architecture of random CNN model.111
embedding (TSNE) was utilized to generate contrast group. As
shown in Fig. 20, the SVM, BPNN and RF using raw vibration signals have a low F1 scores of 49.6%, 48.3% and
52.8%. Although the application of TSNE can multiply the
diagnosis performance of these shallow models, the final detection rates of 88.5%, 86.7% and 91.7% are unacceptable in precise and strict engine diagnosis. On the contract, the proposed
RCNN without data preprocessing can reach a highest F1
score of 99.6% with a testing time of 0.93 second. The strong
stability, real-time capability and high accuracy of the proposed RCNN provided an optimal choice for the online health
monitoring of diesel engines.
As exhibited in Fig. 21,112 the evolution of the CNN model
has gone through two stages. The first stage is to improve
Fig. 20 Comparison of the average values of F1-score for
different health monitoring schemes.111
Intelligent fault diagnosis methods toward gas turbine
Fig. 21
109
Evolution of convolutional neural network model.112
classification accuracy by deepening the layers displayed in
right-side branch. For example, as residual neural network
(ResNet) is extended from 50 layers to 152 layers and 200 layers, accuracy shows an increasing trend as layers are added.113
However, the increase in the number of layers always results in
a decrease in computing efficiency. Therefore, the second stage
is to explore the way of designing lighter-weight and more efficient CNN models, which can be better implemented on the
hardware processors. The main contributions in lightweight
model are listed in the left-side branch. This two-stage evolution of CNN is consistent with the desirable need for GT fault
diagnosis. It can be anticipated in the near future, that CNNbased fault diagnosis methods can achieve better diagnostic
accuracy and real-time performance, providing an option for
online fault diagnosis systems.
3.3. Recurrent neural network
Widely used as CNN model, it remains the conventional connection from input layer to hidden layer and then to output
layer without connection between nodes in the same layer.
Therefore, CNN fails to process the successive input data,
Fig. 22
which is the main form in the field of GT fault diagnosis, that
is, time series with strong temporal correlation. Elman114
developed simple recurrent network in 1990, providing a novel
network with a dynamic memory to process highly contextdependent data. A simple three-layer structure of RNN is
depicted in Fig. 22, including one input layer, one hidden layer,
and one output layer. It is worth highlighting that the output
of the hidden layer at current time depends on the output at
previous moment, implementing an intra-layer connection
mode. In 1997, Hochreiter and Schmidhuber115 proposed long
short-term memory to solve the vanishing gradient problem of
RNN by replacing the neural nodes with LSTM units for a
wider range of data preservation and transmission. At present,
RNN based on LSTM is continuously gaining popularity in
language modeling, machine translation, automatic speech
recognition, and industrial large-scale data processing.
Xue et al.116 conducted a comparison experiment of fault
diagnosis method based on RNN with that based on BPNN
and SVM. The hardware-in-the-loop testing validated the relatively higher diagnostic accuracy of RNN due to excavation
of deeper information in fault signals. Also, RNN was proved
to perform well in detecting weak fault signal with strong noise
Simple structure of recurrent neural network.
110
X. LIU et al.
at an early stage of GT engine system in the study of Gao
et al.117 In view of the outstanding capability to analyze
large-scale data with nonlinear nature and time-dependent
characteristics, multiple researchers118–120 applied RNN to
mechanical fault diagnosis and got expected results, revealing
its suitability and bright prospects for fault diagnosis in highly
interconnected systems.
However, Choi and Lee121 pointed that RNN is sensitive to
wrong inputs with unexpected large degradation in performance. The shortcomings in robustness greatly limit the application of RNN, especially in GT fault diagnosis with high
measurement uncertainty and interfering noise. At present,
few researches have been published to optimize RNN inherent
attribute, while some valid approaches to this matter have
focused on combining RNN with other algorithms to fulfil
the diagnosis task. The combination of CNN and RNN is
the most widely studied hybrid methods, which can compensate for each other to achieve better fault diagnostic performance. Integrate the processing ability of temporal
correlation of RNN and the feature extraction ability under
measurement uncertainty of CNN to form a novel convolutional recurrent neural network (CRNN) model for fault diagnosis. Furthermore, by stacking multiple CRNNs, multiple
fault diagnosis tasks can be handled simultaneously.122 The
combination of different methods provides a solution to
numerous problems in GT fault diagnosis.
The application details of DL methods for GT fault diagnosis are summarized in Table 7.123
4. Hybrid intelligent methods
Hybrid intelligent methods for fault diagnosis, in a broad
sense, include the fusion, in which AI as the main body, with
Table 7
data preprocessing methods, network optimization methods
and multi-algorithm fusion. Hybrid intelligent methods in
the present review mainly refer to the multi-algorithm fusion
in a narrow sense. The multi-algorithm fusion begins with
the simple superposition of networks designed for different
conditions, gradually develops into AI algorithms fusion based
on ensemble learning (EL) theory, and the combination of different AI algorithms for mutual complementarity. Moreover,
the fusion of intelligent diagnosis methods with traditional
MB diagnosis methods and other advanced tools also presents
a promising research direction for interpretable hybrid fault
diagnosis methods. The above evolution and taxonomy of
hybrid intelligent methods is intuitively described in Fig. 23.
4.1. Simple superposition of networks
The constantly changing working conditions of GT engine systems make the single diagnosis model suffer from severe performance fluctuations, remaining one of the most challenging
issues in engine fault diagnosis. The superimposed algorithms
are initially fueled by the need for implementing steady diagnosis under different operating states of GT. The earlier studies
solved the problem by dividing diagnostic tasks into different
stages according to different working conditions, where independent models are trained. Vanini et al.124 proposed a fault
detection and isolation (FDI) scheme for an aircraft jet engine
based on multiple dynamic neural networks (DNNs), where
each DNN was specific to a certain operation condition. In
the proposed system, the threshold for each network was
determined by the residuals between the output of each
DNN with the measurement of the aero-engine in different
stages. Similarly, Sun ZR and Sun YG125 divided the whole
flight envelope into multiple stages and built the corresponding
Applications of deep learning methods for GT fault diagnosis.
Technique
91
DBN
Optimized DBN92
Multi-branch CNN with integrated crossentropy29
Using continuous wavelet transform to
transform the signal recognition problem
into an image recognition problem for
CNN to diagnose101
Inception-CNN110
Combination of CNN with ensemble
learning111
One-dimensional convolutional LSTM
network with adaptive dropout104
Database
Application
Diagnosis effect
13-dimension data adopted from a flight
parameter recorder of a domesticallymade airplane
A dataset of 34000 samples simulated on
a component-level turbofan engine
model
Using the TBD234 diesel engine test
bench to collect abnormal valve
clearance data under various operating
conditions
Various sensor signals of different faults
simulation based on a certain type of
aircraft engine simulated model
Fault diagnosis without
mathematical modeling and
article feature extraction.
