CJA 2396
27 July 2022
Chinese Journal of Aeronautics, (2022), xxx(xx): xxx–xxx
No. of Pages 22
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Chinese Society of Aeronautics and Astronautics
& Beihang University
Chinese Journal of Aeronautics
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Digital twin model of gas turbine and its application
in warning of performance fault
Pr
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cja@buaa.edu.cn
www.sciencedirect.com
Minghui HU a,b, Ya HE a,b,*, Xinzhi LIN c, Ziyuan LU d, Zhinong JIANG a,b,
Bo MA b
13
Received 8 February 2022; revised 6 March 2022; accepted 19 April 2022
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a
Key Lab of Engine Health Monitoring-Control and Networking of Ministry of Education, Beijing University of
Chemical Technology, Beijing 100029, China
b
Beijing Key Laboratory of High-end Mechanical Equipment Health Monitoring and Self-Recovery, Beijing University of Chemical
Technology, Beijing 100029, China
c
Capital Aerospace Machinery Corporation Limited, Beijing 100076, China
d
Hangli (Group) Industrial Co, Ltd, Chengdu 611936, China
7
KEYWORDS
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Gas turbine;
Digital twin model;
Gas-path fault warning;
Deviation degree analysis;
Performance simulation
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Abstract The digital twin-driven performance model provides an attractive option for the warn
gas-path faults of the gas turbines. However, three technical difficulties need to be solved: (1)
low modeling precision caused by individual differences between gas turbines, (2) poor solution efficiency due to excessive iterations, and (3) the false alarm and missing alarm brought by the traditional fixed threshold method. This paper proposes a digital twin model-based early warning
method for gas-path faults that breaks through the above obstacles from three aspects. Firstly, a
novel performance modeling strategy is proposed to make the simulation effect close to the actual
gas turbine by fusing the mechanism model and measurement data. Secondly, the idea of controlling the relative accuracy of model parameters is developed. The introduction of an error module to
the existing model can greatly shorten the modeling cycle. The third solution focuses on the early
warning based on the digital twin model, which self-learns the alarm threshold of the warning feature of gas-path parameters using the kernel density estimation. The proposed method is utilized to
analyze actual measured data of LM2500 +, and the results verify that the new-built digital model
has higher accuracy and better efficiency. The comparisons show that the proposed method shows
evident superiority in early warning of performance faults for gas turbines over other methods.
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Ó 2022 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/).
* Corresponding author.
E-mail address: heya1301@163.com (Y. HE).
Peer review under responsibility of Editorial Committee of CJA.
Production and hosting by Elsevier
1. Introduction
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The gas turbine has become the essential power unit in aviation, shipbuilding, and power industry1–2. However, longterm service easily results in performance faults such as foul-
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https://doi.org/10.1016/j.cja.2022.07.021
1000-9361 Ó 2022 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/).
Please cite this article in press as: HU M et al. Digital twin model of gas turbine and its application in warning of performance fault, Chin J Aeronaut (2022), https://
doi.org/10.1016/j.cja.2022.07.021
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Thus, there is still research work to be done in improving
the performance simulation of the gas turbines.
The volume inertia substitution method plays an important
role in improving simulation efficiency24–25. This method
mainly involves the unsteady mass balance across the plenum,
and establishes the differential equation of pressure and flow
to replace the transient flow balance equation. The calculation
is simplified by a differential equation instead of a balanced
equation. Obviously, this technique avoids each iteration of
the correct function in the balanced equation, so it reduces
the calculation time of each integration step and improves
the efficiency and real-time of the design point. However, the
technique still has the problem of easily falling into the local
optimum in the off-design point. The differential equation
established by the inertial substitution method may also lead
to non-convergence of simulation due to the excessive pursuit
of the local exact solution.
Many scholars have explored the application of performance simulation to gas path fault detection. Urban firstly
proposed the gas-path analysis (GPA) method based on a linear model26, which promotes the development of fault diagnosis technology for gas turbines. Since then, the nonlinear gaspath diagnosis method27 and adaptive gas-path analysis
method11 have been developed successively. Although hundreds of documents have been related to the application of
the GPA model in actual gas turbines since 2000, the simulation model to be embedded in the monitoring system has been
in the testing stage, and has not been popularized and applied.
Two main reasons are as follows. (1) Due to the variety of fault
sources, degrees, and combinations, GPA and its improved
version encounter many difficulties in actual fault diagnosis.
(2) Most gas turbines are equipped with an online monitoring
system when put into use to ensure safe and reliable operation.
However, most of these systems achieve early warning using
fixed threshold alarm, which has poor performance under variable operating conditions. Specifically, it is easy to lead to false
alarms and missed alarms. Although the system can save data
after failure for subsequent analysis, users prefer the system to
provide early warning in case of early performance failure,
because it can avoid more cumbersome maintenance and even
fatal accidents.
The digital twin model was first defined by NASA in
201028, and Tao and Qi commented on its development in
201929. More specifically, some scholars have explored it to
design, manufacturing, operation, and maintenance of
machinery equipment, such as aero engines and gas turbines30–33. Among the application in gas turbines, one of the
most important ideas is developed from performance simulation. For gas turbines and similar equipment, many frameworks of the digital twin have been proposed to monitor
performance and detect failure33–34. Researchers not only
focus on establishing an accurate digital temperature but also
study gas turbine performance prediction and fault diagnosis
based on the digital twin models35–37. Moreover, Panov and
Cruz-Manzo38 have explored the development of performance
digital twin based on real-time embedded computing, which
can be leveraged with Internet-of-Things (IoT) cloud platforms. However, the research on performance fault early warning driven by the digital twin model needs to be supplemented.
To tackle the above issues, a digital twin model-based
warning method for performance faults of gas turbines was
ct
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ing, erosion, corridors, abrasion, and damage. When the early
fault evolves into more severe gas circuit failure, it is likely to
be inseparable from enormous economic losses and potential
safety hazards3–4. Therefore, it is urgent to accurately and
timely warn performance faults to ensure the reliability and
availability of gas turbines5–7. The performance model driven
by the digital twin provides an effective solution for fault early
warning of gas turbines8–10.
The performance model is the rudiment of the digital twin;
In other words, before defining the term the digital twin, some
scholars have studied the performance model and suggested
applying it to fault warning11–12. The general idea is that the
simulation results of the performance model are regarded as
a reference for the gas path parameters, and the gas path state
can be judged by comparing the measured data with the reference value. However, this method has not been popularized for
the following reasons. (1) It is well known that the performance model is based on component maps. In fact, the manufacturer provides a set of general component maps for the
same type of gas turbine, that is, the performance models of
the same type share the same map13. However, due to different
manufacturing, assembly, and service conditions, there are
component performance differences among individuals of the
same type, thus bringing obvious deviation between the simulation results of the model and the actual values. It is difficult
to meet the high-precision requirements of the digital twin
model. (2) Traditionally, higher simulation precision of the
model is achieved by ensuring solution accuracy of each balance equation, which inevitably requires a large number of
iterative calculations. However, this will seriously reduce the
simulation efficiency, leading to excessive simulation and poor
convergence, contrary to the real-time ability of the digital
twin model. (3) Most works of literature focus on the establishment and optimization of gas turbine performance models14,
but few are devoted to solving the interaction between model
simulation parameters and the measured data and exploring
excellent early fault features to achieve effective gas-path fault
warning.
