aerospace
Article
Thrust Prediction of Aircraft Engine Enabled by Fusing Domain
Knowledge and Neural Network Model
Zhifu Lin 1 , Hong Xiao 1, * , Xiaobo Zhang 1,2 and Zhanxue Wang 1
1
2
*
School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, China
Collaborative Innovation Center for Advanced Aero-Engine, Beijing 100191, China
Correspondence: xhong@nwpu.edu.cn
Abstract: Accurate prediction of aircraft engine thrust is crucial for engine health management
(EHM), which seeks to improve the safety and reliability of aircraft propulsion. Thrust prediction
is implemented using an on-board adaptive model for EHM. However, the conventional methods
for building such a model are often tedious or overly data-dependent. To improve the accuracy
of thrust prediction, domain knowledge can be leveraged. Hence, this study presents a strategy
for building an on-board adaptive model that can predict aircraft engine thrust in real-time. The
strategy combines engine knowledge and neural network architecture to construct a prediction model.
The whole-model architecture is divided into separate modules that are mapped in a one-to-one
form using a domain decomposition approach. The engine domain knowledge is used to guide
feature selection and the neural network architecture design in the method. Furthermore, this study
explains the relationships between aircraft engine features and how the model can predict engine
thrust in flight condition. To demonstrate the effectiveness and robustness of the architecture, four
different testing datasets were used for validation. The results show that the thrust prediction model
created by the given architecture has maximum relative deviations below 4.0% and average relative
deviations below 2.0% on all testing datasets. In comparison to the performance of the models created
by conventional neural network architecture on the four testing datasets, the model created by the
presented architecture proves more suitable for aircraft propulsion.
Citation: Lin, Z.; Xiao, H.; Zhang, X.;
Wang, Z. Thrust Prediction of
Aircraft Engine Enabled by Fusing
Keywords: thrust prediction; on-board adaptive model; artificial neural network; tailoring
architecture; domain decomposition
Domain Knowledge and Neural
Network Model. Aerospace 2023, 10,
493. https://doi.org/10.3390/
aerospace10060493
Academic Editors: Erinc Erdem and
Ernesto Benini
Received: 17 January 2023
Revised: 15 March 2023
Accepted: 19 May 2023
Published: 23 May 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1. Introduction
As a complex system with high-reliability requirements, aircraft engines are developed
with engine health management (EHM) to increase reliability [1]. With the advancements in
avionics, research focused on EHM is developing from off-board to on-board [2]. Compared
to the off-board EHM, on-board EHM enables real-time continuous engine performance
monitoring [3]. One important task in on-board EHM is building an on-board adaptive
model to predict the engine performance, specifically thrust [4].
In general, an on-board adaptive model consists of an on-board real-time model and
a modifier [5]. The on-board real-time model is typically a linearized model based on an
aerothermodynamics-based component-level model of engine [6]. Currently, the Kalman
filter [7] is commonly used, and effective methods for correcting the results are predicted by
an on-board real-time model. Many improvements to the Kalman filter were given [8–10]
to increase the accuracy of parameter prediction. Further, the e-storm model for parameter
estimation was presented based on the Kalman filter method by NASA [11]. A novel
linear parameter-varying approach was made for thrust estimation [12], and developing an
on-board adaptive model is still attractive. It is remarkable that on-board real-time model
accuracy is crucial for the on-board adaptive model. However, complex objecting modeling
such as aircraft engines require conditional assumption and can suffer from errors caused
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Aerospace 2023, 10, 493
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by modeling methods and model solving, decreasing the model accuracy [13,14]. For
aircraft engines, the strong coupling in the engine systems and the degradation of engine
performance is difficult to be represented by the high-precision physical model.
On the other hand, data-driven methods have been developed for an on-board adaptive model for predicting engine parameters [15,16]. Data-driven methods discard physical
equations and obtain information from data. Through sufficient representative data, datadriven methods use mathematics to find a model or a combination of models that approximate the exact physical model. Four typical data-driven methods, including Random Forest
(RF), Generalized Regression Neural Network (GRNN), Support Vector Regression (SVR),
and Radial Basis Neural Network (RBNs) have been used to develop a temperature baseline
model for aircraft engine performance health management [17]. Zhao et al. performed
much research on support vector machines (SVMs) and used SVMs for aircraft engine
parameter estimation [18]. Zhao studied other methods for thrust prediction, such as radial
basis networks [19]. An extreme learning machine is also used in aircraft engine parameter
estimation [20]. However, the quality and quantity of data greatly affect the final result in a
data-driven method. Relying solely on the data without physical constraints may produce
an unreasonable result in data-driven methods [21].
To address the issue that the accuracy of the data-driven method model is limited
by the training dataset, hybrid methods that incorporate physical information have been
developed [22,23]. Reference [24] describes three methods for adding physical information
to neural networks (a kind of data-driven method), namely observational biases, inductive
biases, and learning biases. Observational biases add data that reflect underlying physical
principles to the neural network. For example, data augmentation techniques [25] such as
rotating, zooming, flipping, and shifting an image can create additional data that reflect
physical invariance. Inductive bias is how to tailor a neural network architecture to satisfy
a set of physical functions; for example, a node in a neural network can represents a physical symbol, and the connection between the nodes can satisfy the operator in a physical
function [26,27]. Learning biases can be introduced by the intervening training phase of a
data-driven model, and the training of a model converges towards a solution that adheres
to underlying physical constraints. One way to introduce learning biases is by imposing
physical equations or principles to penalize the loss function of conventional neural networks [28,29]. The above-mentioned methods for the hybrid model relate to differential
or algebraic equations. However, due to the complexity of the physical equations related
to aircraft engine systems, these methods for an on-board model may be challenging to
implement in the short term.
To avoid the complexity of dealing with mathematical physical equations, the focus
of this study was to explore the combination of aircraft engine knowledge and the neural
network models. In this study, an on-board adaptive model for predicting engine thrust
is given by blending engine domain knowledge and the neural network models. In
Section 2, the architecture of the hybrid model is presented in detail, which fuses networks
for predicting engine parameters. The section also provides a brief introduction to the
traditional neural network model. Additionally, the relationships between aircraft engine
features are described to explain why the model trained with ground measurable data can
be used in the flight condition. Next, a model for predicting engine thrust based on the
architecture is discussed. In Section 3, the models are verified using simulation data and
compared with conventional neural network models. Finally, Section 4 concludes the study.
2. On-Board Adaptive Model
2.1. Architecture by Fusing Physical Structure and Neural Network
Inspired by the integration of coupling relationships between engine components
(such as Figure 1a), the domain decomposition approach is used to deconstruct the neural
network structure. In the digital space, a large neural network is divided into multiple
independent neural networks, corresponding to engine components in the physical space.