Gas-path fault diagnosis of
multiple types of aero-engines
through a little expansion
Fault classification of diesel
engine under multiple
operating conditions
Accuracy of 98%
and 96.6% without
data preprocessing
Accuracy of 96.59%
Capable of extracting essential
time–frequency characteristics
from relatively few sample sets
Accuracy over 97%
Using the Monte Carlo simulation
method 123 to generate dataset based on
a geared turbofan engine model of
NASA/T-MATS master
Operating datasets sampled from a 4 S
high-speed diesel engine under 5 working
conditions
Online condition monitoring data of a
four-stroke diesel engine numbered
TBD234 under 12 different operating
conditions
Single or simultaneous
multiple sensor faults
diagnosis in the steady and
transition state of the engine
Suitable for online health
monitoring of diesel engines
Accuracy of 95.41%
Multi-factor operating
condition recognition
Accuracy over 99%
for each category
Accuracy over 98%
and testing time less
than 1 s
Accuracy of 99.08%
and high
generalization of
different engine
types
Intelligent fault diagnosis methods toward gas turbine
Fig. 23
111
Structure of hybrid intelligent methods.
BPNN models based on the correlational analyses of systemic
parameters which may influence the operating states of the
engine. It was proved that the proposed region-varying BPNN
models can eliminate instability caused by the fluctuations of
transition when switching flight phases, thus improving the
robustness of the network in the full flight envelope.
4.2. Ensemble learning methods
The superimposed networks mentioned above are essentially a
simple combination of individual networks on the basis of a
region partition method. Only one classifier makes one prediction in a certain condition with large waste of system memory
as other classifiers are in idle state. Therefore, an integrated
framework developed based on the concept of EL has become
a research hotspot recently. Concretely, EL is a learning paradigm which can compose multiple learning models into a
whole for better learning effect. The training process of EL
can be generally divided into two stages. Firstly, multiple
learning algorithms, known as the based classifiers, are utilized
to produce preliminary predictive results in a parallel mode.
Then, these weak predictive results are fused into an informative output based on a certain selection scheme or voting rule
for deeper knowledge excavation and stronger predictive performance.126 Specific implementation of EL in fault diagnostic
framework can be learned in the study of Zhong et al.127 In the
first stage, multiple pairwise-coupled sparse Bayesian ELMs
were trained independently on preprocessed data from three
different signal sources. In the second stage, a new probabilistic committee machine (PCM) method was utilized to assign an
optimal weight to each classifier by analyzing their accuracy
and reliability. Fig. 24 describes the general framework of fault
diagnosis strategy based on PCM. The final diagnosis was the
weighted combination of single outcomes. The result of fault
detection and classification showed that not only the accuracy
but the number of detectable faults of the proposed method
increased a lot.
In the EL model proposed by Pang et al.128, a number of
denoising multilayer ELMs were chosen as the base classifier
with specifically set activation functions and denoising criteria
to accommodate different operation conditions or noise interference. The main difference between the proposed EL method
and the stack of networks to cope with the various working
conditions was the proposal of a novel real-valued outputbased diversity metric. The candidate classifiers were compacted as an ensemble by the diversity metric and developed
for fault diagnosis of rolling bearing in engine system. The
integrated model was proved to gain better prognostic accuracy and adaptiveness, which outperformed not only single
intelligent diagnosis methods but also other state-of-the-art
112
X. LIU et al.
Fig. 24
General framework of PCM-based fault diagnosis.127
adaptive methods. In addition to the EL methods mentioned
above, the rapid development of single intelligent diagnosis
methods contributes to diverse choices of base classifier including CNN model in the proposed framework of Wang et al.111
and LSTM network in the developed ensemble model of
Cheng et al.129 While the single base models is getting increasingly powerful, the number of integrated base models is also
growing steadily. In the EL model established by Wang
et al.130, 100 parallelly trained broad learning system (BLS)
models were integrated into a bagging-BLS model. The final
diagnostic result was further optimized by the selection rules
with the accuracy stable at 0.988. Specifically, the selection
scheme to fuse the outputs of the base networks for the optimal estimation should be further researched, gaining more
progress in intelligence and adaptivity.
4.3. Mutually reinforcing of different methods
Hybrid methods mentioned above are mostly superposition of
a certain type of algorithm, but the idea of ensemble learning is
not limited to this. In fact, every single fault diagnosis method
has its positives and negatives. The combination of different
types of algorithms can complement each other and generate
better performance. DL algorithms, for instance, can automatically extract features from raw data for adaptive training,
avoiding the data missing during preprocessing or errors of
manual feature extraction. However, to achieve excellent classification ability, accurate and complete database is needed to
train the network, which prevents promotion and application
with few annotated samples, especially for fault diagnosis
toward GT engines. In the meantime, typical classifiers based
on shallow models, such as BPNN and SVM are limited by
the inability to deal with complex features in higher dimensions. Although data preprocessing methods131,132 have been
applied to data dimension reduction or artificial feature extraction and have compensated for deficiencies to some extent,
there are still some limitations in the single intelligence algo-
rithm. In this context, the fusion of multi-algorithms has a
broader prospect. On the one hand, the fusion of different
intelligent methods can achieve better diagnostic performance,
as was proved in the work of Zhao et al.133 that BPNN can
preserve the actual distribution of the raw data for nonlinear
fitting, which can supply complementary information for
CNN model to reach higher diagnosis accuracy. On the other
hand, an application of integrating CNN with SVM for GT
fault diagnosis134 demonstrated that the addition of SVM to
CNN or other DL algorithms could extend the application
of DL-based fault diagnosis methods to small sample
conditions.
As information fusion and decision fusion is proved to be
an effective way to resolve data deficiency and diagnosis conflict,135 the combination of intelligent diagnosis methods and
knowledge-driven Dempster-Shafer evidence theory (DSET)
is showing a promising research prospect. As a theoretical
inference method dealing with uncertainty, DSET is considered as a powerful tool for the representation and fusion of
decision level uncertain information. Hu et al.136 proposed a
muti-information fusion method composed of a BPNNbased data fusion layer, a SVM-based feature fusion layer,
and a DSET-based decision fusion layer. The multiple classification results of the first two layers were fused in the decision
fusion layer to achieve an overall evaluation based on reasonable allocation of the diagnosis outcomes instructed by DSET.
In the research of Lu et al.137 to optimize the K-ELM for the
real-time fault diagnosis requirements of aero-engine, a DSETbased fusion scheme was added to ensure the accuracy after
fusion. The experiment results verified the effectiveness of
DSET as a decision fusion methodology in engineering fault
diagnosis.
