Gas Path On-line Fault Diagnostics Using a Nonlinear Integrated Model for Gas Turbine Engines

Abstract

Gas turbine engine gas path fault diagnosis is closely related technology that assists operators in managing the engine units. However, the performance gradual degradation is inevitable due to the usage, and it result in the model mismatch and then misdiagnosis by the popular model-based approach. In this paper, an on-line integrated architecture based on nonlinear model is developed for gas turbine engine anomaly detection and fault diagnosis over the course of the engine's life. These two engine models have different performance parameter update rate. One is the nonlinear real-time adaptive performance model with the spherical square-root unscented Kalman filter (SSR-UKF) producing performance estimates, and the other is a nonlinear baseline model for the measurement estimates. The fault detection and diagnosis logic is designed to discriminate sensor fault and component fault. This integration architecture is not only aware of long-term engine health degradation but also effective to detect gas path performance anomaly shifts while the engine continues to degrade. Compared to the existing architecture, the proposed approach has its benefit investigated in the experiment and analysis.

Full text

Int. J. Turbo Jet-Engines, Vol.xx(2013), pp.xxx-xxx Copyright © 2013 De Gruyter. DOI xx.xxxx/TJJ.2013.xxx
1
Feng Lu, Jin-quan Huang*, Chun-sheng Ji, Dong-dong Zhang, Hua-bin Jiao
Gas path on-line fault diagnostics using a nonlinear
integrated model for gas turbine engines
Abstract: Gas turbine engine gas path fault
diagnosis is closely related technology that
assists operators in managing the engine units.
However, the performance gradual degradation
is inevitable due to the usage, and it result in the
model mismatch and then misdiagnosis by the
popular model-based approach. In this paper, an
on-line integrated architecture based on
nonlinear model is developed for gas turbine
engine anomaly detection and fault diagnosis
over the course of the engine’s life. These two
engine models have different performance
parameter update rate. One is the nonlinear real-
time adaptive performance model with the
spherical square-root unscented Kalman filter
(SSR-UKF) producing performance estimates,
and the other is a nonlinear baseline model for
the measurement estimates. The fault detection
and diagnosis logic is designed to discriminate
sensor fault and component fault. This
integration architecture is not only aware of
long-term engine health degradation but also
effective to detect gas path performance
anomaly shifts while the engine continues to
degrade. Compared to the existing architecture,
the proposed approach has its benefit
investigated in the experiment and analysis.
Keywords: gas turbine engine; performance
degradation; gas path fault diagnostics;
nonlinear baseline model; spherical square-root
unscented Kalman filter
Corresponding author: Feng Lu: Jiangsu Province Key
Laboratory of Aerospace Power Systems, Nanjing
University of Aeronautics and Astronautics, Nanjing,
210016, P. R. China; and Aviation Motor Control
System Institute, Aviation Industry Corporation of
China, Wuxi 214063, P. R. China. (e-mails:
lufengnuaa@126.com)
Jin-quan Huang: Jiangsu Province Key Laboratory of
Aerospace Power Systems, Nanjing University of
Aeronautics and Astronautics, Nanjing, 210016, P. R.
China.
Chun-sheng Ji: Aviation Motor Control System
Institute, Aviation Industry Corporation of China, Wuxi
214063, P. R. China.
Dong-dong Zhang: Jiangsu Province Key Laboratory of
Aerospace Power Systems, Nanjing University of
Aeronautics and Astronautics, Nanjing, 210016, P. R.
China.
Hua-bin Jiao: Beijing Power Machinery Institute,
Beijing 100074, P. R. China.
1. Introduction
Gas turbine engines are highly complex
systems, and required to provide reliable power
generation over thousands of flight cycles while
being subjected to a broad range of operating
loads and conditions, including extreme
temperature, pressure and vibration
environments. The life of many gas path
components will be consumed over repeated
flight cycles, and engine malfunctions may
occur [1-2]. Engine health management (EHM)
plays a critical role to ensure the safety,
reliability, and affordability of gas turbine
engines, and it has been paid more attentions [3-
4]. Gas path anomaly detection and fault
diagnostics as the important parts of EHM
provide an important basis for assessing engine