The coupling relationships guide the interconnection of independent neural networks in
Aerospace 2023, 10, 493
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the digital space. The architecture integrates neural networks and aircraft engine domain
knowledge using the following points:
1.
2.
3.
4.
Aerospace 2023, 10, x FOR PEER REVIEW
Based on domain decomposition, a neural network is divided into multiple subnetworks and the number of which corresponds to the number of engine components.
A subnetwork represents an engine component, and the input features of the subnetwork are related to the corresponding engine component.
The subnetworks are interconnected based on the interconnection between the engine
components. The order of data flowing through the subnetwork is based on the
order in which air flows through the engine component. For example, the air flows
sequentially through an inlet, a fan, and then a compressor. Correspondingly, the
data flow sequentially through an inlet subnetwork, a fan subnetwork, and then a
compressor subnetwork.
The physical constraint on the networks is that the rotation speed of the components
4 of 17
on the same axial is equal. For example, the same rotation speed is used as input to a
fan subnetwork and a low-pressure turbine subnetwork.
Direction of airflow in aeroengine
Airflow in air system
Control order
Control System
Bypass
Inlet
Fan
Compressor
HP Turbine
Combustor
LP Turbine
Air System
(a)
Target parameters
Mapping Layer
Coupling
Layer
Inlet
network
Measured
parameters
Compressor
network
Combustor
network
HP
Turbine
network
System
network
……
LP
Turbine
network
Fan
network
Input from data
Input from network
(b)
Figure
engine
structure
and
neural
network
architecture.
(a) A
sketch
of anof
Figure1.1.Aircraft
Aircraft
engine
structure
and
neural
network
architecture.
(a)constructure
A constructure
sketch
aircraft
propulsion.
(b) A sketch
of the architecture
enabledenabled
by fusingbyengine
and neural
an aircraft
propulsion.
(b) A sketch
of the architecture
fusingstructure
engine structure
and
network.
neural network.
Specifically,
thedescription,
architectureitconsists
three
that makearchitecture
up the neural
networks.
From
the above
can be of
seen
thatlayers
the presented
serves
as a
The first layer
is the component/system
learning
second
is referred
to as
designing
framework
for a predicting model
and itlayer,
is notthe
limited
tolayer
a particular
engine
the coupling
layer,
and the lastneural
layer is
the mapping
layer, as shown
inrelationships
Figure 1b. Each
type.
Compared
to conventional
networks,
incorporating
coupling
of
engine components into neural networks simplifies feature selection. The input features
are filtered and clustered based on the requirements of the component/system networks.
Moreover, the presented architecture does not mandate all input features to be input at
once. Instead, a component/system learning network only reads relevant sensor parame-
Aerospace 2023, 10, 493
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layer performs its function. The component/system learning layer processes the input
features based on the coupling relationships of the engine components. The coupling layer
integrates features according to the operation order of the engine components. The mapping
layer is a regressive analysis that connects abstract features with target parameters.
The component/system learning layer comprises multiple independent neural networks, each of which represents an engine component or system and is referred to as a
component/system learning network. A sequence of component learning networks forms
the main body of the component/system learning layer. The networks are arranged in
the order of components located in the engine main flow. A component network reads
features from two parts: sensor parameters that measure the corresponding component and
the feature from a component network in the same shaft. For example, the inlet network
reads the total pressure at the inlet entry, and the high-pressure turbine network reads
the corresponding component feature and the feature from the compressor network. The
combustor network receives the fuel flow rate as input, and the turbine network reads the
temperature and pressure measured at the component section. Thus, the physical constraint
that components working on the same shaft have an equal rotation speed is mapped to the
digital space. A system learning network, such as an oil system network or a control system
network, also reads the corresponding parameters to learn the system characteristics. The
position of a system network is determined by the role of the corresponding system in
the engine. Therefore, the number of component/system learning networks equals the
number of engine components/systems. After processing the measured variables, the
component/system learning layer outputs the abstract features as input to the coupling
layer. The role of the coupling layer is to learn the relation between components/systems
and extract a coupling feature from the discrete features of component/system networks.
Like the sequence in which air flows through engine components, the data transmission in
the coupling layer follows this order. Finally, the mapping layer associates the feature from
the coupling layer with the aircraft engine performance parameter.
From the above description, it can be seen that the presented architecture serves as
a designing framework for a predicting model and it is not limited to a particular engine
type. Compared to conventional neural networks, incorporating coupling relationships of
engine components into neural networks simplifies feature selection. The input features
are filtered and clustered based on the requirements of the component/system networks.
Moreover, the presented architecture does not mandate all input features to be input at once.
Instead, a component/system learning network only reads relevant sensor parameters,
thereby reducing the need for network nodes and avoiding direct processing of unrelated
input features.
2.2. Component Network
The component networks play a crucial role in the training of presented architecture.
One of the simplest methods for component network is to use the mature artificial neural
network (ANN) [30], such as a fully connected neural network (FNN), recurrent neural
networks (RNNs), convolutional neural networks (CNNs), etc. The neural network model
consists of stacked neural networks, where the network is made up of nodes that store
information. Nodes receive input data and distribute independent weights for each output.
Figure 2 illustrates the standard mode of node connection. In a fully connected neural
network, the connections between nodes are unidirectional and only exist from one layer to
the next layer. As such, a fully connected neural network focuses on extracting features from
single data but ignores the relationship between the data in space or time. To address this
issue, recurrent neural networks were introduced. RNN is an ANN with a self-circulating
structure composed of nodes participating in recursive computations, which is called a
cell in terminology. The cell transfers information from the previous calculation to the
following calculation, thereby improving the performance on sequence data. However,
long-term dependence issues such as information morphing and vanishing may occur
Aerospace 2023, 10, 493
network, the connections between nodes are unidirectional and only exist from one layer
to the next layer. As such, a fully connected neural network focuses on extracting features
from single data but ignores the relationship between the data in space or time. To address
this issue, recurrent neural networks were introduced. RNN is an ANN with a self-circulating structure composed of nodes participating in recursive computations, which is
5 of 17
called a cell in terminology. The cell transfers information from the previous calculation
to the following calculation, thereby improving the performance on sequence data. However, long-term dependence issues such as information morphing and vanishing may ocwhen
vanilla
RNN RNN
processes
overtime
sequences.
Long short-term
memorymemory
(LSTM) (LSTM)
neural
cur when
vanilla
processes
overtime
sequences.
Long short-term
network
was
introduced
to
handle
long-term
dependence
[31].
neural network was introduced to handle long-term dependence [31].
ANN
RNN
CNN
Direction of kernel moving
Direction of information transfer
Node
Cell
Kernel
Figure2.2.The
Thestandard
standardmodes
modesofofnode
nodeconnection
connectionininartificial
artificialneural
neuralnetworks.
networks.