Moreover, Amare et al.138 developed a hybrid fault diagnosis method for GT engine system, where an auto-associative
neural network (AANN), several nested machine learning classifiers, and a MLP were integrated and respectively corresponded to three phases of FDI tasks. AANN was assigned
Intelligent fault diagnosis methods toward gas turbine
for data preprocessing and feature extraction in the first step,
followed by five different machine learning classifiers to identify the fault modes. An approximator based on MLP was creatively added to evaluate the severity of component faults by
analyzing physical indices of GT system. Conclusion was
reached in the end of the research that derivable advantages
could be derived from mutually reinforcing of different methods in GT fault diagnosis. And it can be further concluded that
by dividing the diagnosis task into phases with the coordination of suited networks, there are still great development space
for more powerful integrated diagnosis framework.
4.4. Interpretable methods
The DD diagnosis method has made great progress because it
overcomes insufficient diagnostic performance and harsh
implementation conditions. However, the black-box models
developed by DD methods eliminate the need for professional
knowledge to model the engine system but forfeit the model
interpretability in the meanwhile. For users of EHM system,
the lack of interpretability means untrustworthiness. The invisible working mechanism and unreliable model outputs hinder
the development of intelligent methods in the user-oriented
engine fault diagnosis field. Till now, traditional MB diagnosis
methods are the preferred choice in the practical industrial
application. For researchers, inexplicable model makes it hard
for developers to optimize the network or to correct underlying
logic when errors occur. Moreover, due to the diversity, specificity and scarcity of fault training samples, AI algorithms may
achieve high accuracy by chance but with an error logic inside.
The model interpretability can be used as a supplementary
evaluation indicator to avoid above risks. Therefore, network
interpretability is blessed with significant research value.
Fig. 25
113
Network interpretability includes the comprehensible working mechanism (also called ante-interpretability) and trustable
output (also called post-interpretability). For the former,
researchers tend to adopt the models that are inherently interpretable such as fault tree analysis,139,140 belief rule base,141
and expert system.142 However, these knowledge-based or
rule-based models extremely dependent on the establishment
of rule base, whose content is usually incomplete and parameters are usually suboptimal. On this occasion, an integration of
AI algorithms with rule-based systems was developed to realize
an interpretable network for state monitoring and field control.142,143 A Bayesian belief network,144 which combines DL
scheme with cause-and-effect representation, can be a successful example of the above idea. Nevertheless, a more common
strategy is reconstructing network with traditional methods
based on expertise to make certain layer endued with specific
physical meaning. Zhao et al.145 creatively replaced the first
layer of standard neural networks with a denoising layer based
on reproducing kernel Hilbert space, which was regarded as a
successful transmission of physical interpretation from traditional signal processing technology to AI method. Similarly,
WT has been widely used to reconstruct the preceding convolution layer of CNN for its definite physics meaning and powerful signal processing capability in fault diagnosis. The WToptimized CNNs in research146,147 was proved by engineering
diagnostic cases that with the interpretable working mechanism layer, the networks performed better in feature extraction
and improved in convergence speed and classification accuracy. Based on this idea, Wang et al.148 utilized tradition methods including WT, square envelope, Fourier transform, and
sparsity measure to reconstruct a five-layer ELM to devise a
fully interpretable neural network for machine condition monitoring, as shown in Fig. 25. Compared with original ELM, the
Fully interpretable neural network architecture for machine condition monitoring.148
114
X. LIU et al.
proposed model possessed stronger robustness by considering
the physical characteristics of the input signals.
For the interpretability of the network output, Oliveira
et al.149 proposed a residual explainer to interpret the behavior
of the DL model. The residual explainer was utilized to analyze
the difference of model outputs when input was reconstructed,
by which the effect of the variations of different inputs can be
understood. This disturbance-based interpretability was used
to provide an interpretable DD method in battery property
predictions by Liu et al.150 and showed helpful to facilitate
engineers’ cognitions of complicated manufacturing behavior
for better battery management strategy. The same can be
applied in FDI scheme for GT system. With increasing attention to interpretability of neural networks, a wave of new interpretable tools is emerging. As the most intuitive way for
comprehension, visualization methods151–153 are integrated in
black-box models for interpretability of local structure or individual input. In 2016, Ribeiro et al.154 proposed a local interpretable model-agnostic explanations (LIME), a powerful
interpretable tool that can explain the predictions of any classifier by approximating the complex model with an agent
model. Fig. 26 exhibits the general training process of LIME.
In the following example, a random forest classification model
was trained on an open database of white wine quality to predict the quality of the wine depending on multiple physicochemical properties.155 LIME was used to interpret the
predicted results of the selected sample, as shown in Fig. 27.
Title of the chart displays the binary result of the explained
sample with green stripes representing positive effects and
red ones representing negative effects. The left sidebar further
shows the thresholds of each input, depending on which the
positive or negative effects are determined. In the field of GT
fault diagnosis, interpretability efforts made by LIME have
far-reaching implications especially in determination of threshold value for different fault modes.
At present, the importance of interpretability is widely recognized in academia and industry. For GT fault diagnosis, the
interpretability of the AI-based methods not only helps to
make better health management strategies depend on the
knowledge of the output mode, but also acts as an evaluation
criterion to assess the relative reliability of different intelligent
methods. Researchers may hunt for a new hybrid method by
comminating of MB methods and interpretable DD methods,
to develop accurate, efficient, reliable, and user-friendly fault
diagnosis system for GT engine system.
5. Conclusions and perspectives
Fig. 26
General training process of LIME.
Fig. 27
Based on the different AI algorithms applied, abundant intelligent fault diagnosis methods are overviewed in the present
review. According to the analysis and discussions above, intelligent fault diagnosis methods can not only process hidden
complex fault information of high nonlinearity and uncertainty with higher accuracy and efficacy, but also overcome
the reliance on expertise knowledge during modeling and
implement difficulty of model incompatibility in actual application of traditional MB methods. The merits and demerits
of commonly used methods are summarized, the existing and
possible optimized directions are indicated, and the trends in
hybrid algorithms are highlighted, providing guidance for fur-
Local explanation of a random forest by local interpretable model-agnostic explanations.
Intelligent fault diagnosis methods toward gas turbine
ther explorations and applications of novel intelligent fault
diagnosis methods for GTs. Conclusion can be further reached
by reviewing the developing course of diagnosis methods (from
MB methods to DD methods, from SL methods to DL methods, from single methods to hybrid methods) and the optimization directions of specific method, that the development
of diagnosis methods towards higher accuracy, better realtime performance, stronger robustness, wider potability and
interpretability are extremely consistent with the complexity,
digitization and intellectualization of GT system. Although
these intelligent diagnosis methods have already achieved some
expected results, challenges and opportunities are still existing
in present researches. Fig. 28 presents the possible future development of GT fault diagnosis, which are detailed as follows:
1) Method validation is a critical issue for any novel
method proposed for industrial applications. The effectiveness and practicability of the newly raised algorithms
should be evaluated before it is incorporated into the
real system. For GT fault diagnosis methods, different
training data and experiment settings (different applicative engine types, fault modes division and degree evaluation criteria) make it vague for users to judge the
feasibility when implemented. A widely accepted validation methods is implanting general fault cases to evaluate the performance of the diagnostic methods.