Int. J. Turbo Jet-Engines, Vol.xx(2013), pp.xxx-xxx Copyright © 2013 De Gruyter. DOI xx.xxxx/TJJ.2013.xxx
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health status and performance, developing a
maintenance strategy [5].
To achieve a real-time gas path fault
diagnosis capability, a large number of studies
have been performed. Luppold proposed using
Kalman filter to estimate in-flight engine
performance variations [6], and then Kerr
discussed a control-based Kalman filter
algorithm for the gas turbine engine damage
real-time estimation [7]. Brotherton presented a
hybrid model called enhanced STORM
(eSTORM) fused a physical model called self
tuning on-board real-time model (STORM) with
a neural-net compensation model for engine
fault diagnostics [8]. Volponi developed the
eSTORM, and provided a means to
automatically tune for the engine model to a
particular configuration as the engine evolved
over the course of its life, furthermore, aligned
the model to the particular engine being
monitored to insure accurate performance
tracking, while not compromising real-time
operation [9,10]. Simon D. applied constrained
Kalman filtering, along with constraint tuning
on the basis of measurement residuals, to
estimate engine health parameters [11]. Litt
proposed a real-time Kalman filter approach for
estimation of helicopter engine degradation
caused by compressor erosion [12]. Simon D. L.
separately developed a reduced-order Kalman
filter to select sensor and optimal tuners for the
STORM [13]. Li reported a nonlinear weighted-
least-squares method for gas turbine diagnosis
[14]. Borguet disscussed adaptive filters to track
both of gradual deterioration and rapid
deterioration [15]. Naderi proposed a nonlinear
multiple model fault detection and isolation
scheme for health monitoring of jet engines [16].
From the researches above [6-19], we can see
that different model-based approaches for the
dynamic systems gas path fault diagnostics are
mainly used, the most common being the
Kalman filter, and variants of the Kalman filter
algorithm has proven its capability to track
degradation with a good accuracy.
Gas path fault diagnostics model-based
approach via Kalman filter is pursued based on
the fact that the engine measurements deviate
from their reference values (deriving from the
on-board real-time engine model) when the
engine experiences a fault. However, note that
the deviations are influenced not only by faults
but also by the gradual deterioration of engine
performance. Engine health deterioration is a
normal aging process due to usage, but it can’t
be considered as a fault. Given both outputs of
the measured engine and the initial baseline
model, it is difficult to discriminate whether the
engine output deviations are due to a fault or
health deterioration. Unless the baseline model
can well reflect the engine current health
condition over its lifetime. To address this issue,
one method is that the engine health condition is
estimated off-line based on steady-state data
recorded during flight, and then used to update
the performance parameters of the on-board
baseline model [20-22]. The shortcomings of
the off-line estimate include the post-flight
processing of a small number of the
measurements collected each flight and only
available in ground-station. Kobayashi
separately developed a baseline system and an
enhanced system for aircraft engine on-line
diagnostics [23], while they are focused on the
dual-channel sensor measurements.
An enhanced on-board linear architecture for
trend monitoring and gas path fault diagnosis is
presented in references 24, and 25, which gains
real-time access to an expanded quantity of
engine parameters, and provides advanced on-
board model-based estimation capabilities. The
architecture contains real-time adaptive
performance model and performance baseline
model, both of which are built up with
piecewise-linear dynamic scheduled models.
However, the linear model is derived from the