Figure
AnLSTM
LSTMnetwork
networkisis
a kind
RNN
with
a gate
function.
There
are three
funcAn
a kind
of of
RNN
with
a gate
function.
There
are three
gate gate
functions
tions
in an LSTM
cell: gates,
input gates,
and output
The input
gate controls
in
an LSTM
cell: input
forget forget
gates, gates,
and output
gates. gates.
The input
gate controls
how
much
input information
is transmitted.
The forget
selects
part of athe
information
in
how much
input information
is transmitted.
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forget
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The three
are
asformulas
follows: are as follows:
gate
f t = σ W f [ h t −1 , x t ] + b f
(1)
f = σ ( W f  ht -1 , xt  + b f )
(1)
t
it = iσ (=Wσi [(hWt−
, x ]+b )
i 1ht −1 ,t xt  + ibi )
(2)
(2)
= tanh
 +bbcc))
C t =Ctanh
htc− 1ht,−1x,tx]t+
(Wc([W
t
(3)
(3)
t
f ⊗ C
+ i ⊗ C
Ct C=t f=t ⊗
t Ct−1t −+
1 it ⊗
t Ct t
O
(
= σ Wo  ht −1 , xt  + bo
)

Ot = tσ(Wo [ht−1 , xt ] +
bo )
(4)
(4)
(5)
(5)
h = O ⊗ tanh ( Ct )
(6)
t
t
ht = Ot ⊗ tanh(Ct )
(6)
wherebbrepresents
representsthe
thebias;
bias;W
Wrepresents
representsthe
thelearnable
learnableweights
weightsof
ofthe
thenodes;
nodes;xxrepresents
represents
where
the
input
features;
h
represents
the
hidden
state
of
the
LSTM
cell
that
is
the
cell
output
the input features; h represents the hidden state of the LSTM cell that is the cell output
features;
subscript
t
represents
the
number
of
cells;
subscript
f
represents
the
forget
gate
features; subscript t represents the number of cells; subscript f represents the forget gate
parameters;subscript
subscriptiirepresents
representsthe
theinput
inputgate
gateparameters,
parameters,and
andsubscript
subscriptoorepresents
represents
parameters;
⊗
σ
the
output
gate
parameters.
represents
the
tensor
product.
is
a
sigmoid
function
the output gate parameters. ⊗ represents the tensor product. σ is a sigmoid function
that
that
produces
a
result
range
of
0
to
1.
The
information
flow
process
of
an
LSTM
cell is
produces a result range of 0 to 1. The information flow process of an LSTM cell is shown
shown
in3.
Figure
3. Generally,
gradient
descent
algorithms
arecommon
the common
methods
in
Figure
Generally,
gradient
descent
algorithms
are the
methods
usedused
for
for training
artificial
neural
networks.
More
details
about
training
algorithms
available
training
artificial
neural
networks.
More
details
about
training
algorithms
are are
available
in
in references
[32–34]
included
in detail.
references
[32–34]
andand
are are
not not
included
in detail.
In some cases, it may be useful to analyze the input features in the reverse order
of the input sequence. In such cases, a bidirectional LSTM (Bi-LSTM) can be employed.
A bidirectional LSTM network is a composite structure of two LSTM networks with the
same cell, where one LSTM network processes the input data in the original order of the
input sequence, and the other processes the same input data in the reverse order of the
input sequence. The outputs of the two LSTM networks are combined into one as the final
network output.
Aerospace 2023, 10, 493
In some cases, it may be useful to analyze the input features in the reverse order of
the input sequence. In such cases, a bidirectional LSTM (Bi-LSTM) can be employed. A
bidirectional LSTM network is a composite structure of two LSTM networks with the
same cell, where one LSTM network processes the input data in the original order of the
input sequence, and the other processes the same input data in the reverse order of the
6 of 17
input sequence. The outputs of the two LSTM networks are combined into one as the final
network output.
Cell state
Current Cell state
Current Hidden state
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the rear component affects the front component when an adverse pressure gradient occurs
in the engine. Therefore, a bidirectional LSTM is selected for the coupling layer.
According
above
Algorithm
outlines the steps involved in develgatedescription,
Pending state
forget gateto the input
output1gate
oping a thrust prediction model based on the presented architecture.
Algorithm 1. The hybrid architecture-based thrust predictionoutput
model.
Hidden state
Determine theconcatenate
number of component networks according tomultiplication
the aircraft engine
addition
Input
type.
2
Connect the component network to build the component learning layer.
Figure
sketch
of an
an LSTM
cell.
arrows
in
indicate
direction
of of
data
transmission.
Figure
AAsketch
of
cell. The
Theare
arrows
inthe
thefigure
figure
indicate
the
direction
data
trans3 3.3.The
component
networks
arranged
in the
orderthe
in
which
air
flows
through
mission.
the
components
in
the
engine.
2.3. Model for Predicting Thrust
4
The output of component networks points to the coupling layer;
Based
the presented
2.3. Model
foron
Predicting
Thrustarchitecture, a model for predicting thrust was built. Firstly,
The output of the coupling layer points to the mapping layer;
the Based
parameters
for
model
training
werea discussed.
The model
training
supervised
the presented
architecture,
model
predicting
thrust
was is
built.
Firstly,
Theon
output
of the mapping
layer is
a targetfor
parameter.
learning
where
the
input
data
and
the
corresponding
output
data
are
provided
to the
the parameters
for
model
training
were
discussed.
The
model
training
is
supervised
learn5
Determine the neural network type for each layer:
model
during
the
training
phase.
For
the
on-board
model,
the
training
phase
of
the
model
ing where theComponent
input data learning
and the corresponding
output data are
provided to the model
layer
(component
FNN;
is typically
completed
in a ground
system,
while
the network):
usage
of the
model
place
on the
during
the training
phase.
For
the
on-board
model,
the
training
phasetakes
of the
model
is
Coupling
Bi-LSTM;
airborne system.
Thus,layer:
the selection
of input features for the model is limited, as both the
typically completed
in
a
ground
system,
while
the
usage
of
the
model
takes
place
on
the
Mapping
layer: FNN.
ground system
and airborne
system must be capable of measuring the selected features.
airborne
system. Thus,
the selection
of input features
for the model
is limited, as both the
6
Measurable
parameters
are classified
component
Thrust is associated with the aircraft
engineby
status,
controlcorrelation;
law, and engine operating
ground system
and
airborne
system
must
be
capable
of
measuring
thethrust
selected
features.
Measurable
parameters
the input for
component
network,
as the
target.
environment.