NASA’s evaluation software referred to as the Propul-
Fig. 28
115
sion Diagnostic Method Evaluation Strategy (ProDiMES) has proved the effectiveness of using
benchmark fault cases to develop and evaluate the performance of diagnostic algorithms.156,157 Standardized
evaluation criterion and comprehensive benchmark fault
cases for the comparison among different methods need
to be addressed in future research.
2) Characteristics that can reflect the degradation state of
engine system are diverse, including gas path performance, vibration signal, and chemical constituents of
the exuviation. However, most of the present researches
generally conduct fault diagnosis using a single physical
source information. On the one hand, diagnosis based
on single physical can be lopsided. On the other hand,
as a way to defend information’s confidentiality and
integrity, operating data of engine is impossible to share
for model training. Owing to this particularity in GT
fault diagnosis field, information fusion is of great significance in compensating data deficiency to improve
accuracy. Information fusion technology has been
proved effectiveness in fault diagnosis of other industrial
fields.93,94 But its combination with engine mechanism is
relative absence. Future studies should focus more on
the coupling property and the fusion rule of multisource signal in GT system for its promotion and
application.
Future development of GT fault diagnosis.
116
3) As is previously mentioned, GT fault diagnosis is limited
by insufficient sensors information, which causes inability of MB methods to deal with underdetermined estimation problem and incomplete training of DD
methods. In this context, sensing technology is one of
the crucial constraints on fault diagnosis methods.
Incumbent sensors on GT are mainly facing two challenges.158,159 For one thing, little space is reserved for
sensors installment and due to high rotation speed of
dynamic components, sensors are widely installed on
static components for offline data analysis. For another,
wired sensors are space wasted and easily damaged while
wireless technology is constrained by limited battery
capacity and being susceptible to interference. Thus, a
new technology by integrating energy harvesting technology with wireless sensors to achieve real-time selfpowered engine monitoring shows a promising future.160
4) Hybrid methods could still take up the mainstream
research in the coming decade as single technology
always has its strengths and weakness. Followed the
evolution of hybrid intelligent methods in section Ⅳ, a
more organized and well-founded combination of different diagnosis methods can be found as a research trend.
For EL-based integrated model, the greatest challenges
lie in the selection of number of based models and the
combining scheme. However, with constantly deepen
research of optimization algorithms, more powerful
methods can be developed specific to certain diagnostic
need. It is foreseeable that a hierarchical diagnosis
framework of using different methods to match different
implementation aspects can be mutually reinforcing and
has great room for development.
5) Data-driven methods omitted the process of modeling
the complex engine system, making the diagnosis difficult to explain. The lack of interpretability not only
makes users distrust the output of the model, but also
makes it difficult for developers to understand the
underlying mechanism of decision-making process for
further optimization. A more common solution is to
replace certain layer of deep learning model with traditional MB methods to give it definite physical meaning.
Besides reconstructing interpretable network, rational
use of state-of-the-art interpretable tools such as visualization system and linear interpreter can bring some
unexpected advantages to solve the inherent problem
in fault diagnosis.
6) Wisdom system is a general development trend of intelligent methods, the same to the GT diagnosis. Intelligent
fault diagnosis can only complete certain inference procession for possible results, giving reference for final
human decision. One of the biggest challenges in intelligent fault diagnosis of GT system is the inability of classification besides training data. Wisdom diagnosis
system, however, can integrate model training, data processing, adaptive learning, result inferring, and decision
making as a whole implemented by machine algorithms.
With the constantly developing of gas turbine towards
electrification, intelligence and digitalization, a selfdiagnosis and self-renewal wisdom engine system can
be an irreversible trend in the near future.
X. LIU et al.
Declaration of competing interest
The authors declare that they have no known competing
financial interests or personal relationships that could have
appeared to influence the work reported in this paper.
Acknowledgements
This study was financially supported by the National Natural
Science Foundation of China (No. 61890921, 61890923, and
52372371) and the key projects of Aero Engine and Gas Turbine Basic Science Center (No. P2022-B-V-001-001 and P2022B-V-002-001).
References
1. Zhang S, Su L, Gu J, et al. Rotating machinery fault detection
and diagnosis based on deep domain adaptation: a survey. Chin J
Aeronaut 2023;36(1):45–74.
2. Zhou X, Lu F, Huang J. Fault diagnosis based on measurement
reconstruction of HPT exit pressure for turbofan engine. Chin J
Aeronaut 2019;32(5):1156–70.
3. Hanachi H, Liu J, Mechefske C. Multi-mode diagnosis of a gas
turbine engine using an adaptive neuro-fuzzy system. Chin J
Aeronaut 2018;31(1):1–9.
4. Stanton I, Munir K, Ikram A, et al. Predictive maintenance
analytics and implementation for aircraft: challenges and opportunities. Syst Eng 2023;26(2):216–37.
5. Tang SN, Yuan SQ, Zhu Y. Deep learning-based intelligent fault
diagnosis methods toward rotating machinery. IEEE Access
2020;8:9335–46.
6. Zhang H, Long LN, Dong KQ. Detect and evaluate dependencies between aero-engine gas path system variables based on
multiscale horizontal visibility graph analysis. Phys A
2019;526:120830.
7. Simon DL, Thomas R, Dunlap KM. Considerations for the
extension of gas path analysis to electrified aircraft propulsion
systems. J Eng Gas Turbines Power-Trans ASME 2022;144
(3):031004.
8. Togni S, Nikolaidis T, Sampath S. A combined technique of
kalman filter, artificial neural network and fuzzy logic for gas
turbines and signal fault isolation. Chin J Aeronaut 2021;34
(2):124–35.
9. Yan LP, Zhang HL, Dong XZ, et al. Unscented Kalman-filterbased simultaneous diagnostic scheme for gas-turbine gas path
and sensor faults. Meas Sci Technol 2021;32(9):095905.
10. Kalman RE. A new approach to linear filtering and prediction
problems. J Basic Eng 1960;82(1):35–45.
11. Fentaye AD, Baheta AT, Gilani SI, et al. A review on gas turbine
gas-path diagnostics: state-of-the-art methods, challenges and
opportunities. Aerospace 2019;6(7):83.
12. Yuan Y, Ding ST, Liu XF, et al. Hybrid diagnosis system for
aeroengine sensor and actuator faults. J Aerosp Eng 2020;33
(1):04019108.
13. Liu XF, Xue NY. An improved hybrid kalman filter design for
aircraft engine based on a velocity-based LPV framework. In:
28th Chinese Control and Decision Conference; 2016 May 28-30;
Yinchuan, Peoples R China; 2016. p. 1873-8.
14. Ding S, Yuan Y, Xue N, et al. An onboard aeroengine modeltuning system. J Aerosp Eng 2017;30:04017018.
15. Simon D. Kalman filtering with inequality constraints for
turbofan engine health estimation. IEE Proc-Control Theory
Appl 2006;371–8.