Int. J. Turbo Jet-Engines, Vol.xx(2013), pp.xxx-xxx Copyright © 2013 De Gruyter. DOI xx.xxxx/TJJ.2013.xxx
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engine component level model, and linearization
errors are introduced in the modeling process
that will decrease the accuracy of performance
estimation [26]. The linear approaches for gas
path analysis (GPA) are effective only within a
limited linearized range, and it requires the
linear relationship between the health parameter
and the measurements. Additionally, the health
parameters derivative equal to zero in the state
variable model on the assumption of the
performance varying slowly with time, and then
it could only be used for estimating performance
gradually degradation but the component abrupt
shift [37]. Therefore, with the on-board
computational performance greatly improving,
nonlinear approaches are gradually introduced
to the state estimation for aircraft engine. The
unscented Kalman filter [27, 28], as a
derivative-free alternative to the extended
Kalman filter (EKF), is one of the common
nonlinear methods and had been used to health
estimation [26]. Merwe proposed the UKF with
the square-root forms to improve the numerical
stability and guarantee positive semi-
definiteness of the state covariances [29]. To
improve the computational loads, Julier present
a spherical simplex sigma point selection
strategy for decreasing the number of sigma
points in the UKF [30, 31].
In this paper, an integrated architecture that
utilizes dual nonlinear on-board engine model is
developed for a gas turbine engine on-line gas
path fault diagnostics, and the benefit of this
integration is investigated in the experiments
and analysis. The SSR-UKF is present and is
used for state estimation of the gas turbine
engine. The nonlinear self-tuning real-time
performance engine model, including the on-
board nonlinear model and the SSR-UKF, is
referred to real-time performance estimation.
The baseline model is built up with the same on-
board nonlinear engine model, and its
performance parameters are updated from the
estimates with certain period. The gas path fault
detection and diagnosis (FDD) system is
designed, through which the architecture
achieves the following objectives: 1) real-time
anomaly detection, 2) on-line sensor fault and
component fault diagnosis.
The remaining sections are organized as
follows in this paper. In section 2, the problems
of conventional engine gas path performance
estimate approach commonly used today are
discussed, and the spherical square-root
unscented Kalman filter algorithm is presented
in detail. In section 3, the nonlinear integrated
architecture is developed, including the
nonlinear real-time adaptive performance model,
on-board nonlinear baseline model, and the
FDD system. Experiments are carried out in
Section 4, and the results show that compared to
the conventional architecture, the proposed one
in this paper has better capability to diagnose
both of sensor and component faults with
gradual deterioration. Finally, our work is
summarized in the last section.
2. State estimation for nonlinear systems
In this section we first present the description
of a gas turbine engine. Then the standard
Kalman filter for linear system is summarized,
and the spherical square-root unscented Kalman
filter algorithm for nonlinear system is
presented, respectively.
2. 1 Gas turbine engine description
A gas turbine engine for on-line gas path
fault diagnostics is described by nonlinear
equations of the following form.
, 1 1 1 1
, 1 1 1
,
( , , )
( , )
( , , ) ( , )
k
aug k k k k k
k
aug k k k
k k k k k aug k k k
x
x f x h u w
h
f x u w
y h x h u v h x u v
   
  

  



   
(1)

Int. J. Turbo Jet-Engines, Vol.xx(2013), pp.xxx-xxx Copyright © 2013 De Gruyter. DOI xx.xxxx/TJJ.2013.xxx
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Where
k
is the time index,
x
is the state vector,
h
is the performance vector,
u
is the know
control input,
y
is the measurement.
 
k
w
and
 
k
v
are separately the process noise sequences,
 
k
v
is the measurement noise sequences, and
they are uncorrelated zero mean Gaussian noises.
The performance parameters, representing the
engine health status, are mainly efficiencies and
flow capacities of the rolling components such
as fan, compressor and turbines.
2. 2 Linear Kalman filter
Taylor series is used to expand the Equation
1 around a nominal steady state
0, 0,
,T
kk
xh


, and
the corresponding nominal control input
0,k
u
,
the nominal output
0,k
y
. The augmented linear
equations of the engine with performance
parameters are as follows.
 