Consequently,
theare
parameters
related
to the condition
are selected
as
input
Thrust
isPreprocess
associateddata
withwith
the aircraft
engine normalization
status, control method.
law, and engine operating en7
the
Min–Max
features. The relationship between the component performance parameters and the aircraft
vironment.
Consequently,
the the
parameters
related
to the
condition
are MSE
selected
as loss
input
8
Set
the batch size
and
node
number
of the
network;
choose
as the
engine
performance
parameters
reflects
the physical
matching
of components
and the
features.function
The relationship
between
the
component
performance
parameters
and
the
airand
RMSE
for optimization.
entire engine. The
model
represents
the physical matching when these parameters are used
craft9 engine
performance
parameters
reflects
the
physical
matching
of
components
and
to train Training
the modelmodel:
as input and target features. Thus, the thrust data collected from engine
the entireFor
engine.
The
model represents the physical matching when these parameters are
i = 1 to
iter:
testing, including
ground
and high-altitude tests, can be training data for a thrust prediction
used to train Tune
the modelweight
as input
andoftarget
features.
Thus, thethe
thrust
collected from
value
the model
minimize
loss data
function.
model. In this way,the
it is equivalent
to expand
the to
number
of measurable
parameters on the
engine testing,
including
ground
and
high-altitude
tests,
can
be
training
data
for a thrust
airborneEnd
system. The relationship between the parameters is shown in Figure 4.
prediction model. In this way, it is equivalent to expand the number of measurable parameters
on the airborne system. The relationship
between the parameters is shown in
Target feature for Model
Input features for Model
Figure 4.
Next, the specific neural network used in the architecture layer for the prediction
The performance
The parameters
measured
model isparameters
discussed.
For example, the independent
component/system
networks and the
measured in
Expand
in testing
but no in
in flying
mappingboth
layer
fully connected neural
network
the prediction model, while the
flyinguse
and atesting
coupling layer
uses
a bidirectional LSTM. Since the order of engine components is se3、T6
e.g. P
Thrust
quenced in space, LSTM is prioritized to complete the coupling layer. An LSTM reads and
analyses
the inputparameters
features in the forward order of the sequence. For an aircraft engine,
Environmental
1
e.g. P0、T0
Control parameters
e.g. Nl、Nh
Ps:
P0: Total Pressure at exit of Inlet
T0: Total Temperature at exit of Inlet
P3: Total Pressure at exit of Compressor
T6: Exhaust gas Temperature
Nl : Low Pressure Rotor Speed
Nh : High Pressure Rotor Speed
Figure
Figure4.4.The
Therelationship
relationshipbetween
betweenthe
theparameters
parametersin
inthe
thepredicting
predictingmodel.
model.
3. Verification and Discussion
3.1. Case Settings
The dataset used to verify the given method was collected from the performance simulation of a two-spool mixing exhaust turbofan. The engine performance simulation utilized component-level modeling where the thermodynamic cycle in each component is
Aerospace 2023, 10, 493
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Next, the specific neural network used in the architecture layer for the prediction
model is discussed. For example, the independent component/system networks and
the mapping layer use a fully connected neural network in the prediction model, while
the coupling layer uses a bidirectional LSTM. Since the order of engine components is
sequenced in space, LSTM is prioritized to complete the coupling layer. An LSTM reads
and analyses the input features in the forward order of the sequence. For an aircraft engine,
the rear component affects the front component when an adverse pressure gradient occurs
in the engine. Therefore, a bidirectional LSTM is selected for the coupling layer.
According to the above description, Algorithm 1 outlines the steps involved in developing a thrust prediction model based on the presented architecture.
Algorithm 1 The hybrid architecture-based thrust prediction model
1
2
Determine the number of component networks according to the aircraft engine type.
Connect the component network to build the component learning layer.
The component networks are arranged in the order in which air flows through the
3
components in the engine.
4
The output of component networks points to the coupling layer;
The output of the coupling layer points to the mapping layer;
The output of the mapping layer is a target parameter.
Aerospace 2023, 10, x FOR PEER REVIEW
8 of 17
5
Determine the neural network type for each layer:
Component learning layer (component network): FNN;
Coupling layer: Bi-LSTM;
The engine
performance
simulation generated five datasets; one is the training daMapping
layer: FNN.
taset
andMeasurable
four are testing
datasets.
The component
characteristic
6
parameters
are classified
by component
correlation; maps used to generate
Measurable
parameters
are the input for
component network,
the target.
these datasets
are different.
High-pressure
components
work in thrust
harshas
environments
and
7
Preprocess
data
with
the
Min–Max
normalization
method.
have a faster decay rate than other engine components. Thus, different combinations of
8
Set the
batch size and
the node
theaccount
network;for
choose
MSEdegrees
as the loss
component
characteristic
maps
werenumber
createdofto
varying
of degradafunction and RMSE for optimization.
tion in high-pressure components. The four testing datasets are named Testing 1, 2-1, 2-2,
9
Training model:
and 2-3. For
There
are four combinations of the component characteristic maps: Maps A, Maps
i = 1 to iter:
B, Maps C, and
D. Maps
and
D were
generated
by multiplying
the correction
TuneMaps
the weight
valueB,ofC,the
model
to minimize
the loss
function.
factor based
on
Maps
A,
where
the
correction
coefficient
ranged
from
0.7
to
0.99. Maps A
End
were used to generate the training dataset and Testing 1, while Maps B, C, D were used to
generate
Testing
2-1,
Testing 2-2, and Testing 2-3, respectively. Therefore, the training da3.
Verification
and
Discussion
tasetCase
andSettings
Testing 1 simulate an aircraft engine state without performance degradation,
3.1.
while Testing 2 simulates aircraft engine states with varying degrees of performance degThe dataset used to verify the given method was collected from the performance
radation.
simulation of a two-spool mixing exhaust turbofan. The engine performance simulation
The training dataset characterizes the entire operation of an engine from start to stop.
utilized component-level modeling where the thermodynamic cycle in each component
To include as many engine states as possible, the training dataset has 10,001 samples. Testis simulated using a given component characteristic map. Figure 5 shows a sketch of
ing 1 has 40,044 samples and characterizes engine operation under four different control
the component-level model of the engine, which includes an inlet, a fan, a high-pressure
laws, compared to the training dataset. Testing 2 has 10,001 samples and is used to verify
compressor (HPC), a combustor, a high-pressure turbine (HPT), a low-pressure turbine
model aaccuracy
under engine
degradation
state.
(LPT),
mixing chamber,
a bypass,
and a nozzle.
Figure 5. A sketch of the component-level model of the two-spool mixing exhaust turbofan.
Figure 5. A sketch of the component-level model of the two-spool mixing exhaust turbofan.