Intelligent fault diagnosis methods toward gas turbine
16. Simon D. A comparison of filtering approaches for aircraft
engine health estimation. Aerosp Sci Technol 2008;12(4):
276–84.
17. Jin P, Lu F, Huang JQ, et al. Life cycle gas path performance
monitoring with control loop parameters uncertainty for aeroengine. Aerosp Sci Technol 2021;115:106775.
18. Xiao M, Zhang Y, Wang Z, et al. An adaptive three-stage
extended Kalman filter for nonlinear discrete-time system in
presence of unknown inputs. ISA Trans 2018;75:101–17.
19. Rodriguez Obando D, Martinez JJ, Bérenguer C. Deterioration
estimation for predicting and controlling rul of a friction drive
system. ISA Trans 2021;113:97–110.
20. Wang W, He NB, Yao KM, et al. Improved Kalman filter and its
application in initial alignment. Optik 2021;226(2):165747.
21. Li KQ, Zhou F, Chen X, et al. State-of-charge estimation
combination algorithm for lithium-ion batteries with frobeniusnorm-based qr decomposition modified adaptive cubature Kalman filter and h-infinity filter based on electro-thermal model.
Energy 2023;263(11):125763.
22. Xu JC, Zhang X, Mu PC, et al. FOA-based QR-factorized CKF
algorithm for AUV navigation. In: OCEANS Hampton Roads
Conference; 2022 Oct 17-20: Electr Network; 2022.
23. Liu XF, Zhu JQ, Luo CS, et al. Aero-engine health degradation
estimation based on an underdetermined extended kalman filter
and convergence proof. ISA Trans 2022;125:528–38.
24. Hanachi H, Mechefske C, Liu J, et al. Performance-based gas
turbine health monitoring, diagnostics, and prognostics: a survey.
IEEE Trans Reliab 2018;67(3):1340–63.
25. Luo YL. Application of reinforcement learning algorithm model
in gas path fault intelligent diagnosis of gas turbine. Comput
Intell Neurosci 2021;2021:3897077.
26. Zhong GQ, Ling X, Wang LN. From shallow feature learning to
deep learning: benefits from the width and depth of deep
architectures. Wiley Interdiscip Rev-Data Mining Knowl Discov
2019;9(1):e1255.
27. Hinton GE, Salakhutdinov R. Reducing the dimensionality of
data with neural networks. Science 2006;313:504–7.
28. Schmidhuber J. Deep learning in neural networks: an overview.
Neural Netw 2015;61:85–117.
29. Zhao HP, Mao ZW, Zhang JJ, et al. Multi-branch convolutional
neural networks with integrated cross-entropy for fault diagnosis
in diesel engines. Meas Sci Technol 2021;32(4):045103.
30. Kim H. Ai, big data, and robots for the evolution of biotechnology. Genomics & informatics 2019;17(4):e44.
31. Yigitcanlar T, Desouza KC, Butler L, et al. Contributions and
risks of artificial intelligence (AI) in building smarter cities:
insights from a systematic review of the literature. Energies
2020;13(6):1473.
32. Gursoy D, Chi OHX, Lu L, et al. Consumers acceptance of
artificially intelligent (AI) device use in service delivery. Int J Inf
Manage 2019;49:157–69.
33. Tschandl P, Rinner C, Apalla Z, et al. Human-computer
collaboration for skin cancer recognition. Nat Med 2020;26
(8):1229–34.
34. Liu RN, Yang BY, Zio E, et al. Artificial intelligence for fault
diagnosis of rotating machinery: a review. Mech Syst Signal Proc
2018;108:33–47.
35. Sherwani F, Ibrahim B, Asad MM. Hybridized classification
algorithms for data classification applications: a review. Egypt
Inform J 2021;22(2):185–92.
36. Higgins I. Generalizing universal function approximators. Nat
Mach Intell 2021;3(3):192–3.
37. Yan Y, Chen R, Yang ZH, et al. Application of back propagation neural network model optimized by particle swarm algorithm in predicting the risk of hypertension. J Clin Hypertens
2022;24(12):1606–17.
38. Wang J, Lu SY, Wang SH, et al. A review on extreme learning
machine. Multimed Tools Appl 2022;81(29):41611–60.
117
39. Li B, Zhao YP. Group reduced kernel extreme learning machine
for fault diagnosis of aircraft engine. Eng Appl Artif Intel
2020;96:103968.
40. Ri J, Kim H. G-mean based extreme learning machine for
imbalance learning. Digit Signal Prog 2020;98:102637.
41. Wang P, Fan E, Wang P. Comparative analysis of image
classification algorithms based on traditional machine learning
and deep learning. Pattern Recogn Lett 2021;141:61–7.
42. Yu WX, Lu Y, Wang JN. Application of small sample virtual
expansion and spherical mapping model in wind turbine fault
diagnosis. Expert Syst Appl 2021;183:115397.
43. Cervantes J, Garcia-Lamont F, Rodriguez-Mazahua L, et al. A
comprehensive survey on support vector machine classification:
applications,
challenges
and
trends.
Neurocomputing
2020;408:189–215.
44. Rumelhart DE, Hinton GE, Williams RJ. Learning representations by back-propagating errors. Nature 1986;323:533–6.
45. Xiao MH, Wang WC, Wang KX, et al. Fault diagnosis of highpower tractor engine based on competitive multiswarm cooperative particle swarm optimizer algorithm. Shock Vib
2020;2020:8829257.
46. Smith J, Wu B, Wilamowski BM. Neural network training with
Levenberg–Marquardt and adaptable weight compression. IEEE
Trans Neural Netw Learn Syst 2019;30:580–7.
47. Ruı́z LGB, Delgado RR, Cuéllar MP, et al. Energy consumption
forecasting based on Elman neural networks with evolutive
optimization. Expert Syst Appl 2018;92:380–9.
48. Yang J, Hu YP, Zhang KX, et al. An improved evolution
algorithm using population competition genetic algorithm and
self-correction BP neural network based on fitness landscape.
Soft Comput 2021;25(3):1751–76.
49. Xie CL, Wang YC, MacIntyre J, et al. Using sensors data and
emissions information to diagnose engine’s faults. Int J Comput
Intell Syst 2018;11(1):1142–52.
50. Zhu ZL, Xu XF, Li LJ, et al. A novel GA-BP neural network for
wireless diagnosis of rolling bearing. J Circuits Syst Comput
2022;31(10):2250173.
51. Ling YJ, Niu CM. Fault diagnosis of automobile engine based on
improved BP neutral network. Wirel Commun Mob Comput
2022;2022:2287776.
52. Liu PF, Zhang W. A fault diagnosis intelligent algorithm based
on improved BP neural network. Int J Pattern Recognit Artif
Intell 2019;33(9):1959028.