Many methods to improve the simulation accuracy are proposed, among which the most popularly used is the adjustment
of component mapping that includes scaling method15, stagestacking method16, and regression-characteristic-fitting
method17. The scaling method can obtain the approximate
component characteristics of the equipment by multiplying
the original curve value by a specific coefficient18. The stagestacking method mainly adjusts the component characteristic
diagram through stage analysis19–20. The regression-featurefitting method aims to establish a new component feature
map generation model, such as the elliptic function and
trigonometric function21–23. The above method can improve
simulation precision, but its premise is that the initial performance state of the model is consistent with that of the actual
gas turbine, which limits its engineering application. Moreover, sufficient component data is unavailable in many cases,
resulting in the actual design point performance of gas turbines
with complex configurations that may not match the performance provided by the manufacturer. In addition, the above
modeling only considers the main parts such as compressor,
combustion chamber, and turbine, while ignoring the auxiliary
parts such as fuel system. The differences in fuel composition
significantly impact the gas turbine’s overall performance.
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M. HU et al.
Please cite this article in press as: HU M et al. Digital twin model of gas turbine and its application in warning of performance fault, Chin J Aeronaut (2022), https://
doi.org/10.1016/j.cja.2022.07.021
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Digital twin model of gas turbine and its application
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2. Theoretical background
2.1. Basic performance model
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2.1.1. Plenum
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The plenum module represents the flow connection part with a
certain volume. In the dynamic calculation, the plenum module mainly considers the pressure change between the inflow
and outflow of the volume:
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dp RTout ðqout qin Þ
¼
dt
V
ð1Þ
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where q represents mass flow rate, p represents pressure, T represents temperature, R represents the gas constant, V represents volume; and the subscripts ‘‘out” and ‘‘in” indicate
outlet and inlet, respectively.
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2.1.2. Combustor
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The combustor mainly produces high-temperature and highpressure gas after the mixture of compressed air and fuel.
According to the principle of mass conservation and energy
conservation, the combustor module takes the volume inertia
of the combustor into account and ignores the thermal inertia
of the combustor. The equations are as follows:
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dpout RTout ðqin þ qf qout Þ pout dTout
¼
þ
dt
Tout dt
V
ð2Þ
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where cp represents the specific heat at constant pressure, Hf
represents heating value, gb represents combustion efficiency;
and the subscript f refer to the fuel.
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2.1.3. Compressor module and turbine module
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Both the compressor and turbine are important parts of a gas
turbine with strong nonlinearity. The former consumes the
power produced by high-temperature and high-pressure gas,
and its working medium is air; the latter expands the gas and
emits power, and the working medium is mixed gas. The solution of their characteristic parameters is similar. In the following section, this paper takes the compressor as an example to
describe the solution process of the working characteristics.
According to the similarity theory, the compressor performance can be expressed by the relationship between four
parameters: pressure ratio (PR), corrected rotational speed
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(n= Tamb =T0 corrected mass flow rate (qð Tamb =T0 Þ=
ðpamb =p0 Þ), and efficiency (g). Herein, amb and 0 indicate ambient and standard conditions, respectively. Given any two
parameters, the working state of the compressor can be completely determined. It is a widely accepted approach to model
compressor modules using compressor maps. If both the speed
and pressure ratio is given, we can obtain the efficiency and
corrected mass flow by the maps. Then, other thermodynamic
parameters can be calculated from the following aerodynamic
and thermodynamic equations.
R
c
Tout ¼ Tin þ Tin PRcp 1 =gc
ð4Þ
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ð3Þ
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At present, modular modeling by volume inertia is the most
generally used performance simulation method to obtain the
basic simulation model of the gas turbines. According to the
volume inertia method23,39, the gas turbine system can be
divided into two modules. One is the plenum module, with a
certain control volume (such as pipeline connection section
and combustor). It considers the volume inertia, the imbalance
of its inlet, and the outlet flow that caused the change in fluid
pressure in the volume. The other is the compressor and turbine module, which is characterized by the clear model physical interface, and its flow characteristics are usually given in
the form of characteristic maps or characteristic curves of
the whole component. Moreover, the assistant modules, such
as the rotor module and load module, can be combined to
form the modular model of the whole system. The establishment of each module is briefly introduced as follows.
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Hf gb qf
Tout ¼ Tin þ
qout cp
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proposed. First, a high-precision performance model was
established by fusing the mechanism model and measured
data, specifically, the initial point of the model was adapted
to make the simulation performance match the actual performance. Then, a relative precision control strategy is proposed
to enhance the modeling efficiency. And the calculation of the
model is reduced appropriately to avoid the troubles of over
simulation and non-convergence. Thus, a digital twin model
obtained will meet the demands of higher accuracy and lower
time cost. Finally, based on the results of the model, a deviation degree is defined as the warning feature for performance
faults of the gas turbines. The threshold is self-learned by kernel density estimation of the measured data. Therefore, the
warning of performance fault can be realized by using the digital twin model of the gas turbine.
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3
0
1
Tout ¼ Tin Tin @1 1 A
gt
R
c
PRtp
R
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c
Pc ¼ qc cp Tin PRcp 1
gc
0
Pt ¼ qt cp Tin @1 210
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ð5Þ
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ð6Þ
1
1 A
gt
R
c
PRtp
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ð7Þ
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where q represents mass flow rate; P represents power; and the
subscripts c and t refer to the compressor and turbine,
respectively.
The thermodynamic properties of the turbine are different
from those of the compressor, but the thermodynamic parameters of the turbine can be obtained by a method similar to the
compressor module mentioned above. Moreover, the turbine
components can also be modeled using component maps.
The precision of the design point in the component maps plays
an essential role in the accuracy of the overall performance
simulation.
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2.1.4. Assistant module
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In addition to the above basic components, some assistant
modules such as the rotor module must be added to form a
complete system model of a gas turbine. The rotor is a component that connects the compressor and the turbine. One end of
the rotor is the turbine that sends out the power, which, in
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Please cite this article in press as: HU M et al. Digital twin model of gas turbine and its application in warning of performance fault, Chin J Aeronaut (2022), https://
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turn, drives the shaft to rotate. The other end is the compressor
that consumes the power caused by the shaft, and the kinetic
energy changes with speed. In the earlier stage, the rotor accelerates or decelerates due to the unbalanced power on the rotor.
In the simulation model, the process from the initial simulation
point to the calculation of target operating conditions can be
regarded as dynamic. In the actual simulation, the rotor module is often over-simulated due to the pursuit of absolute
power equality, which leads to a decrease in simulation speed
or the non-convergence of simulation. According to the law
of momentum, the differential equation of the rotational inertia of the rotor is as follows.
8
>
<
>
:
I dx
¼ ðMeT gmech MeC Þ
dt
2p dN
60
I 60 dt ¼ 2pN
ðPeT gmech PeC Þ
dN
dt
¼
ð8Þ
900
ðPeT gmech PeC Þ
Ip2 N
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2.1.5. Thermal properties of gas
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The properties of working fluid have a crucial influence on the
performance of a gas turbine. In the process of simulation,
these characteristics must be treated strictly.
Specific heat at constant pressure cp, specific heat at constant
volume cv: This is the heat absorbed by raising the temperature
of 1 kg of gas by 1 °C at constant pressure or constant volume.
For a gas turbine, gas flow is stable, so only cp can be used
directly. In the performance calculation, when the Mach number is less than 0.4, the total temperature can be used to calculate cp, which is negligible for the loss of accuracy because the
dynamic temperature is small in proportion to the total
temperature.