1
100
0
k k k
k
k k k
k
k k k
k
x x w
A L B u
h h n
I
xD
y C M u v
h



     
   
   
     
   

   
     



    




(2)
The

quantities are defined as deviations
from the nominal value:
0
x x x  
,
0
u u u  
,
0
y y y  
. The matrices A, B, C,
D, L, M can be calculated by the QPSO hybrid
linearization method [27], and define the
following matrices
 
,,T
aug k k k
x x h   
,
0
aug
AL
AI



,
0
aug
B
B


,
 
aug
C C M
,
0
aug
D
D


. We assume that the following
standard conditions are satisfied.
 
 
0
0
0
k
k
k
k m km
k
k m km
k
km
Ew
Ev
E w w Q
E v v R
E w v













(3)
Where
 
E
is the expect operator, and
km

is
the delta function. In the steady state, then
0
k
u
, and the linear Kalman filter (LKF) is
given as follows.
, | 1 , 1 1
, | 1 , 1
1
, | 1 , | 1
, , | 1 , | 1
, , | 1
ˆ ˆ
()
ˆ ˆ ˆ
()
()
aug aug
aug aug
aug aug
aug k k aug aug k aug k
T
x k k aug x k aug
TT
k x k k aug aug x k k aug
aug k aug k k k k aug aug k k aug k
x k k aug x k k
x A x B u
P A P A Q
K P C C P C R
x x K y C x D u
P I K C P
  





    


        

(4)
2. 3 Spherical square-root unscented Kalman
filter
The LKF summarized in the section 2.2 is
based on off-line linearizing the nonlinear
system around a nominal state trajectory. The
errors are inevitably produced in the model
linearization process, and it will directly
influence the estimation accuracy. The nonlinear
state estimation algorithm, the unscented
Kalman filter (UKF), are widely used in the gas
turbine engine application. The conventional
UKF uses a set of “sigma points”, 2L+1(L is the
state dimension), to depict mean and covariance.
The detailed procedure of the UKF algorithm is
as follows:
(1) Initialize the mean and covariance of the
n
-dimension state vector:
,0 ,0
ˆaug aug
x E x


(5)
,0 ,0 ,0 ,0 ,0
ˆ ˆ
aug
T
x aug aug aug aug
P E x x x x
   
  
   
(6)

Int. J. Turbo Jet-Engines, Vol.xx(2013), pp.xxx-xxx Copyright © 2013 De Gruyter. DOI xx.xxxx/TJJ.2013.xxx
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 
 
 
0
2
0
/
/ (1 )
1/ 2 , 1, , 2
m
c
mc
ii
Wn
Wn
W W n i n

   


    

   

(7)
Where
W
is the weight factor, and the scaling
factor

usually equals to 10-3. The parameter

depicts the information of the state
distribution, typical equals to 2 for Gaussian
system. The superscript
s
and
c
separately
denote state and covariance.
(2) Compute sigma points:
 
 
0, 1 , 1
, 1 , 1 ,1
, 1 , 1 ,1
ˆ
ˆ( ) 1, ,
ˆ( ) 1, ,2
aug
aug
k aug k
i k aug k x ik
i k aug k x i n k
x
x n P i n
x n P i n n




 
 

   
    
(8)
Where

is the sigma point of the state vector
aug
x
, at the time index k-1 the sigma points
1k


can be denoted as
, 1 , 1
ˆ ˆ
[,
aug k aug k
xx


, 1 , 1 , 1
ˆ
( ) , ( ) ]
aug aug
x k aug k x k
n P x n P

  
  
.
(3) Time update:
 
, | 1 , 1 1
2
, | 1 , | 1
0
,
ˆ
i k k i k k
nm
aug k k i i k k
i
fu
xW


  







(9)
, | 1
2
, | 1 | 1 , | 1 | 1 1
0
ˆ ˆ
aug k k
nT
c
x i i k k k k i k k k k k
i
P W x x Q

    

   
   
   

(10)
 