53. Li LY, Su TX, Ma FK, et al. Research on a small sample fault
diagnosis method for a high-pressure common rail system. Adv
Mech Eng 2021;13(9):16878140211046103.
54. Xu L, Zhao SB, Li NN, et al. Application of QGA-BP for fault
detection of liquid rocket engines. IEEE Trans Aerosp Electron
Syst 2019;55(5):2464–72.
55. Yu HH, Wang T. A method for real-time fault detection of liquid
rocket engine based on adaptive genetic algorithm optimizing
back propagation neural network. Sensors 2021;21(15):5026.
56. Eberhart R, Kennedy J. A new optimizer using particle swarm
theory. In: MHS’95 Proceedings of the Sixth International
Symposium on Micro Machine and Human Science; 1995 Oct 46; 1995. p. 39-43.
57. Kandasamy T, Rajendran R. Hybrid algorithm with variants for
feed forward neural network. Int Arab J Inf Technol 2018;15
(2):240–5.
58. Li L. Research on comparison of different algorithms in
diagnosing faults of aircraft engines. J Aerosp Technol Manage
2021;13:e3821.
59. Niu B, Zhu YL, He XX, et al. MCPSO: a multi-swarm
cooperative particle swarm optimizer. Appl Math Comput
2007;185(2):1050–62.
60. Ma J, Wu JD, Wang XD. Fault diagnosis method based on
wavelet packet-energy entropy and fuzzy kernel extreme learning
machine. Adv Mech Eng 2018;10(1):168781401775144.
118
61. Yang X, Pang S, Shen W, et al. Aero engine fault diagnosis using
an optimized extreme learning machine. Int J Aerosp Eng
2016;2016:7892875.
62. Pang S, Yang XY, Zhang XF. Aero engine component fault
diagnosis
using
multi-hidden-layer
extreme
learning
machine with optimized structure. Int J Aerosp Eng
2016;2016:1329561.
63. You CX, Huang JQ, Lu F. Recursive reduced kernel based
extreme learning machine for aero-engine fault pattern recognition. Neurocomputing 2016;214:1038–45.
64. Liang N, Huang G, Saratchandran P, et al. A fast and accurate
online sequential learning algorithm for feedforward networks.
IEEE Trans Neural Netw 2006;17(6):1411–23.
65. Lu JJ, Huang JQ, Lu F. Sensor fault diagnosis for aero engine
based on online sequential extreme learning machine with
memory principle. Energies 2017;10(1):39.
66. Lu F, Wu JD, Huang JQ, et al. Restricted-boltzmann-based
extreme learning machine for gas path fault diagnosis of turbofan
engine. IEEE Trans Ind Inform 2020;16(2):959–68.
67. Zhao YP, Huang G. Soft one-class extreme learning machine for
turboshaft engine fault detection. Proc Inst Mech Engineers Part
G-J Aerosp Eng 2022;236(13):2708–22.
68. Zhao YP, Huang G, Hu QK, et al. Soft extreme learning machine
for fault detection of aircraft engine. Aerosp Sci Technol
2019;91:70–81.
69. Zhao YP, Chen YB. Extreme learning machine based transfer
learning for aero engine fault diagnosis. Aerosp Sci Technol
2022;121:107311.
70. Tharwat A. Parameter investigation of support vector machine
classifier with kernel functions. Knowl Inf Syst 2019;61
(3):1269–302.
71. Gharoun H, Keramati A, Nasiri MM, et al. An integrated
approach for aircraft turbofan engine fault detection based on
data mining techniques. Expert Syst 2019;36(2):e12370.
72. Fang ZC, Wang Y, Duan HX, et al. Comparison of general
kernel, multiple kernel, infinite ensemble and semi-supervised
support vector machines for landslide susceptibility prediction.
Stoch Environ Res Risk Assess 2022;36(10):3535–56.
73. Xue YT, Zhang L, Wang BJ, et al. Nonlinear feature selection
using gaussian kernel svm-rfe for fault diagnosis. Appl Intell
2018;48(10):3306–31.
74. Nakayama Y, Yata K, Aoshima M. Bias-corrected support
vector machine with gaussian kernel in high-dimension, lowsample-size settings. Ann Inst Stat Math 2020;72(5):1257–86.
75. Armaghani DJ, Asteris PG, Askarian B, et al. Examining hybrid
and single svm models with different kernels to predict rock
brittleness. Sustainability 2020;12(6):2229.
76. Zhao HS, Gao YF, Liu HH, et al. Fault diagnosis of wind
turbine bearing based on stochastic subspace identification and
multi-kernel support vector machine. J Mod Power Syst Clean
Energy 2019;7(2):350–6.
77. Shi XY, Jiang DG, Qian WW, et al. Application of the gaussian
process regression method based on a combined kernel function
in engine performance prediction. ACS Omega 2022;7
(45):41732–43.
78. Wang B, Zhang X, Sun C, et al. A quantitative intelligent
diagnosis method for early weak faults of aviation high-speed
bearings. ISA Trans 2019;93:370–83.
79. Zhu W, Wei YS, Xiao H. Fault diagnosis of neural network
classified signal fractal feature based on svm. Cluster Comput
2019;22(2):S4249–54.
80. Wang B, Ke HW, Ma XD, et al. Fault diagnosis method for
engine control system based on probabilistic neural network and
support vector machine. Appl Sci-Basel 2019;9(19):4122.
81. Wumaier T, Xu C, Guo HY, et al. Fault diagnosis of wind
turbines based on a support vector machine optimized by the
sparrow search algorithm. IEEE Access 2021;9:69307–15.
X. LIU et al.
82. Yazdani S, Montazeri-Gh M. A novel gas turbine fault detection
and identification strategy based on hybrid dimensionality
reduction and uncertain rule-based fuzzy logic. Comput Ind
2020;115:103131.
83. Ji SX, Han XH, Hou YC, et al. Remaining useful life prediction
of airplane engine based on pca-blstm. Sensors 2020;20(16):
4537.
84. Ju YY, Cui ZL, Xiao QT. Fault diagnosis of power plant
condenser with the optimized deep forest algorithm. IEEE Access
2022;10:75986–97.
85. Shao M, Wang J, Wang S. Research on marine diesel engine fault
diagnosis based on the manifold learning and elm. J Phys Conf
Ser 2020;1549(4):042113.
86. Komorska I, Puchalski A. On-line diagnosis of mechanical
defects of the combustion engine with principal components
analysis. J Vibroeng 2015;17(8):4279–88.
87. Liu H, Zhang J, Cheng Y, et al. Fault diagnosis of gearbox using
empirical mode decomposition and multi-fractal detrended crosscorrelation analysis. J Sound Vibr 2016;385:350–71.
88. Bai HJ, Zhan XB, Yan H, et al. Research on diesel engine fault
diagnosis method based on stacked sparse autoencoder and
support vector machine. Electronics 2022;11(14):2249.