The gas constant R: The gas constant often appears in the
pressure and temperature change formula. It is numerically
equal to the difference between cp and cv. The gas constant
of a gas is equal to the general gas constant divided by the
molecular weight of the gas. In addition, the general gas constant is equal to 8314.3 J=ðmol KÞ and is mainly affected by
the fuel properties. When the fuel is gas, the gas constant
changes significantly with a change in the fuel–air ratio; when
the fuel is kerosene or other liquid, the gas constant can be
considered constant.
Calculation method of gas constant: Many reports have
detailed the basic gas properties. To facilitate the calculation,
the polynomial fitting Eq. (9) (describing the relationship
between the gas constant of natural gas as fuel and the change
in the fuel–air ratio) is used in the simulation40–41.
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R ¼ 287:05 þ 212:85FR 197:89FR2
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where FR represents the fuel–air ratio.
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2.2. Calculation and application of gas-path parameters
deviation
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ð10Þ
ð9Þ
After the basic performance model is established, the deviation
of gas-path parameters can be defined using the simulation
model and the measured data, as shown in Eq. (10). The devi-
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where EP is the deviation between the measured value and the
simulated value of the gas-path parameter, Pm is the measured
value of the gas-path parameter, and Ps is the simulated value
of the gas-path parameter, normal value.
The term normal value is considered to be the value of gaspath parameters when the gas turbine operates without faults
under certain atmospheric conditions and control parameters.
The normal value can be achieved in two ways:
(1) Experimental measurement; (2) Establishing a gas turbine performance model. As we all know, it takes a lot of manpower and time to measure the normal value of gas-path
parameters under each atmospheric environment and fuel consumption. Therefore, it is a simple and effective way to get the
normal value through performance simulation, which also
requires high accuracy.
The deviation of gas path parameters can be applied to
fault diagnosis and fault early warning. In the application of
fault diagnosis, the deviation value of component performance
parameters is iteratively solved by using the deviation value of
measured parameters, and then the gas path fault is identified
by using this value according to the corresponding diagnosis
rules. In the application of fault warning, the deviation value
of measured parameters is compared with the alarm threshold,
so as to judge whether the components are unhealthy. The traditional alarm threshold is set based on the experience or
experiment, which is relatively simple and ineffective. The
threshold setting plays a decisive role in judging the fault state.
Therefore, it is an urgent necessity to study the threshold and
alarm rules for accurate early earning.
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3. Proposed method
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A digital twin-based performance fault warning method is proposed in this paper. The principle of the method is shown in
Figs. 1, 3, and 4, and the basic steps are as follows:
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3.1. Establishment of the digital twin model
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3.1.1. Basic performance model
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According to the modularization method, the gas turbine consists of a compressor, combustor, turbine, rotor, plenum, and
other major component performance modules. The compressor module and the turbine module are composed of a characteristic part, a temperature part, and a power part, wherein the
characteristic part is composed of individual characteristic
maps, the temperature part is composed of Eqs. (4) and (5),
and the power part is composed of Eqs. (6) and (7). The combustor module is composed of the pressure part and temperature part in Eqs. (2) and (3), respectively. The rotor module
and the plenum module are composed of Eqs. (8) and (1),
respectively.
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3.1.2. High-precision performance model
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An initial point optimization method is presented to improve
the basic model’s accuracy, and a high-precision performance
model can be obtained.
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ct
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EP ¼ jPm Ps j
ed
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where N represents shaft rotational speed; I represents the
moment of inertia; Pe represents power of shaft; Me represents
torque of shaft; and subscripts C and T refer to the compressor
and turbine, respectively.
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ation is mainly used for fault diagnosis and fault warning of
gas turbines.
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Please cite this article in press as: HU M et al. Digital twin model of gas turbine and its application in warning of performance fault, Chin J Aeronaut (2022), https://
doi.org/10.1016/j.cja.2022.07.021
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3.1.3. Virtual entity: A real-time simulation model
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To further obtain a highly efficient model, the concept of
parameter relative accuracy control is proposed and applied
to the high-precision performance model. The specific processes are as follows.
First, before calculating the power difference,
PeT gmech PeC ¼ DPe in Eq. (8), the gas turbine’s current operating condition should be identified, and then different error
acceptance ranges ½DPe have to be set according to the high
or low operating conditions. If the power difference is acceptable, set the power difference to zero; otherwise, output the
original value of the power difference. Finally, the corrected
power difference has to be output for subsequent calculations.
According to the above steps, we make it run in real-time
based on the high-precision performance model. Then, the virtual entity of the digital twin model can be obtained, as shown
in Fig. 1.
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FRm
T3cal ¼ ðT3 T2 Þ þ T2
FRcal
3.1.4. Digital twin model
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After the virtual entity has been established, a digital twin
model of the gas turbine can be obtained, as shown in
Fig. 2. The physical entity is the actual gas turbine, and we
mainly focus on the measurable performance data. The virtual
entity is the real-time and high-precision simulation model,
and can simulate the performance data under normal status.
Specifically, the physical entity provides some measured data,
such as inlet pressure and temperature of the compressor, as
the input parameters of the virtual entity. Then, the virtual
entity holds that the gas turbine with no-fault and real-time
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nc
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First, temperature (T), pressure (p), and the fuel flow (qf) in
each section from the measured parameters under design conditions are selected as input parameters. The compressor inlet
flow (qc) and the combustor outlet temperature (T3) are preset
as initial values and generally set as design values. Then the
fuel–air ratio (FR) is calculated by the measured fuel flow,
and FRcal is calculated by the preset T3. Using Eq. (6), we iteratively calculate T3 and FRcal until FR and FRcal are equal.
Then, T3 under the current condition can be obtained.
From the calculated T3, the power of a high-pressure turbine (PeT) and compressor (PeC) can be obtained. Then, we
compare PeT and PeC; if the two are equal, we further calculate
the efficiency (g) and flow rate (q) of the current operating conditions of each component; if they are not equal, we repeat the
first step (reset the qc).
The formula for calculating the T3ca of the combustor
according to the FR iteration is as follows.
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Establishment of virtual entity.
ct
Fig. 1
ed
Pr
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Digital twin model of gas turbine and its application
ð11Þ
where T2 represents combustor inlet temperature; T3 represents combustor outlet temperature; FRm represents fuel–air
ratio calculated by measured fuel flow; and FRcal represents
fuel–air ratio calculated by the inlet and outlet temperature
of the combustor, respectively.
According to this step, the initial point of the simulation is
calculated and optimized, and the new initial point is introduced to the basic model to obtain the high-precision performance model.
Please cite this article in press as: HU M et al. Digital twin model of gas turbine and its application in warning of performance fault, Chin J Aeronaut (2022), https://
doi.org/10.1016/j.cja.2022.07.021
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No. of Pages 22
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Framework of digital twin model.
or
Fig. 2
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simulated performance data according to input parameters.
The virtual entity supplies simulated data to the physical entity
as the baseline for comparative analysis.
The measured data and the simulated data compose the
digital-twin data. It includes pressures, temperatures, and rotation speeds in each key unit such as compressor, turbine, and
power turbine. Finally, the digital-twin data can be utilized to
condition monitoring and fault warning of gas turbines, and its
application effect continuously interactive feedback with the
digital twin model.