, | 1 , | 1
2
| 1 , | 1
0
,
ˆ
i k k i k k k
nm
k k i i k k
i
hu
yW










(11)
The estimate of the state and covariance is
propagated from one measurement time to the
next.
(4) Measurement update:
,
2
, | 1 , | 1 , | 1 | 1
0
ˆ ˆ
aug k k
T
nc
x y i i k k aug k k i k k k k
i
P W x y

   



  



(12)
2
, | 1 | 1 , | 1 | 1
0
ˆ ˆ
k
T
nc
y i i k k k k i k k k k k
i
P W y y R

   

   
   
   

(13)
,
1
,
aug k k k
k x y y
K P P

(14)
 
, , | 1 | 1
ˆ ˆ ˆ
aug k aug k k k k k k
x x K y y

  
(15)
, , | 1
aug aug k
T
x k x k k k y k
P P K P K


(16)
In the standard UKF algorithm, computing
the new set of sigma points in Equation 8 needs
to take a matrix square root of the state
covariance matrix P, while it is the most
computationally expensive process and
sometimes numerically unstable. An efficient
implementation using square-root of the state
covariance matrix has been successfully used in
the linear Kalman filter, and it then extended to
the UKF for guaranteeing the matrix P positive
semi-definiteness [29].
Assume that the matrix S is the square root of
the state covariance,
T
P SS
. and the initial
matrix
,0aug
x
S
can be represented by a Cholesky
factor as follows:


  


,0 ,0
T
,0 ,0
ˆ ˆ
aug aug
xx
aug aug aug aug
S chol P
chol E x x x x


  


(17)
In order to avoid calculating the time-update
of the state covariance in Equation 10, the
Cholesky factor time-update,
, | 1aug k k
x
S
, is
calculated via a QR decomposition and the
subsequent Cholesky update.
 


 
, | 1
, | 1 , | 1
1 1 2 , | 1
0 , | 1 0
ˆ
ˆ
,,
aug k k
aug k k aug k k
c
x : n,k aug k k k
c
x x ,k aug k k
S qr W x Q
S cholupdate S x W







  


(18)
The same process as the state vector, the
Cholesky factor of is calculated as follows:
 


 
1 1 2
00
ˆ
ˆ
,,
k
kk
c
y : n,k k k
c
y y ,k k
S qr W y R
S cholupdate S y W



  


(19)
The gain matrix
k
K
can be directly
calculated without need to the inversion of the
measurement error covariance:
 
,//
aug k k k k
T
k x y y y
K P S S
(20)
The matrix square root of the state
covariance can be computed by the posterior
measurement update:

Int. J. Turbo Jet-Engines, Vol.xx(2013), pp.xxx-xxx Copyright © 2013 De Gruyter. DOI xx.xxxx/TJJ.2013.xxx
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

, , | 1aug k aug kk k
x x k y
S cholupdate S , K S ,' '


(21)
From the Equation 8, we can see that the
number of sigma points requires 2n+1, for n-
dimensional state. While the computational
loads are proportional to the sigma points scale,
there is a strong suggestion to minimize the
points number. Then a sigma point selection
strategy is proposed in the S-UKF algorithm
that requires n+2 points for n dimensions [31].
Before create the sigma point set, the point
weights are calculated, replacing the equation 4
in the standard UKF, as follows:
 
11,11
10
0
0


ninWW
W
i
(22)
Then compute n+2 sigma points, for n-
dimensional state.
 
1 1 1
0 1 1 2 1
0 , 1 2 , 1 2WW
  
   
   
   
(23)






































1
1
0
1
11
0
0
1
1
1
1
1
0
ji,
)Wj(jj
j,i
)Wj(j
θ
i
θ
θ
j
j
i
j
j
i
(24)
The vector sequence is initialized in Equation
23, and is expanded in the following equation.
For the gas turbine engine health estimate
based on the nonlinear model, the convergence
and computational loads need to be considered.
Therefore, the spherical SR-UKF is presented,
which is combined the spherical simplex point
selection strategy with the SR-UKF. The
detailed procedure of the spherical SR-UKF is
given out in Figure 1.
Initialization
,0 ,0
ˆaug aug
x E x