89. Wu B, Xi L, Fan S, et al. Fault diagnosis for wind turbine based
on improved extreme learning machine. J Shanghai Jiaotong Univ
(Sci) 2017;22(4):466–73.
90. Li HW, Xu BS, Du CH, et al. Performance prediction and power
density maximization of a proton exchange membrane fuel cell
based on deep belief network. J Power Sources 2020;461:228154.
91. Guo C, Zheng XF, Yao B. The fault detection of aero-engine
sensor based on deep belief networks. In: 7th International
Conference on Mechatronics, Control and Materials (ICMCM);
2016 Oct 29–30; Changsha, China; 2016. p. 85–92.
92. Xu JG, Liu XY, Wang BB, et al. Deep belief network-based gas
path fault diagnosis for turbofan engines. IEEE Access
2019;7:170333–42.
93. Zhu DQ, Cheng XL, Yang L, et al. Information fusion fault
diagnosis method for deep-sea human occupied vehicle thruster
based on deep belief network. IEEE T Cybern 2022;52
(9):9414–27.
94. Jiao J, Zheng XJ. Fault diagnosis method for industrial robots
based on DBN joint information fusion technology. Comput
Intell Neurosci 2022;2022:4340817.
95. Zhang XX, Zhou JZ, Chen WR. Data-driven fault diagnosis for
PEMFC systems of hybrid tram based on deep learning. Int J
Hydrog Energy 2020;45(24):13483–95.
96. Zhu J, Hu TZ, Jiang B, et al. Intelligent bearing fault diagnosis
using PCA-DBN framework. Neural Comput & Applic 2020;32
(14):10773–81.
97. Guo XJ, Shen CQ, Chen L. Deep fault recognizer: an integrated
model to denoise and extract features for fault diagnosis in
rotating machinery. Appl Sci-Basel 2017;7(1):41.
98. Yamashita R, Nishio M, Do RKG, et al. Convolutional neural
networks: an overview and application in radiology. Insights
Imaging 2018;9(4):611–29.
99. Lecun Y, Bottou L, Bengio Y, et al. Gradient-based learning
applied to document recognition. Proc IEEE 1998;2278–324.
100. Zhang JQ, Sun Y, Guo L, et al. A new bearing fault diagnosis
method based on modified convolutional neural networks. Chin J
Aeronaut 2020;33(2):439–47.
101. Gou LF, Li HH, Zheng H, et al. Aeroengine control system
sensor fault diagnosis based on cwt and CNN. Math Probl Eng
2020;2020:5357146.
102. Hsieh CH, Li YS, Hwang BJ, et al. Detection of atrial fibrillation
using 1D convolutional neural network. Sensors 2020;20(7):2136.
103. Yuan XZ, Tanksley D, Li LJ, et al. Faster post-earthquake
damage assessment based on 1d convolutional neural networks.
Appl Sci-Basel 2021;11(21):9844.
Intelligent fault diagnosis methods toward gas turbine
104. Jiang ZN, Lai YH, Zhang JJ, et al. Multi-factor operating
condition recognition using 1D convolutional long short-term
network. Sensors 2019;19(24):5488.
105. Chen CC, Liu Z, Yang GS, et al. An improved fault diagnosis
using 1d-convolutional neural network model. Electronics
2021;10(1):59.
106. Shao XR, Kim CS. Unsupervised domain adaptive 1D-CNN for
fault diagnosis of bearing. Sensors 2022;22(11):4156.
107. Zhang KX, Lin B, Chen JX, et al. Aero-engine surge fault
diagnosis using deep neural network. Comput Syst Sci Eng
2022;42(1):351–60.
108. Gong WF, Wang YZ, Zhang ML, et al. A fast anomaly diagnosis
approach based on modified cnn and multisensor data fusion.
IEEE Trans Ind Electron 2022;69(12):13636–46.
109. Pacheco F, Drimus A, Duggen L, et al. Deep ensemble-based
classifier for transfer learning in rotating machinery fault
diagnosis. IEEE Access 2022;10:29778–87.
110. Du X, Chen JJ, Zhang HB, et al. Fault detection of aero-engine
sensor based on inception-CNN. Aerospace 2022;9(5):236.
111. Wang RH, Chen H, Guan C. Random convolutional neural
network structure: an intelligent health monitoring scheme for
diesel engines. Measurement 2021;171:108786.
112. Peng XY, Yu JX, Yao BW, et al. A review of FPGA-based
custom computing architecture for convolutional neural network
inference. Chin J Electron 2021;30(1):1–17.
113. Bang S, Park S, Kim H, et al. Encoder-decoder network for pixellevel road crack detection in black-box images. Comput-Aided Civ
Infrastruct Eng 2019;34(8):713–27.
114. Elman JL. Finding structure in time. Cogn Sci 1990;14
(2):179–211.
115. Hochreiter S, Schmidhuber J. Long short-term memory. Neural
Comput 1997;9:1735–80.
116. Xue ZY, Xiahou KS, Li MS, et al. Diagnosis of multiple opencircuit switch faults based on long short-term memory network
for DFIG-based wind turbine systems. IEEE J Emerg Sel Top
Power Electron 2020;8(3):2600–10.
117. Gao DW, Zhu YS, Ren ZJ, et al. A novel weak fault diagnosis
method for rolling bearings based on LSTM considering quasiperiodicity. Knowledge-Based Syst 2021;231:107413.
118. Liu H, Zhou JZ, Zheng Y, et al. Fault diagnosis of rolling
bearings with recurrent neural network based autoencoders. ISA
Trans 2018;77:167–78.
119. Shahnazari H. Fault diagnosis of nonlinear systems using
recurrent neural networks. Chem Eng Res Des 2020;153:233–45.
120. Zhu JJ, Jiang QS, Shen YH, et al. Application of recurrent neural
network to mechanical fault diagnosis: a review. J Mech Sci
Technol 2022;36(2):527–42.
121. Choi J, Lee SJ. A sensor fault-tolerant accident diagnosis system.
Sensors 2020;20(20):5839.
122. Qin N, Liang KW, Huang DQ, et al. Multiple convolutional
recurrent neural networks for fault identification and performance degradation evaluation of high-speed train bogie. IEEE
Trans Neural Netw Learn Syst 2020;31(12):5363–76.
123. Simon DL, Bird J, Davison C, et al. Benchmarking gas path
diagnostic methods: a public approach. In: Proceedings of the
ASME Turbo Expo 2008: Power for Land, Sea, and Air; 2008
June 9-13; Berlin, Germany: Electric Power; 2008. p. 325-36.
124. Vanini ZNS, Khorasani K, Meskin N. Fault detection and
isolation of a dual spool gas turbine engine using dynamic
neural networks and multiple model approach. Inf Sci
2014;259:234–51.