The engine performance simulation generated five datasets; one is the training dataset
The are
features
fordatasets.
model training
are clustered
based onmaps
Section
2.3,toas
presented
in
and four
testing
The component
characteristic
used
generate
these
Table
1.
Since
the
selected
features
have
difference
magnitudes,
they
are
normalized
using
datasets are different. High-pressure components work in harsh environments and have a
Min–Max normalization. To evaluate the effectiveness of the presented architecture, multiple thrust predicting models are developed based on the conventional neural network
architecture (Figure 6a), simplified block neural network architecture (Figure 6b), and hybrid neural network architecture (Figure 6c). The number of nodes in the predicting mod-
Aerospace 2023, 10, 493
8 of 17
faster decay rate than other engine components. Thus, different combinations of component
characteristic maps were created to account for varying degrees of degradation in highpressure components. The four testing datasets are named Testing 1, 2-1, 2-2, and 2-3. There
are four combinations of the component characteristic maps: Maps A, Maps B, Maps C,
and Maps D. Maps B, C, and D were generated by multiplying the correction factor based
on Maps A, where the correction coefficient ranged from 0.7 to 0.99. Maps A were used
to generate the training dataset and Testing 1, while Maps B, C, D were used to generate
Testing 2-1, Testing 2-2, and Testing 2-3, respectively. Therefore, the training dataset and
Testing 1 simulate an aircraft engine state without performance degradation, while Testing
2 simulates aircraft engine states with varying degrees of performance degradation.
The training dataset characterizes the entire operation of an engine from start to
stop. To include as many engine states as possible, the training dataset has 10,001 samples.
Testing 1 has 40,044 samples and characterizes engine operation under four different control
laws, compared to the training dataset. Testing 2 has 10,001 samples and is used to verify
model accuracy under engine degradation state.
The features for model training are clustered based on Section 2.3, as presented in
Table 1. Since the selected features have difference magnitudes, they are normalized
using Min–Max normalization. To evaluate the effectiveness of the presented architecture,
multiple thrust predicting models are developed based on the conventional neural network
architecture (Figure 6a), simplified block neural network architecture (Figure 6b), and
hybrid neural network architecture (Figure 6c). The number of nodes in the predicting
models is close to the training sample size. To prevent overfitting, a dropout layer with a
0.3 drop rate is added before the mapping layer in every predicting model based on the
number of training samples. Table 2 presents the configuration of the predicting models.
The models AN-1, AN-2, AN-3, and LS-1 are developed based on the conventional neural
network architecture. The models Str-1, Str-2, Str-3, and Str-4 are developed based on the
simple block architecture. The models Str-5, Str-6, and Str-7 are developed based on the
hybrid neural network architecture.
Table 1. The input features for the predicting model.
Type of Parameter
Cross-Section of Component/
Acronym
Component Network
Total temperature/K
Outlet of inlet/T0
Outlet of fan/T25
Exhaust gas temperature/T6
Inlet network
Fan network
LP turbine network
Total pressure/kPa
Outlet of inlet/P0
Outlet of fan/P25
Outlet of compressor/P3
Inlet network
Fan network
Compressor network
Low-pressure rotor speed/Nl
Fan network
LP turbine network
High-pressure rotor speed/Nh
Compressor network
HP turbine network
Fuel flow rate/Wf
Combustor network
Thrust/Fn
Target parameter
Control/controlled
parameter
Aircraft engine performance
parameter
Control/controlled
parameter
LP turbine network
Compressor network
HP turbine network
Combustor network
High-pressure rotor speed/Nh
Fuel flow rate/Wf
Aircraft engine performance parameter
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Thrust/Fn
Target parameter9 of 17
Target parameters
Target
parameters
Mapping Layer
Mapping
Layer
Other
Layer
Second
Layer
Second
Layer
Network
Block
Network
Layer
First
Layer
Network
Layer
Network
Block
Network
Block
Network
Block
First
Layer
Network
Block
(a)
(b)
Target parameters
Mapping Layer
Second
Layer
Compressor
network
Inlet
network
Combustor
network
Fan
network
HP
Turbine
network
Input from data
Input from network
LP
Turbine
network
First
Layer
(c)
Figure 6.
6. The
predicting
model.
(a) (a)
Conventional
network
architecture.
(b)
Figure
Thearchitectures
architecturesfor
forthrust
thrust
predicting
model.
Conventional
network
architecture.
Simple block architecture. (c) Hybrid neural network architecture.
(b) Simple block architecture. (c) Hybrid neural network architecture.
Table 2. The configuration of the thrust predicting model.
Model Name
Architecture
First Layer
Second Layer
Other Layers
The Total Number
of Nodes
AN-1
AN-2
AN-3
Conventional
Conventional
Conventional
FC (100)
FC (100)
FC (100)
FC (100)
FC (60)
FC (50)
\
FC (60)
FC (50)-FC (40)
11,201
10,781
10,681
Str-1
Str-2
Str-3
Str-4
Str-5
Str-6
Str-7
Simple block
Simple block
Simple block
Simple block
Hybrid
Hybrid
Hybrid
BiL (4)
FC (50)-FC (4)
FC (100)
BiL (2)
FC (4)
FC (8)
FC (4)
BiL (32)
BiL (32)
BiL (30)
BiL (32)
BiL (32)
BiL (32)
BiL (48)
\
\
Lambda
\
\
\
\
11,713
11,513
10,101
9821
10,149
10,313
13,857
LS-1
Conventional
BiL (12)
BiL (24)
Sequence Length
(9)
11,569
For a model developed with conventional architecture, all input features are combined
into a vector and fed into the model. In contrast, a model developed using the other two
architectures, input features are grouped into multiple vectors. The input and output layers
for each model are shown in Figure 7. In Table 2, FC represents the fully connected neural
network layer, while BiL represents the bidirectional long short-term memory network
Aerospace 2023, 10, 493
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layer. The value in parentheses indicates the hyperparameter of the network layer. For
example, AN-3 model has four fully connected neural network layers stacked, and the
output nodes of each layer are 100, 50, 50, and 40, respectively. For models developed using
the simple block architecture or hybrid neural network architecture, the configuration of
the first layer network column in Table 2 pertains to each substructure in the first layer of
the model, i.e., the network block structure or component network. For instance, in the
Aerospace 2023, 10, x FOR PEER REVIEW
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Str-5 model, all component networks (the inlet network, the fan network, the compressor
network, etc.) are fully connected neural network layers with five output nodes.
Thrust Output
Thrust Output
Thrust Output
……
……
……
(1×9) Input
(1×2)
(a)
(1×3)
(1×2)
(1×1) (1×1)
(1×2)
Input
(b)
(c)
Thrust Output
……
(1×1)
dimension of feature
(1×2)
(1×3)
(1×2)
(1×1) (1×1)
Input
(d)
Figure
input
layers
and
output
layers
for for
eacheach
model.