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3.2. Warning feature construction and threshold self-learning
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To deal with the false alarm and missing alarm caused by the
fixed threshold, a parameter deviation degree is defined as the
warning feature, and the alarm threshold of this feature is selflearned using the measured data of the gas turbine. The specific steps are as follows.
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3.2.1. Deviation degree of gas-path parameters
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First, the actual operating conditions are simulated by the digital twin model. The simulated data obtained by the model is
used as the reference value of the current conditions, and the
maximum and minimum values of the reference value are calculated. Then, we calculate the deviation degree between the
measured data and the reference value according to Eq. (12).
448
r¼
jPm Ps j
100%
ðPmax Pmin Þ=2
ð12Þ
where r represents the deviation degree; Pmax is the simulation
maximum value of the gas-path parameter, and Pmin is the
simulation minimum value of the gas-path parameter. When
the r value exceeds a given threshold, the parameter has serious
deviation, and the system generates an alarm. The threshold
setting was described in detail in Section 3.2.2.
Herein, how to calculate the maximum and minimum value
of the simulation is described in detail. The intake temperature
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o
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Digital twin model of gas turbine and its application
Flow chart of performance fault early warning method.
ed
Fig. 4
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Pðx 6 ½rÞ ¼ 1 a
ð14Þ
where P(x) is the probability in the range, and ½r is the
data boundary under confidence 1-a, that is, the alarm
threshold.
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3.3. Warning of performance fault
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500
For the r defined above, a reasonable alarm threshold has to be
set so that the system can effectively warn performance fault.
We utilize kernel density estimation and normal data to set
the threshold.
First, we select the normal data of the gas turbine with a
certain sample capacity and calculate the r value of each
parameter. Then, we perform a kernel density estimation based
on the r value samples of the normal data to get the kernel density function:
The performance fault warning of gas turbines can be realized
based on the digital twin model and the deviation degree of the
gas path parameters. The specific processes are as follows.
First, the measured ambient temperature, pressure, and fuel
flow are fed to the model, and the simulated value of each
parameter is calculated through the digital twin model. After
that, the simulated value and the measured value are substituted into Eq. (12) to calculate the r value of each parameter.
Finally, the r-value of each parameter is compared with its
alarm threshold. If the alarm threshold is exceeded, the performance of the gas turbine is considered to be in a fault state. As
shown in Fig. 3 and Fig. 4.
x x 1
1
i
f^h ðxÞ ¼
Kh ðx xi Þ ¼
K
h
n i¼1
nh i¼1
4. Analysis of Case 1
512
To verify the effectiveness of the proposed method, the data
under normal and fault states of a gas turbine are used for
modeling and validation. The validation can be divided into
two aspects: 1) the accuracy and efficiency of the digital twin
model; 2) the effectiveness of the warning method.
513
3.2.2. Threshold self-learning based on kernel density estimation
(KDE)
U
nc
473
re
466
and pressure of the model are changed to the upper and lower
limits of the working ambient temperature and ambient pressure of the gas turbine. Then, the maximum value and minimum value of the simulation under the current operating
condition can be obtained.
or
465
ct
Fig. 3 Construction of warning feature and self-learning-alarm
threshold based on KDE.
Finally, the data boundary value under the confidence 1-a
of the selected sample can be obtained, and it is defined as
the alarm threshold of the r value of the parameter:
n
X
n
X
ð13Þ
where K(x) is a kernel function, and it is non-negative, the integral is 1, and the mean is 0, which is consistent with the property of probability density. Commonly used kernel functions
include Gaussian kernel, gamma kernel, triangular, and uniform kernel functions. Moreover, h is the bandwidth, and n
is the sample size.
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4.1. Basic information of gas turbine
519
545
The gas turbine used in this study is LM2500+, a double-shaft
gas turbine for a gas transmission pipeline42. The main components of the gas turbine are a high-pressure compressor (HPC),
a combustor, a high-pressure turbine (HPT), and a power turbine, and the power turbine is connected with the load. The
main design parameters of LM2500+ are shown in Table 143,
and the rated operation parameters of LM2500+ are shown in
Table 2.
The gas turbine selected in this study was overhauled on
November 26, 2017. Fouling was found in the blades of the
HPT and the power turbine during the overhaul. Therefore,
the data of the gas turbine after the last overhaul and before
this overhaul are analyzed. The data of the four operating condition points from May 19 to May 25 are used to validate the
accuracy and real-time ability of the digital twin model, and
representative data are shown in Table 3. A total of 673 sets
of data under normal conditions from June to November are
used for alarm threshold self-learning. The data distribution
interval is shown in Table 4. The data before the overhaul
on November 24 is used to validate the fault warning method,
as shown in Table 5. In the table, P1 represents the inlet pressure of compressor; T1 represents the inlet temperature of compressor; P2 represents the outlet pressure of compressor; T2
represents the outlet temperature of compressor; P4 represents
the outlet pressure of turbine; T4 represents the outlet temperature of turbine; T5 represents the outlet temperature of power
turbine (see Fig. 5).
546
4.2. Establishment of digital twin model
547
4.2.1. Basic performance model
548
According to the structure of LM2500+ and the steps in Section 3.1.1, we establish a basic performance model. The software platform used in this study is MATLAB / Simulink.
The model consists of six modules: the compressor, combustor, high-pressure turbine, power turbine, plenum, and rotor
module, as is shown in Fig. 6. The input parameters are ambient temperature, ambient pressure, and fuel flow, and the output parameters are temperature, pressure, flow, efficiency,
rotational speed, and the power-turbine output power of each
component.
Compressor module: this component comprises a characteristic module, temperature module, and power module. The
characteristic module uses compressor component maps, the
temperature module is represented by Eq. (4), and the power
module is represented by Eq. (6), as is shown in Fig. 7. The
input parameters of the compressor module are air temperature, pressure, outlet pressure, and rotational speed. The air
526
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528
529
530
531
532
533
534
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536
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538
539
540
541
542
543
544
549
550
551
552
553
554
555
556
557
U
nc
558
559
560
561
562
563
564
Table 1
101.3
288.15
9600
2206.3
749.75
1516
482.6
1099.85
of
525
Value
Inlet pressure(kPa)
Inlet temperature(K)
Rotational speed(r/min)
Compressor outlet pressure(kPa)
Compressor outlet temperature(K)
Combustor outlet temperature(K)
Power turbine inlet pressure (kPa)
Power turbine inlet temperature(K)
temperature and pressure are from the external input of the
model, the outlet pressure is from the combustor, and the rotational speed is from the rotor module. Furthermore, the output
parameters of the compressor module are the outlet flow, temperature, and power, in which the outlet flow and temperature
are transmitted to the combustor, and the power is transmitted
to the rotor module.
High-pressure turbine module (HPT): it consists of the
characteristic module, temperature module, and power module. The characteristic module uses the characteristic maps of
the HPT components. The temperature module is represented
by Eq. (5), and the power module is represented by Eq. (7), as
is shown in Fig. 8. The input parameters of the HPT module
are inlet temperature, pressure, fuel–air ratio, outlet pressure,
and rotational speed. The inlet temperature, pressure, and
fuel–air ratio are from the combustor, the outlet pressure is
from the plenum, and the rotational speed is from the rotor
module. The output parameters of the HPT module are inlet
flow, outlet flow, outlet temperature, and power. The inlet flow
is transmitted to the combustor, the outlet flow is transmitted
to the plenum, the outlet temperature is transmitted to the
power turbine, and the power is transmitted to the rotor
module.