125. Sun ZR, Sun YG. Research of real-time fault diagnosis platform
of aero-engine’s fuel flow sensors. In: International Conference on
Mechanical, Electronic and Engineering Technology (ICMEET);
2014 May 9-11; Taipei, Taiwan; 2014. p. 206-9.
126. Dong XB, Yu ZW, Cao WM, et al. A survey on ensemble
learning. Front Comput Sci 2020;14(2):241–58.
119
127. Zhong JH, Wong PK, Yang ZX. Fault diagnosis of rotating
machinery based on multiple probabilistic classifiers. Mech Syst
Signal Proc 2018;108:99–114.
128. Pang S, Yang XY, Zhang XF, et al. Fault diagnosis of rotating
machinery components with deep elm ensemble induced by realvalued output-based diversity metric. Mech Syst Signal Proc
2021;159:107821.
129. Cheng YW, Wu J, Zhu HP, et al. Remaining useful life prognosis
based on ensemble long short-term memory neural network.
IEEE Trans Instrum Meas 2021;70:3503912.
130. Wang MM, Ge QB, Jiang HY, et al. Wear fault diagnosis of
aeroengines based on broad learning system and ensemble
learning. Energies 2019;12(24):4750.
131. Pang S, Yang XY, Zhang XF, et al. Fault diagnosis of
rotating machinery with ensemble kernel extreme learning
machine based on fused multi-domain features. ISA Trans
2020;98:320–37.
132. Palmer KA, Bollas GM. Active fault diagnosis for uncertain
systems using optimal test designs and detection through
classification. ISA Trans 2019;93:354–69.
133. Zhao L, Mo C, Sun T, et al. Aero engine gas-path fault diagnose
based on multimodal deep neural networks. Wirel Commun Mob
Comput 2020;2020:8891595.
134. Zhong S-s, Fu S, Lin L. A novel gas turbine fault diagnosis
method based on transfer learning with CNN. Measurement
2019;137:435–53.
135. Gao XE, Jiang PL, Xie WX, et al. Decision fusion method for
fault diagnosis based on closeness and dempster-shafer theory. J
Intell Fuzzy Syst 2021;40(6):12185–94.
136. Hu J, Huang TF, Zhou JP, et al. Electronic systems diagnosis
fault in gasoline engines based on multi-information fusion.
Sensors 2018;18(9):2917.
137. Lu JJ, Huang JQ, Lu F. Distributed kernel extreme learning
machines for aircraft engine failure diagnostics. Appl Sci-Basel
2019;9(8):1707.
138. Amare DF, Aklilu TB, Gilani SI. Gas path fault diagnostics
using a hybrid intelligent method for industrial gas turbine
engines. J Braz Soc Mech Sci Eng 2018;40(12):578.
139. Waghen K, Ouali MS. Interpretable logic tree analysis: a datadriven fault tree methodology for causality analysis. Expert Syst
Appl 2019;136:376–91.
140. Waghen K, Ouali MS. Multi-level interpretable logic tree
analysis: a data-driven approach for hierarchical causality
analysis. Expert Syst Appl 2021;178:115035.
141. Li C, Shen Q, Wang LX, et al. A new adaptive interpretable fault
diagnosis model for complex system based on belief rule base.
IEEE Trans Instrum Meas 2022;71:1–11.
142. Chen XY, Zeng YY, Kang SK, et al. Inn: An interpretable neural
network for ai incubation in manufacturing. ACM Trans Intell
Syst Technol 2022;13(5):1–23.
143. Nadim K, Ragab A, Ouali MS. Data-driven dynamic causality
analysis of industrial systems using interpretable machine learning and process mining. J Intell Manuf 2023;34(1):57–83.
144. Yang WT, Reis MS, Borodin V, et al. An interpretable
unsupervised bayesian network model for fault detection and
diagnosis. Control Eng Practice 2022;127(3):105304.
145. Zhao BX, Cheng CM, Tu GW, et al. An interpretable denoising
layer for neural networks based on reproducing Kernel Hilbert
space and its application in machine fault diagnosis. Chin J Mech
Eng 2021;34(1):1–11.
146. Li TF, Zhao ZB, Sun C, et al. WaveletKernelNet: an interpretable deep neural network for industrial intelligent diagnosis.
IEEE Trans Syst Man Cybern-Syst 2022;52(4):2302–12.
147. Yuan J, Cao SW, Ren GX, et al. LW-Net: an interpretable
network with smart lifting wavelet kernel for mechanical feature
extraction and fault diagnosis. Neural Comput & Applic 2022;34
(18):15661–72.
120
148. Wang D, Chen YK, Shen CQ, et al. Fully interpretable
neural network for locating resonance frequency bands for
machine condition monitoring. Mech Syst Signal Proc 2022;
168:108673.
149. Oliveira DFN, Vismari LF, Nascimento AM, et al. A new
interpretable unsupervised anomaly detection method based on
residual explanation. IEEE Access 2022;10:1401–9.
150. Liu KL, Niri MF, Apachitei G, et al. Interpretable machine
learning for battery capacities prediction and coating parameters
analysis. Control Eng Pract 2022;124(4):105202.
151. Chen BA, Liu TT, He C, et al. Fault diagnosis for limited
annotation signals and strong noise based on interpretable
attention mechanism. IEEE Sens J 2022;22(12):11865–80.
152. An BT, Wang SB, Zhao ZB, et al. Interpretable neural network
via algorithm unrolling for mechanical fault diagnosis. IEEE
Trans Instrum Meas 2022;71:1–11.
153. Tang J, Zheng GH, Wei C, et al. Signal-transformer: a robust
and interpretable method for rotating machinery intelligent fault
diagnosis under variable operating conditions. IEEE Trans
Instrum Meas 2022;71:1–11.
X. LIU et al.
154. Ribeiro M, Singh S, Guestrin C. ‘‘Why should I trust you?”
Explaining the predictions of any classifier. Arxiv 2016;62(3): 927–50.
155. Cortez P, Cerdeira A, Almeida F, et al. Modeling wine
preferences by data mining from physicochemical properties.
Decis Support Syst 2009;47(4):547–53.
156. Koskoletos AO, Aretakis N, Alexiou A, et al. Evaluation of
aircraft engine gas path diagnostic methods through prodimes. J
Eng Gas Turbines Power-Trans ASME 2018;140(12):121016.
157. Perez-Ruiz JL, Tang Y, Loboda I. Aircraft engine gas-path
monitoring and diagnostics framework based on a hybrid fault
recognition approach. Aerospace 2021;8(8):232.
158. Zhang Y, Cao J, Zhu H, et al. Design, modeling and
experimental verification of circular halbach electromagnetic
energy harvesting from bearing motion. Energy Conv Manage
2019;180:811–21.
159. Zhang L, Zhang F, Qin Z, et al. Piezoelectric energy harvester for
rolling bearings with capability of self-powered condition monitoring. Energy 2022;238:121770.
160. Wang Y, Yang Z, Li P, et al. Energy harvesting for jet engine
monitoring. Nano Energy 2020;75:104853.