(a) AN-1,
AN-2,AN-2,
AN-3.AN-3.
(b) Str-5,
Figure7.7.The
The
input
layers
and
output
layers
model.
(a) AN-1,
(b)Str-6,
Str-5,
Str-7. (c) LS-1. (d) Str-1, Str-2, Str-3, Str-4. The arrows in the figure indicate the direction of data
Str-6, Str-7. (c) LS-1. (d) Str-1, Str-2, Str-3, Str-4. The arrows in the figure indicate the direction of
transmission.
data transmission.
Table
2. The configuration
3.2. Performance
Metric of the thrust predicting model.
Model Name
AN-1
AN-2
AN-3
Str-1
Str-2
Str-3
Str-4
Str-5
Str-6
Str-7
LS-1
A scoring indicator, namely the root mean squared error (RMSE), was used
measure
ThetoTotal
the
loss
in
a
training
process
and
is
denoted
e
(i).
The
RMSE
is
defined
as
follows:
Architecture
First Layer
Second Layer rms
Other Layers
Number of
Nodes
2
N
1
Conventional
FC (100)
(100)
11,201 (7)
eFC
rms (i ) =
∑ (Yi − Ŷi ) \
Conventional
FC (100)
FC (60) N i=1
FC (60)
10,781
Conventional
FC (100)
FC (50)
FC (50)-FC (40)
10,681
The maximum relative deviation (MRD) and the average relative deviation (ARD)
Simple block
BiL (4)
BiL (32)
\
11,713
were chosen as the evaluation indices to evaluate the performance of the presented model:
Simple block
FC (50)-FC (4)
BiL (32)
\
11,513
Simple block
FC (100)
BiL V
(30)
Lambda
10,101
p − Vt
RDi =
, i = 1, 2, . . . , N
(8)
Simple block
BiL (2)
BiL (32)
\
9821
Vt
Hybrid
FC (4)
BiL (32)
\
10,149
Hybrid
FC (8)
(32)( RD , i = 1, 2, . . . \
10,313 (9)
MRD BiL
= max
, N)
i
Hybrid
FC (4)
BiL (48)
\
13,857
Conventional
BiL (12)
BiL (24)
Sequence Length (9)
11,569
1 N
ARD = ∑ ( RDi )
(10)
N i =1
3.2. Performance Metric
where
N represents
the number
of instances
the testing
dataset,
Vpwas
andused
Vt denote
the
A scoring
indicator,
namely the
root meaninsquared
error
(RMSE),
to measpredictive
and the process
test data,and
respectively,
values
are divided
by as
thefollows:
maximum
(i). The
RMSE
is defined
ure
the lossvalue
in a training
is denotedand
ermsthe
value of the dataset. RDj is the relative deviation of the instance
of the jth testing dataset,
2
1 N
ˆ
(7)
e
(i) =
 (Y − Yi )
rms
N i =1 i
The maximum relative deviation (MRD) and the average relative deviation (ARD)
were chosen as the evaluation indices to evaluate the performance of the presented model:
RD
=
V p −Vt
, i = 1, 2,  , N
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MRD denotes the maximum relative deviation of the testing dataset, and ARD denotes the
average relative deviation of the testing dataset.
3.3. Results and Discussion
Each model is trained five times using a training dataset to reduce the randomness
of the training process. The maximum value, minimum value, mean value, and standard
deviation of ARD and MRD for the five results are computed and rounded up to four
decimal places. The results of the models on the four testing datasets are presented in
Tables 3 and 4. The trends of the model prediction results on the four testing datasets are
depicted in Figure 8. Figure 9 displays a histogram of the average MRD of the predicting
models on the four testing datasets. Notably, the performance of LS-1 model on Testing
1 differs greatly from the other models, and its result is not shown in Figure 9a. For ease
of discussion, the models generated with the conventional architecture are collectively
referred to as the conventional models, while the other models are collectively referred to
as the structural models.
Table 3. Results of the thrust predicting models on the testing datasets 1.
ARD
Model
Max
%
Min
%
MRD
Std.
Mean
%
Max
%
Min
%
Std.
Mean
%
2.3970
3.3842
6.0953
3.8817
4.0064
2.0010
4.0629
2.8639
5.0158
3.4931
31.642
1.0077
0.7831
2.0993
0.5153
1.2529
1.0146
0.7235
0.7364
1.2956
1.7716
29.221
0.0065
0.0101
0.0166
0.0149
0.0117
0.0037
0.0133
0.0092
0.0139
0.0067
0.0117
1.5453
2.1747
3.3400
2.7367
2.4521
1.4305
2.6834
2.0084
3.3564
2.6448
30.407
7.7096
6.9304
10.203
7.8605
7.2269
6.9090
6.0721
5.4286
8.0805
4.8455
8.0474
6.0131
2.7426
5.1283
2.2850
1.3958
2.7207
1.6456
1.8546
1.8475
3.2047
4.1085
0.0071
0.0164
0.1871
0.0223
0.0250
0.0157
0.0183
0.0137
0.0305
0.0071
0.0145
6.9651
5.3353
7.1988
4.9320
4.6247
4.9956
3.9637
3.3643
4.7318
4.1794
6.1554
Testing Dataset 1
AN-1
AN-2
AN-3
Str-1
Str-2
Str-3
Str-4
Str-5
Str-6
Str-7
LS-1
1.3633
1.332
2.3639
2.0158
2.9108
1.2415
2.5134
1.6190
2.6263
2.0936
1.2987
0.3610
0.2609
0.8563
0.2241
0.4683
0.3763
0.2215
0.2531
0.5867
0.0780
0.3633
0.0048
0.0045
0.0068
0.0070
0.0098
0.0035
0.0101
0.0053
0.0081
0.0054
0.0042
0.7324
0.8602
1.534
1.3764
1.2643
0.6599
1.4086
0.8957
1.9309
1.3602
0.9355
Testing Dataset 2-1
AN-1
AN-2
AN-3
Str-1
Str-2
Str-3
Str-4
Str-5
Str-6
Str-7
LS-1
3.7842
2.9477
4.2153
5.4999
4.5492
3.1393
2.5373
2.2245
3.6926
3.6972
4.0474
2.6882
1.0322
2.1237
1.2474
0.2893
1.2299
0.6163
0.8123
0.6533
1.4409
1.6943
0.0045
0.0078
0.0095
0.0168
0.0172
0.0076
0.0090
0.0055
0.0154
0.0101
0.00916
3.3160
2.3805
3.1021
2.6325
2.5289
2.0684
1.5616
1.3605
2.0156
2.3213
2.8629
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Aerospace 2023, 10, 493
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Model
Max
%
AN-1
AN-2
AN-3
Str-1
Str-2
Str-3
Str-4
Str-5
Str-6
Str-7
LS-1
3.8091
3.0014
4.2774
5.5318
4.6903
3.1902
2.8107
2.4076
3.7327
3.7408
4.0642
AN-1
AN-2
AN-3
Str-1
Str-2
Str-3
Str-4
Str-5
Str-6
Str-7
LS-1
3.9344
3.1761
4.4586
5.7983
4.8208
3.4819
3.1511
2.5754
3.8069
3.8111
4.3430
2 model, Str-3 model, Str-4 model, and Str-5 model, it can be observed that although the
Table 4. Results
of the thrust
models
onaffect
the testing
2. of the models, they cannot
structures
of networks
usedpredicting
in the first
layer
the datasets
accuracy
play a decisive
role in model accuracy. For model accuracy,
the architectural design of a
ARD
MRD
model is more important than which structure of a network is used in a model. In general,
Mean
Mean
Max
Min
Min
Std.