Power turbine module: the power turbine and HPT have
similar thermodynamic properties so that the power turbine
module can be established in the same way. The module is
mainly composed of the characteristic module, temperature
module, and power module, in which the characteristic module
uses the maps of power turbine components, the temperature
module is represented by Eq. (5), and the power module is represented by Eq. (7). The structural diagram of the power turbine module is similar to that shown in Fig. 8. The input
parameters of the power turbine module are inlet pressure,
outlet pressure, inlet temperature, and fuel–air ratio. The inlet
pressure is from the plenum, the outlet pressure is from the
outside of the model, the inlet temperature is from the HPT,
and the fuel–air ratio is from the combustor. The output
parameters of the power turbine module are inlet flow, outlet
temperature, output power, and outlet flow. The inlet flow is
transmitted to the plenum, and the outlet temperature, output
power, and outlet flow are transmitted outside of the model.
Combustor module: this is mainly composed of the plenum
and temperature rise part, wherein the plenum is represented
by Eq. (2), and the temperature rise part is composed of Eq.
(3), as is shown in Fig. 9. The input parameters of the combustor module are inlet flow, inlet temperature, outlet flow, and
fuel flow. The inlet flow and inlet temperature are from the
compressor, the outlet flow is from the HPT, and the fuel flow
is from outside of the model. The output parameters of the
Pr
o
524
Parameter
ed
523
LM2500 + rated operation parameters.
ct
522
re
521
or
520
Table 2
LM2500 + main design parameters43.
Parameter
Value
Output shaft power(MW)
Corrected mass flow rate(kg/s)
Corrected rotational speed(r/min)
Compressor pressure ratio
Polytrophic efficiency
29
84.5
9586
23.3
91%
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doi.org/10.1016/j.cja.2022.07.021
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566
567
568
569
570
571
572
573
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575
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577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
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CJA 2396
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No. of Pages 22
Digital twin model of gas turbine and its application
Data of four operating condition points from May 19 to May 25.
Table 4
2017/5/19 10:55
2017/5/21 0:05
2017/5/25 14:25
2017/5/25 18:29
1.18
9660
5893
91.55
1751.43
363.12
295.11
743.24
1065.94
780.67
1.00
9238
5675
92.32
1604.19
335.10
278.99
697.07
980.89
734.27
0.94
9310
5291
91.56
1521.76
317.49
286.74
686.18
972.44
720.86
0.84
9103
5311
92.32
1419.40
297.66
282.70
665.93
919.86
707.73
Data distribution interval for alarm threshold self-learning.
Above 1.0
1.0–0.85
Sample size
9
201
Table 5
Data before this overhaul on November 24.
614
615
616
617
618
Below 0.7
282
133
48
2017/11/24 13:05
2017/11/24 18:33
2017/11/24 19:29
0.94
9164
5536
92.45
1495.78
313.15
282.89
674.84
990.13
743.8
0.86
9068
5336
93.02
1433.66
299.87
282.74
661.73
952.87
739.61
or
U
nc
Fig. 5
0.8–0.7
1.06
9211
5653
92.36
1641.82
337.51
279.12
685.15
1015.25
745.21
re
1.17
9624
5891
92.70
1789.52
366.63
275.86
713.75
1078.3
761.09
ct
2017/11/24 10:19
qf(kg/s)
Ngg(r/min)
Npt(r/min)
P1(kPa)
P2(kPa)
P4(kPa)
T1(K)
T2(K)
T4(K)
T5(K)
0.85–0.8
ed
Interval
(Operating condition)
of
qf(kg/s)
Ngg(r/min)
Npt(r/min)
P1(kPa)
P2(kPa)
P4(kPa)
T1(K)
T2(K)
T4(K)
T5(K)
Pr
o
Table 3
9
42
LM2500 + gas turbine .
combustor module are inlet pressure, outlet temperature, outlet pressure, and fuel–air ratio, in which the inlet pressure is
transmitted to the compressor, the outlet temperature and
pressure are transmitted to the HPT, and the fuel–air ratio is
transmitted to HPT and power turbine.
Pure plenum module and rotor module: the pure plenum
module is represented by Eq. (1), as is shown in Fig. 10. The
input parameters of the pure-plenum module are inlet temperature, inlet flow, and outlet flow, in which the inlet temperature
and inlet flow are from the HPT, and the outlet flow is from
the power turbine. The output parameters of the pure plenum
module are the outlet pressure, which is transmitted to the
HPT and power turbine. The rotor module is composed of
Eq. (8), as is shown in Fig. 11. The input parameters of the
rotor module are the compressor power and HPT power, in
which the compressor power is from the compressor, and the
power of HPT comes from the HPT. The output parameters
of the rotor module are rotational speed, which is transmitted
to the compressor and HPT.
The simulation results of the basic performance model are
shown in Table 6.
To compare the measured and simulated parameters, we
define an error, and its calculation formula is as follows.
ER ¼
Ps Pm
100%
Pm
ð15Þ
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27 July 2022
No. of Pages 22
M. HU et al.
LM2500 + performance model.
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nc
or
re
ct
ed
Fig. 6
Pr
o
of
10
Fig. 7
Compressor module.
648
The measured parameters are shown in Table 3. Then, the
errors of the basic performance model can be obtained, as are
shown in Table 7.
In the table, ER1_P2 represents the error of P2 in the basic
performance model, ER1_P4, ER1_T2, ER1_T4 and ER1_T5
are the same.
From Table 7, we can see that the simulation error of the
basic performance model is large, which cannot characterize
the actual gas turbine.
649
4.2.2. Improvement of the simulation accuracy
650
To enhance the precision of the simulation, on the basis of the
basic performance model, we optimize the initial simulation
point according to Section 3.1.2, and the adaptation of each
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parameter is shown in Table 8. The selected parameters are
involved in the simulation, representing the compressor flow,
pressure ratio, and efficiency of each component.
Deviation value: this is the deviation of the selected parameter before and after adaptation in the initial state of the simulation. It can be defined as follows.
Pa Pd
dv ¼
100%
Pd
653
654
655
656
657
658
659
ð16Þ
where dv represents the deviation value; Pa is the adapted
value of the gas-path parameter, and Pd is the design value
of the gas-path parameter.
A high-precision performance model can be obtained by
optimizing the initial simulation point. The simulation results
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No. of Pages 22
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High-pressure turbine module.
or
re
ct
ed
Fig. 8
Pr
o
of
Digital twin model of gas turbine and its application
U
nc
Fig. 9
Fig. 10
Plenum module.
Combustor module.
of the high-precision performance model are shown in Table 9,
and errors of the high-precision performance model can be
obtained, as are shown in Table 10.
In the table, ER2_P2 represents the error of P2 in the highprecision performance model, ER2_P4, ER2_T2, ER2_T4 and
ER2_T5 are the same.
Then, the simulation results of the basic and high-precision
models are compared. Fig. 12(a)–12(d) show the error comparison between the simulation results of the basic model and the
high-precision model under the design point condition, 0.85
condition, 0.8 condition, and 0.7 condition, respectively. The
abscissa in the figure is the comparison parameter, the ordinate
is the error between the simulation results and the measured
data under normal operation.
The main comparison results are as follows:
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Fig. 11
Simulation results of the basic performance model.
P2(kPa)
P4(kPa)
1
0.85
0.8
0.7
2092.91
1908.25
1822.65
1674.70
456.34
420.87
400.08
373.85
Table 7
Errors of the basic performance model.