  


,0 ,0
T
,0 ,0
ˆ ˆ
aug aug
xx
aug aug aug aug
S chol P
chol E x x x x


  


 
0
0
01
1 1, 1 1
i
W
W W n i n


    

 
1 1 1
0 1 1 2 1
0 , 1 2 , 1 2WW
  
   
   
   
1
0
1
1
1
1
0
0
1
11
01
1
j
j
i
j
i
j
θi
θ
θi , j
j(j )W
, i j
j j(j )W





















Time update
 
, | 1 , 1 1
ˆ ˆ ,
aug k k aug k k
x f x u
  

 
, | 1 , 1
aug aug
x k k x k k
S S Chol Q


 
,,
,
i k i k k
hu


1
| 1 ,
0
ˆ
nm
k k i i k
i
yW





Measurement update
 


 
 
1 1 1 | 1
0 0 | 1
ˆ
ˆ
, ,' '
k
kk
y :n ,k k k k
y y ,k k k
S qr W y R
S cholupdate S W y





  

  
,
1
, , | 1 , | 1
0
ˆ ˆ
aug k k
T
n
x y i i k aug k k i k k k
i
P W x y






  



, , | 1 , | 1
ˆaug
i k aug k k x k k i
xS



 
,//
aug k k k k
T
k x y y y
K P S S
 
, , | 1 | 1
ˆ ˆ ˆ
aug k aug k k k k k k
x x K y y

  
k
ky
U K S
 
, , | 1, ,' '
aug aug
x k x kk
S cholupdate S U


k=k+1
Figure 1. The spherical SR-UKF algorithm procedure
3. Nonlinear integrated architecture for gas
path analysis
The conventional architecture has several
notable shortcomings. First, it conducts off-line
fault diagnostics based on the post-flight
processing of a small number of engine
snapshot measurements recorded each flight.
Significant diagnostics latency happens because
of this processing often done until several days
after the flight has occurred. Engine health
degradation estimates produced are only
available off-line, and can’t be used for on-

Int. J. Turbo Jet-Engines, Vol.xx(2013), pp.xxx-xxx Copyright © 2013 De Gruyter. DOI xx.xxxx/TJJ.2013.xxx
7
board health management applications, thus are
not utilized to their full potential [19-21].
With the development of computer and
information processing technology, the
limitations of on-board computational resources
for model real time calculation are gradually
relieved. A linear integrated on-board gas
turbine engine diagnostic architecture is
proposed [24, 25], it includes a real-time
adaptive performance model (RTAPM) and an
independent performance baseline model (PBM).
The RTAPM implements a linear Kalman filter,
producing streaming estimates of unmeasured
outputs while tracking engine performance. The
PBM utilizes periodically updated estimates of
engine condition in association with a piecewise
linear engine model to provide estimated sensor
measurements for fault diagnostic purposes.
However, the integrated conventional
architecture is built up with the linear engine
model and the LKF, the performance estimate
accuracy will not always be well because the
linearizing model errors, and it can’t conduct the
performance abrupt shift estimate. Additionally,
the baseline model will also not track the engine
measured outputs well before the periodical
performance update. A nonlinear integrated
architecture is present for the engine gas path
analysis. An overview of the architecture is
illustrated in Figure 2. A nonlinear real-time
adaptive performance model (NRAPM)
implements an extended Kalman filter to real
time provide unmeasured performance estimates,
while an independent nonlinear baseline model
(NBM) with engine condition update with
certain period to produce estimated sensor
measurements. The fault detection and diagnosis
(FDD) system integrates the real-time
information of the engine sensed measurements,
the outputs of the NBM and the NRAPM with
the FDD logic to fulfill the functions of gas path
anomaly detection, sensor and component fault
diagnostics.
Periodical update
switch
Nonlinear on-board
baseline model
Performance buffer
NBM
u
Nonlinear on-board
real time model
The spherical
SSR-UKF
ˆ
h