Std.
the Str-5
with the
is superior to%other mod%
% hybrid architecture,
%
% model, a structural model
els in terms of robustness
and stability. The Str-6 model adjusts the node number of comTesting Dataset 2-2
ponent networks to change the model sizing, while the Str-7 model adjusts the model siz2.7000
0.0044
3.3428
7.6944
6.0316
0.0070
6.9876
ing 1.0153
by changing0.0081
the node number
of the
second layer
network.0.0162
Compared5.5582
to the model
2.4119
6.9846
2.8165
performance
of0.0096
Str-5 and Str-6
on Testing
2, the model
by 1.6% 7.2430
but the MRD
2.1498
3.1463
10.229
5.1809size varies
0.0186
1.2685 by more
0.0168
7.8891
0.0224 which 4.9705
increases
than 1%.2.6604
However, in
the case of2.3098
the Str-7 model,
increased the
0.3445
0.0171
2.6489
7.2254
1.2766
0.0252
4.7164
model
sizing
by
36.53%
compared
to
the
Str-5
model,
it
showed
an
MRD
increase
of less
1.3591
0.0075
2.1474
6.9461
2.8543
0.0154
5.0725
than0.5281
1%. From 0.0130
the results of
the Str-6 model
can be inferred
1.6001
6.3564 and Str-7
1.5174model, it
0.0196
4.0076 that the
0.8850 in the model
0.0063 sizing1.4650
5.6173
1.9695
0.0143
increase
by adjusting
the node number
of the
first layer3.4874
increases the
0.6196
0.0154
2.0597
8.1307
1.9709
0.0301
4.8170
instability of the model.
1.3976
0.0103
2.3859
4.9623
3.1957
0.0075
4.2571
Additionally,
it can be 2.8997
observed that
the performance
models on6.1853
Testing 2-3 is
1.7461
0.0090
8.0599
4.1571 of the
0.0143
the least favorable when
compared to the other testing datasets, suggesting that the disTesting Dataset 2-3
parity between Testing 2-3 and the training dataset is the greatest. Figure 10 shows the
2.8795
0.0042
3.5255
7.8176
6.1732
0.0069
7.1332
thrust
value difference
between
2-3 and the2.9314
training dataset.
on Figure 10
1.0413
0.0087
2.5571 Testing7.1321
0.0163 Based5.7190
and2.3525
the outcomes
of
models
Str-5
to
Str-7
on
Testing
2-3,
it
can
be
concluded
0.0095
3.3026
10.287
5.2857
0.0183
7.3590that a 5%
1.4903
0.0172
2.8747
8.1181
2.4377
0.0229
variation between the training and testing datasets is acceptable. Despite a 5.1395
significant re0.0449
0.0171
2.7945
7.2504
1.4033
0.0246
4.8515
duction
in its MRD
compared
to Testing
1, the LS-12.9540
model performance
on5.2498
Testing 2 re1.5350
0.0079
2.3974
7.1504
0.0158
mains
subpar,
with
an
MRD
still
above
5%.
This
could
be
attributed
to
the
use
of distinct
0.3398
0.0118
1.7532
6.5569
1.4514
0.0194
4.2091
0.8158
0.0072
1.5926
5.7334
2.0804
0.0146
3.5879
component characteristic map in engine performance simulation, resulting in a lower
0.6172
2.1314
8.1673
2.0353
4.8812 value of
thrust
value for0.0155
Testing 2 than
for Testing
1. However,
when the0.0301
predicted thrust
1.3497
0.0106
2.4564
5.0550
3.1940
0.0078
4.3224
the 1.9969
LS-1 model 0.0091
is lower than
the test data,
the model4.3434
performs better
3.1685
8.2561
0.0144 on Testing
6.36922 than on
Testing 1.
(a)
Figure 8. Cont.
(b)
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Aerospace 2023, 10, 493
13 of 17
Aerospace 2023, 10, x FOR PEER REVIEW
(c)
14 of 17
(d)
(c)
(d)
Figure
8.
The
trend
of
model
thrust
prediction
on
testing
datasets.
(a)
1.
(b)
2-1. (c)
Figure 8.
8.The
Thetrend
trendofofmodel
model
thrust
prediction
testing
datasets.
(a) Testing
Testing
1.Testing
(b) Testing
Testing
2-1.
Figure
thrust
prediction
onon
testing
datasets.
(a) Testing
1. (b)
2-1. (c)
Testing
2-2.2-2.
(d)
Testing
2-3.
(c) Testing
2-2.
(d) Testing
Testing
(d) Testing
2-3.2-3.
(a)
(a)
(b)
(c)
(c)
(b)
(d)
(d)
Figure
Testing
1. 1.
Figure 9.
9. Histogram
Histogramon
onthe
theMRD
MRDofofthe
thethrust
thrustpredicting
predictingmodels
modelson
ontesting
testingdatasets.
datasets.(a)(a)
Testing
(b)
Testing
2-1.
(c)
Testing
2-2.
(d)
Testing
2-3.
(b) Testing 2-1. (c) Testing 2-2. (d) Testing 2-3.
Figure 9. Histogram on the MRD of the thrust predicting models on testing datasets. (a) Testing 1.
(b) Testing 2-1. (c) Testing 2-2. (d) Testing 2-3.
Aerospace 2023, 10, 493
14 of 17
Table 3 shows that all models have small ARDs. Furthermore, the maximum and
minimum values of MRD are mostly below 5% for Testing 1. Not all the structural models
perform better than the conventional models on Testing 1. Since the component characteristic maps used in the performance simulation to generate Testing 1 are identical to the
training dataset, a model performing well on Testing 1 may rely on the training data. Thus,
it is more important to evaluate the performance of the models on the testing dataset that
differs from the training data if the model accuracy is met. Additionally, the results of
conventional models indicate that increasing the depth or complexity of the model layer
does not necessarily improve the model performance.