ER1_P2(%)
19.50
18.95
19.77
17.99
682
683
684
685
686
687
688
689
690
1096.83
993.84
990.76
951.34
775.49
709.48
721.72
699.02
ER1_T2(%)
ER1_T4(%)
ER1_T5(%)
4.79
2.37
5.20
3.59
2.90
1.32
1.88
3.42
0.66
3.38
0.12
1.23
re
Deviation value (%)
12.1671
5.50296
17.9753
2.50331
4.29619
4.280213
1.19875
U
nc
pc
pt
ppt
gc
gt
gpt
Gc
T5(K)
ER1_P4(%)
Deviation value of the selected parameters.
Parameters
T4(K)
25.67
25.60
26.01
25.60
or
Table 8
778.81
713.57
721.89
689.87
ct
Operating Condition
1.00
0.85
0.80
0.70
T2(K)
ed
Operating Condition
Pr
o
Table 6
Rotor module.
of
12
(1) The simulation error of the basic performance model for
each parameter is relatively large, and the error of the
high-pressure turbine outlet pressure (P4) is even as high
as 25%.
(2) The simulation errors of the high-precision model to
various parameters are no more than ±4%. It can be
seen from the comparison that the precision of the
high-precision model significantly improves compared
with the basic model.
691
precision performance model by using the step in Section 3.1.3,
as is shown in Fig. 13, so that the digital twin model can be
obtained.
The convergence time of the model is used to evaluate the
simulation efficiency of the digital twin model. We compare
the convergence time of the high-precision model and the digital twin model under various operating conditions, as is
shown in Fig. 14. The abscissa in the figure is the selected operating condition, i.e., the design point operating condition, 0.85
operating condition, 0.8 operating condition, and 0.7 operating condition. The ordinate is the time required for convergence of the simulation model.
The main comparison results are as follows:
695
(1) Under each condition, the convergence time of the highprecision model is more than 0.9 s, and reached as high
as 2.35 s, while the convergence time of the digital twin
model is not more than 0.2 s.
(2) Comparing the time under the same operating condition, it can be seen that the convergence time of the digital twin model is less than one-tenth of that of the highprecision model, which shows that the real-time ability
of the digital twin model is obviously better.
708
696
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701
702
703
704
705
706
707
709
710
711
712
713
714
715
716
717
692
4.2.3. Validation of the digital twin model
693
To further promote the real-time ability of the model, the error
module is introduced into the rotor module of the high-
694
In fact, the minimum data acquisition interval of almost all
gas turbine monitoring systems is 1 s, that is, the running time
interval of the actual physical model. However, as can be seen
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doi.org/10.1016/j.cja.2022.07.021
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CJA 2396
27 July 2022
No. of Pages 22
Digital twin model of gas turbine and its application
Table 9
13
Simulation results of the high-precision performance model.
P2(kPa)
P4(kPa)
T2(K)
T4(K)
T5(K)
1751.41
1592.38
1487.90
1369.19
363.12
334.47
313.49
293.39
743.25
684.88
680.33
654.82
1065.85
980.86
969.15
941.66
780.60
745.58
718.64
722.88
Table 10
Errors of the high-precision performance model.
of
Operating Condition
1
0.85
0.8
0.7
ER2_P2(%)
ER2_P4(%)
ER2_T2(%)
ER2_T4(%)
ER2_T5(%)
0.00
0.74
2.23
3.54
0.00
0.19
1.26
1.44
0.00
1.75
0.85
1.67
0.01
0.00
0.34
2.37
0.01
1.54
0.31
2.14
U
nc
or
re
ct
ed
Pr
o
Operating Condition
1.00
0.85
0.80
0.70
Fig. 12
721
722
723
724
725
726
727
Error comparison of simulation results of two performance models.
from Fig. 14, the running time of the virtual entity is far less
than 1 s. Therefore, the digital twin model can meet the
requirements of real-time monitoring and analysis, while the
high-precision model cannot.
The simulation results of the digital twin model are shown
in Table 11, and the errors of this model can be obtained, as
are shown in Table 12.
In the table, ER3_P2 represents the error of P2 in the digital
twin model, ER3_P4, ER3_T2, ER3_T4 and ER3_T5 are the
same.
To verify whether the digital twin model affects the simulation accuracy in improving the real-time performance, we compare the simulation accuracy of the two models under different
operating conditions, as shown in Fig. 15. The abscissa in the
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doi.org/10.1016/j.cja.2022.07.021
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27 July 2022
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Rotor module after adding error module.
Pr
o
Fig. 13
of
14
747
4.2.4. Comparison of the actual parameters and the modeling
parameters
756
To further validate the simulation accuracy of the virtual
entity of the digital twin model, we utilize the model to analyze
five days of performance data of the gas turbine. Analysis
results are shown in Figs. 16–20.
In Figs. 16–20, subgraph (a) has shown trends of the actual
performance parameters and the virtual entity calculation
parameters, and subgraph (b) has shown relative errors
between the two obtained by Eq. (15). Based on these analysis
results, we can conclude that:
758
(1) Whether the gas turbine operates under constant or variable working conditions, the parameters trend of the virtual entity is consistent with that of the actual
performance values;
(2) The errors between the simulation values of the virtual
entity and the actual performance values are very small,
basically less than ±2%.
767
736
737
738
739
740
U
nc
741
figure is the selected comparison parameter, the ordinate is the
error between the model simulation results and the measured
data under normal operation, and the calculation is shown
in Eq. (15).
As can be seen from Fig. 15, the simulation results of the
high-precision model and the digital twin model have similar
errors, so we conclude that the influence of the error module
on the accuracy is within an acceptable range. Meanwhile,
the simulation accuracy of some parameters not only does
not decrease, but has fewer errors than that of the highprecision model. In general, the simulation error of the digital
twin model is less than ±1.5%, and in most cases, less than
or
735
Comparison of simulation time.
re
Fig. 14
ct
ed
± 1%. The reason for this phenomenon is that the highprecision model over-simulated to pursue absolute balance,
thereby reducing the simulation accuracy of some parameters.
The error module avoids this situation as much as possible and
improves the simulation accuracy.
In conclusion, the digital twin model can ensure high simulation accuracy, reduce the convergence time and improve the
simulation efficiency, which can meet the demands of real-time
monitoring and fault warning of gas turbines.
742
743
744
745
746
Table 11
748
749
750
751
752
753
754
755
757
759
760
761
762
763
764
765
766
768
769
770
771
772
773
774
To summarize, the simulation accuracy of the virtual entity
is high, so the virtual entity of the digital twin model can well
characterize the physical entity.
Simulation results of digital twin model.
Operating condition
P2(kPa)
P4(kPa)
T2(K)
T4(K)
T5(K)
1
0.85
0.8
0.7
1761.36
1614.39
1510.41
1410.20
364.86
338.22
317.25
297.95
745.27
689.29
684.57
659.80
1063.55
974.26
963.51
931.84
777.83
737.98
712.07
711.97
Please cite this article in press as: HU M et al. Digital twin model of gas turbine and its application in warning of performance fault, Chin J Aeronaut (2022), https://
doi.org/10.1016/j.cja.2022.07.021
775
776
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Digital twin model of gas turbine and its application
Table 12
15
Errors of digital twin model.
ER3_P2(%)
ER3_P4(%)
ER3_T2(%)
ER3_T4(%)
ER3_T5(%)
0.57
0.64
0.75
0.65
0.48
0.93
0.08
0.10
0.27
1.12
0.23
0.92
0.22
0.68
0.92
1.30
0.36
0.51
1.22
0.60
re
ct
ed
Pr
o
of
Operating condition
1.00
0.85
0.80
0.70
Simulation accuracy comparison.
U
nc
or
Fig. 15
778
779
780
781
782
783
Fig. 16
Analysis results of P2.
Besides, we also analyze the running time of the virtual
entity. The minimum data acquisition interval is 1 s, and the
simulation time of each group of data is less than 1 s, which
indicates the virtual entity is more efficient than the physical
entity. Therefore, the digital twin model can be used for realtime analysis and fault warning.
4.3. Self-learning of alarm threshold of r value
784
The alarm threshold of r has to be set before the warning
method is carried out. The 673 sets of normal operating data
mentioned above are brought into the model for simulation,
and the r values of the corresponding parameters are calcu-
785
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doi.org/10.1016/j.cja.2022.07.021
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No. of Pages 22
M. HU et al.
Analysis results of P4.
ed
Pr
o
Fig. 17
of
16
Analysis results of T2.
or
re
ct
Fig. 18
Analysis results of T4.
Fig. 20
Analysis results of T5.
U
nc
Fig. 19
789
790
lated. Then, we utilize Eq. (13) to estimate the kernel density
for the r value of each parameter.
In kernel density estimation, two aspects are crucial: one is
the choice of the kernel function K(x), and the other is the
Please cite this article in press as: HU M et al. Digital twin model of gas turbine and its application in warning of performance fault, Chin J Aeronaut (2022), https://
doi.org/10.1016/j.cja.2022.07.021
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choice of bandwidth h. The choice of bandwidth is more
important and has a more significant impact on the final estimation result. The Gaussian kernel is selected as the kernel
function, and its formula is as follows:
curve and the coordinate axis on the left side of the boundary
value in the above figure accounted for 99.7% of the total area.
The boundary-value, i.e., alarm threshold of each parameter is
shown in Table 13.
828
1
1 2
KðxÞ ¼ pffiffiffiffiffiffi e2x
2p
4.4. Validation of warning method
832
This section uses the alarm threshold of r values, and selects
the data of four working points from May 19 to May 25 and
the data before overhaul on November 24 to verify the effectiveness of the proposed alarm method.
833
ð17Þ
The mean integrated squared error (MISE) is usually
selected to measure the accuracy of the kernel density
estimation.
Z 2 MISEðhÞ ¼ E
f^h ðxÞ fðxÞ dx
ð18Þ
In the case of large samples, the kernel density estimation is
asymptotically unbiased and consistent, so there is an asymptotic mean integrated squared error (AMISE):
RðKÞ 1
AMISEðhÞ ¼
ð19Þ
þ mðKÞ2 h4 Rðf00 Þ
nh
4
R
R
whereRðgÞ ¼ gðxÞ2 dx;mðKÞ ¼ x2 KðxÞdx.
To minimize it, we find the point where the first derivative
was 0 to obtain the asymptotic optimal bandwidth hAMISE:
1
hAMISE ¼
819
820
821
822
823
824
825
826
ð20Þ
1
After the K(x) is determined, R(K), M(k), and f00 can be
determined in the above formula to obtain the asymptotic
optimal bandwidth hAMISE.
With the Gaussian kernel function, after obtaining its
hAMISE, we apply Eq. (13) to estimate the kernel density of
the sample. The results are shown in Fig. 21.
The confidence of the sample data selected in this study was
99.7%, so according to the r-value KDE function of P2, P4, T2,
T4, T5, the boundary value can be obtained using Eq. (14).
That is, the area enclosed by the kernel density estimation
834
835
836
838
4.4.2. Analysis of fault data
847
Similarly, we calculated the r value of each parameter in
Table 5, as is shown in Fig. 23.
As Fig. 23 shows, three parameters exceed their alarm
threshold under each operating condition: P4, T4, and T5.
Among them, the r value of T4 exceeded 100% under the 1.0
condition. Therefore, an alarm of performance fault is generated by the proposed method.
The subsequent overhaul revealed that the HPT and power
turbine of the gas turbine has a fouling phenomenon; in particular, the HPT blades have severe fouling. Two parameters
related to compressor fouling, i.e., P2 and T2, do not exceed
848
U
nc
Fig. 21
831
According to Section 3.2.1, we substitute the measured data
under normal state into the calculation. Then, the r value of
each parameter under each operating condition can be
obtained, as is shown in Fig. 22.
Based on the above results, the r value of each parameter is
lower than the alarm threshold value under each operating
condition, so it should be judged that the performance of the
gas turbine is healthy, which is consistent with the actual
situation.
or
re
827
1
830
837
ed
818
2
mðKÞ5 Rðf00 Þ5 n5
829
4.4.1. Analysis of data under normal state
ct
817
RðKÞ5
of
794
Pr
o
793
17
KDE of r value of normal data.
Please cite this article in press as: HU M et al. Digital twin model of gas turbine and its application in warning of performance fault, Chin J Aeronaut (2022), https://
doi.org/10.1016/j.cja.2022.07.021
839
840
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843
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Table 13
M. HU et al.
Alarm thresholds for r values based on KDE.
P2(%)
P4(%)
T2(%)
T4(%)
T5(%)
52.5
48.3
33.9
35.9
30.2
860
861
862
the alarm threshold, while the other three parameters related
to turbine fouling, i.e., P4, T4, and T5, exceed the threshold.
This shows that the analysis results are consistent with the
actual situation.
re
859
r value of each parameter under normal state.
ct
Fig. 22
ed
Pr
o
of
Item
r-value
4.4.3. Comparison of false alarm rate and missing alarm rate
864
The case utilizes the normal and fault data of the design point
condition, 0.85 condition, 0.8 condition and 0.7 condition,
which involves five parameters, namely P2, T2, P4, T4, and T5.
In order to more intuitively evaluate the warning effect of
different methods, the BPM-based TA, HPPM-based TA,
DTM-based TA, and the proposed methods are selected to
compare and analyze the warning effectiveness. Herein, it
can be seen from Figs. 22 and 23 that the early warning accuracy of the proposed method is 100%, that is, the false alarm
rate and missing alarm rate are 0. The BPM-based TA, the
HPPM-based TA, and the DTM-based TA method refer to
utilizing the simulation results of the basic model, the highprecision model, and the digital twin model respectively to
set the threshold so as to realize early warning. For the three
methods, we defined two quantitative indicators that include
missed alarm (MA) and false alarm (FA) rate to quantify the
alarming accuracy, as shown in Eqs. (21)–(22).
865
866
U
nc
867
or
863
868
869
870
871
872
873
874
875
876
877
878
879
880
881
P
MA rate ¼ 1 883
ðP1 > Pt1 k ðP2 > Pt2 Þ kjjðP5 > Pt5 ÞÞjFault
100%
Number of data sets
ð21Þ
P
FA rate ¼
ðP1 > Pt1 k ðP2 > Pt2 Þ k jjðP5 > Pt5 ÞÞjNormal
Number of data sets
884
100%
ð22Þ
P
where
ðÞ denotes total number of parameters that satisfy
the condition in brackets. P1, P2, P3, P4, and P5 are the measured value of the gas-path parameter of P2, T2, P4, T4, and
T5 in this paper respectively. Pt represents the threshold set
by Eq. (23).