Engine degradation is a common phenomenon during the lifetime of its use, which
leads to a decrease in thrust. When a model predicts thrust in real-time, the engine state
represented by the input data typically differs from the engine state represented by the
training data. To evaluate the model performance in such situations, it is further tested with
testing datasets representing the engine in the degraded state. Thus, the model performance
in Testing 2 reflects their robustness. The results presented in Tables 3 and 4 show that
the structural models exhibit better robustness than the conventional models. This can be
attributed to the fact that the structural models integrate the domain knowledge, reducing
the reliance on data. Consequently, the performance degradation of the structural models
is lower than that of the conventional models when the testing data significantly differ
from the training data. Figures 8 and 9 indicate that the performance of the models on each
subset of Testing 2 is similar.
The model performance on Testing 2 shows that the average statistics for ARD and
MRD of the structural models are mostly less than 5%. By comparing the Str-1 model,
Str-2 model, Str-3 model, Str-4 model, and Str-5 model, it can be observed that although
the structures of networks used in the first layer affect the accuracy of the models, they
cannot play a decisive role in model accuracy. For model accuracy, the architectural design
of a model is more important than which structure of a network is used in a model. In
general, the Str-5 model, a structural model with the hybrid architecture, is superior to
other models in terms of robustness and stability. The Str-6 model adjusts the node number
of component networks to change the model sizing, while the Str-7 model adjusts the
model sizing by changing the node number of the second layer network. Compared to the
model performance of Str-5 and Str-6 on Testing 2, the model size varies by 1.6% but the
MRD increases by more than 1%. However, in the case of the Str-7 model, which increased
the model sizing by 36.53% compared to the Str-5 model, it showed an MRD increase of
less than 1%. From the results of the Str-6 model and Str-7 model, it can be inferred that the
increase in the model sizing by adjusting the node number of the first layer increases the
instability of the model.
Additionally, it can be observed that the performance of the models on Testing 2-3
is the least favorable when compared to the other testing datasets, suggesting that the
disparity between Testing 2-3 and the training dataset is the greatest. Figure 10 shows the
thrust value difference between Testing 2-3 and the training dataset. Based on Figure 10 and
the outcomes of models Str-5 to Str-7 on Testing 2-3, it can be concluded that a 5% variation
between the training and testing datasets is acceptable. Despite a significant reduction in
its MRD compared to Testing 1, the LS-1 model performance on Testing 2 remains subpar,
with an MRD still above 5%. This could be attributed to the use of distinct component
characteristic map in engine performance simulation, resulting in a lower thrust value for
Testing 2 than for Testing 1. However, when the predicted thrust value of the LS-1 model is
lower than the test data, the model performs better on Testing 2 than on Testing 1.
Aerospace 2023, 10, 493
x FOR PEER REVIEW
1515ofof 17
17
The thrust
thrust value
value difference
difference between Testing 2-3 and the training dataset.
Figure 10. The
4. Conclusions
4. Conclusions
On-board engine health management (EHM) is developed for ensuring aircraft engine
On-board engine health management (EHM) is developed for ensuring aircraft enreliability. One key component of the on-board EHM is an on-board adaptive model that is
gine reliability. One key component of the on-board EHM is an on-board adaptive model
responsible for monitoring and predicting engine performance. In this study, we present
that is responsible for monitoring and predicting engine performance. In this study, we
an on-board adaptive model for predicting engine thrust. The model is built based on a
present an on-board adaptive model for predicting engine thrust. The model is built based
hybrid architecture that combines domain knowledge of the engine with neural network
on a hybrid architecture that combines domain knowledge of the engine with neural netstructure. By fusing the aeroengine domain knowledge and neural network structure, the
work structure. By fusing the aeroengine domain knowledge and neural network struchyperparameters of neural networks are restricted, the interconnections between neural
ture, the hyperparameters of neural networks are restricted, the interconnections between
networks are tailored, and the data processing workload is reduced.
neural networks are tailored, and the data processing workload is reduced.
To evaluate the effectiveness and robustness of our hybrid architecture, we verified
To evaluate
effectiveness
and robustness
our simulation
hybrid architecture,
weexpected,
verified
predicting
modelsthe
with
different architectures
usingoffour
datasets. As
predicting
models
with
different
architectures
using
four
simulation
datasets.
Asdata,
exthe hybrid architecture reduces the dependence of the neural network on training
pected,
the
hybrid
architecture
reduces
the
dependence
of
the
neural
network
on
training
which is important because engine performance deteriorates over time, leading to differdata,
is important
engine
performance
time,
leading
to
ences which
between
the engine because
state used
for model
training. deteriorates
In order to beover
used
on an
airborne
differences
between
the
engine
state
used
for
model
training.
In
order
to
be
used
on
an
system, the robustness of the on-board model is crucial. Thus, the thrust predicting model
airborne
system,
thearchitecture
robustness is
ofmore
the on-board
is crucial. Thus, the thrust predictbuilt by the
hybrid
suitable model
for EHM.
ing model built by the hybrid architecture is more suitable for EHM.
Author Contributions: Software, formal analysis, and writing—original draft preparation, Z.L.;
Author
Contributions:
Software,
formal analysis,
draft preparation,
Z.L.;
writing—review
and editing
and supervision,
H.X.; and
data writing—original
curation and writing—review
and editing,
writing—review
and
editing
and
supervision,
H.X.;
data
curation
and
writing—review
and
editing,
X.Z.; resources and writing—review and editing, Z.W. All authors have read and agreed to the
X.Z.;
resources
andof
writing—review
published
version
the manuscript.and editing, Z.W. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the National Natural Science Foundation of China, grant
Funding:
This research
wasScience
fundedand
by Technology
the NationalMajor
Natural
Science
Foundation
of China, grant
number 52076180;
National
Project,
grant
number J2019-I-0021-0020;
number
52076180;
National
Science
and
Technology
Major
Project,
grant
number
J2019-I-0021-0020;
Science Center for Gas Turbine Project, grant number P2022-B-I-005-001; The Fundamental Research
Science
Center
for GasUniversities.
Turbine Project, grant number P2022-B-I-005-001; The Fundamental Research
Funds for
the Central
Funds for the Central Universities.
Data Availability Statement: The data that support the findings of this study are available from the
Data
Availability
Statement:
The data
that
support the
findings of this study are available from the
corresponding
author,
Hong Xiao,
upon
reasonable
request.
corresponding author, Hong Xiao, upon reasonable request.
Conflicts of Interest: The authors declare no conflict of interest.
Conflicts of Interest: The authors declare no conflict of interest.
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