Pt ¼ Ps þ
Pmax Pmin
2
ð23Þ
Based on the limited case data available, we calculate and
obtain the MA rates, FA rates, and average accuracies of
BPM-based TA, HPPM-based TA, DTM-based TA, and the
proposed method, as shown in Table 14. The results show that
the proposed method has the highest early warning accuracy of
100%, that is, the false alarm rate and missing alarm rate are 0.
This means that this method has obvious superiority compared
to the other three methods in the performance fault warning of
gas turbines. Compared with BPM-based TA, HPPM-based
TA, and DTM-based TA, it can be seen that in addition to
the excellent performance model, the more important reason
for the high early warning rate achieved by the proposed
method is to construct an appropriate warning feature and
self-learning threshold method.
Please cite this article in press as: HU M et al. Digital twin model of gas turbine and its application in warning of performance fault, Chin J Aeronaut (2022), https://
doi.org/10.1016/j.cja.2022.07.021
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No. of Pages 22
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912
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914
915
To further validate the effectiveness of the warning method, we
analyze the normal and the fault data of another gas turbine.
The gas turbine, in this case, is also LM2500+, and a digital
twin model of this gas turbine can be established by the proposed method.
5.1. Alarm threshold self-learning of r value
919
5.2. Validation of warning method
920
The gas turbine has been operating under 0.7 operating condition before the failure causes its shutdown. Therefore, we
mainly analyze the performance parameters before and after
the failure under an operating condition. The calculation
results of r are shown in Fig. 24.
917
U
nc
921
or
918
In the same way, the alarm threshold of each parameter of this
gas turbine can be obtained by kernel density estimation,
which is shown in Table 15.
916
922
923
924
From the above analysis results of this case, it can be concluded that:
925
(1) When the gas turbine is in a normal state, r values of all
parameters are under their thresholds, which means the
warning method has no problem of false alarm.
(2) When the gas turbine is in a fault state, the r value of P4,
36.16% exceeds its threshold, which means that the
warning method sends out the correct alarm.
927
ct
910
5. Analysis of Case 2
re
909
r value of each parameter under fault state.
ed
Fig. 23
Pr
o
of
Digital twin model of gas turbine and its application
Table 14
methods.
Comparison of warning accuracy between four
Methods
BPM-based TA
HHPM-based TA
DTM-based TA
The proposed
method
FA rate (%)
12.5
12.5
0
0
MA rate
(%)
Average
accuracy
(%)
37.5
12.5
25
0
50
75
75
100
926
928
929
930
931
932
933
After the gas turbine was shut down, it is found that blade
tip exhaust edge fracture fault has occurred in the turbine
through borescope, as is shown in Fig. 25. The alarm parameter is the outlet pressure of the turbine P4, which can correspond to the fault phenomenon. Remarkably, the significant
change of the r value of P4 has been enough to attract the
attention of field staff.
In Section 4 and Section 5, it is indicated that the proposed
method can be utilized to realize a real-time and high-precision
performance simulation, moreover, achieve effective warning
of gas-path fault for gas turbine.
934
6. Conclusions
945
This paper presents a digital twin model of gas turbine and
studies its application in warning of performance fault. To
improve accuracy and efficiency, the initial simulation point
is firstly adapted through the measured data so that the performance model is closer to an actual gas turbine. Then, an
operation-condition-related error module is introduced into
the rotor module among the model, which can significantly
promote the real-time ability of the simulation, thus building
the digital twin model with low error and high effectiveness.
Finally, based on the above simulation, a deviation degree of
gas-path parameters is defined as the warning feature, and
946
Please cite this article in press as: HU M et al. Digital twin model of gas turbine and its application in warning of performance fault, Chin J Aeronaut (2022), https://
doi.org/10.1016/j.cja.2022.07.021
935
936
937
938
939
940
941
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950
951
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No. of Pages 22
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Table 15
M. HU et al.
Alarm thresholds of another gas turbine.
P2(%)
P4(%)
T2(%)
T4(%)
T5(%)
50.0
29.6
21.1
36.2
33.4
r values of four parameters under normal and fault state.
U
nc
or
re
Fig. 24
ct
ed
Pr
o
of
Item
Alarm threshold
Fig. 25
957
958
959
960
961
962
963
964
965
966
967
968
Results of a borescope.
the alarm threshold is self-learned of kernel density estimation
of the measured data of gas turbine under normal state.
The proposed method is validated by two actual cases of
LM2500 + gas turbines. The simulation results show that
the errors between the simulated values of the digital model
and the actual values are basically within ±2%, and each calculation time of the model is far less than 1 s. Moreover, the
comparisons indicate that the proposed warning strategy can
achieve accurate warning of performance faults for gas turbines, the false alarm and the missed alarm rate caused by
the fixed threshold can be decreased with the aim of the digital
twin model.
7. Discussions
969
This study presents an early warning scheme with a digital twin
model that enables performance simulation, data sensing, processing, and mapping technologies. This is a good attempt of
the digital twin in the health management of turbomachinery
and realizes the accurate and timely early warning of gas path
failures. There is great hope that it can contribute to the transformation of maintenance strategy for gas turbines. Predictive
maintenance with digital twins will be a bright research
direction.
Traditional gas turbine maintenance strategies mostly stay
in routine maintenance and subsequent maintenance, which
are carried out regularly according to the prior or historical
knowledge of gas turbines. However, lack of accurate fault
warning and diagnosis, the above strategies are conservative
and insecure. This means that it not only increase the cost of
labor, fuel and materials, but also make it difficult to ensure
the reliable operation of the gas turbine. Therefore, by establishing a complete digital twin model, we can intelligently
interact the state data collected in real-time during the operation of a gas turbine with the digital model, and then diagnose
the health state and fault symptoms of the equipment for prognostic and health management. Therefore, the use of gas turbines will meet the requirements of high operation safety,
low maintenance cost, and long availability.
970
Please cite this article in press as: HU M et al. Digital twin model of gas turbine and its application in warning of performance fault, Chin J Aeronaut (2022), https://
doi.org/10.1016/j.cja.2022.07.021
971
972
973
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978
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1001
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1007
1008
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1012
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1014
Nevertheless, the simulation and application of the digital
twin model for gas turbines still face some challenges as follows. (1) The performance model of a gas turbine depends
on the design parameters such as the component characteristic
curve, but it is difficult to obtain a complete curve. (2) In this
paper, two cases have verified the accuracy of the digital twin
model for LM2500 +. However, if this method is used to multiple types of gas turbines, a lot of repeated work will undoubtedly be involved, and the capacity of the model base may be
hard to self-converge. (3) This paper defines an early warning
feature to represent the health state of the gas turbine. Section 4
and 5 have only verified its effectiveness on one type of gas turbine. In the future, it is hoped that this method can be applied
to the real-time early warning engineering of various gas turbines or popularized to other turbomachinery. (4) Digital twin
has great development potential in improving gas turbine from
the design, operation, maintenance of life cycle. Therefore, the
work of this paper still has a lot of research space, which still
requires breakthroughs in crucial technical problems such as
performance model migration, and data-driven analysis.
Declaration of Competing Interest
1018
Acknowledgements
1019
This study was co-supported by the National Postdoctoral
Program for Innovative Talent (No. BX20180031).
1020
ct
1016
ed
1017
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.
1015
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doi.org/10.1016/j.cja.2022.07.021
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