y

y
ˆ
y
xˆ
NRAPM
Fault
detection
and
diagnosis
(FDD)
In-flight
health
report
Figure 2. A nonlinear integrated architecture for the
engine gas path fault diagnostics
3. 1 Nonlinear real-time adaptive performance
model
The purpose of the NRAPM is to provide a
continuous assessment of gas turbine engine
performance. It consists of a nonlinear on-board
real-time model and an associated tracking filter
that on-line tunes the model track the
performance of the physical engine based on
feedback sensor measurements. Performance
parameters, modeled as efficiencies and flow
capacities of each major rolling engine
component, are used as a measure of engine
degradation and reflect the effects of
performance deterioration on engine outputs.
The SSR-UKF is applied to capture gradual
engine performance deterioration, and produces
real-time estimates of the engine’s augment
state variables
ˆaug
x
. The estimate variables
ˆaug
x
,
including the state variable
ˆ
x
and performance
parameters
ˆ
h
, are provided as inputs to the
nonlinear on-board real-time model. This
process allows the model-produced estimates to
track the outputs of the engine
ˆ
y
. The

Int. J. Turbo Jet-Engines, Vol.xx(2013), pp.xxx-xxx Copyright © 2013 De Gruyter. DOI xx.xxxx/TJJ.2013.xxx
8
performance estimates are delivered to the
performance buffer, which stores the engine
health status information with certain scales,
500 sampling points in this paper.
3. 2 Nonlinear on-board baseline model
The NBM sensed estimates differ from actual
engine sensor values, as it updates performance
parameters with the certain period. The
difference will be increased with the operation
time before the performance update to the NBM.
If we have the performance trend not based on
the real time sensed engine values but the
storage performance parameters, and put them
into the performance update of the NBM in the
update intervals, then the NBM will track the
engine outputs with better accuracy.
The NBM provides estimates of sensed
engine values based on periodically updated
engine performance estimates from the NRAPM.
The residuals between true engine sensor values
and the NBM’s sensed estimates are available
for the on-board gas path fault diagnostics. The
NBM incorporates a version of the same
nonlinear on-board model used in implementing
the NRAPM. The NBM captures dynamics
coupled with periodically updated engine
performance parameters to incorporate the
effects of engine performance degradation. The
performance estimates calculated in the
NRAPM will be enabled to pass periodically as
inputs to the NBM, only when there are no
faults detected.
The NBM does not employ instantaneous
performance estimates. As gas-path engine
operation are expected to manifest themselves
as sudden health shifts, the real time
performance estimates generated by the SSR-
UKF in the NRAPM will immediately absorb
sudden health shifts. Because the performance
parameters employed by the NBM are updated
only periodically, a gas-path fault will not be
reflected in the performance parameters inputs
to the NBM, leading to a measurable divergence
of actual sensed values from respective NBM
estimates [32]. The key difference of the two
on-board models is the performance parameters
update rate.
3. 3 Fault detection and diagnostics
A fault detection and diagnostic (FDD)
system is designed based on the nonlinear
integrated architecture for the gas path fault
diagnosis. The probability of multiple
simultaneous failures is very low, and then these
failures are not addressed in the paper. The FDD
logic determines a root cause of the problem
with the following assumptions: all performance
parameters gradual deterioration simultaneously;
only one sensor may be faulty at a time; only
one performance parameter suffers a sudden
shift at a time. The FDD system indicates the
following conditions: no failure, sensor fault
detected, and component fault diagnosed.
After the estimation of the sensor
measurement, denoted as
y
, is obtained by the
NBM, the following groups of residuals are
produced:
i i i
e y y
e y y


(25)
Where the variable
i
y
is the subset of the sensor
measurement that excludes the ith sensor. There
are m sensors, and i is an integer from 1 to m.
From these residuals, the corresponding two
groups of fault indicator signals, weighted sum
of squared residual (WSSK and WSSR), are
calculated:
 
 
1
2
1
2
[]
[]
T
T
i i i i
WSSK e diag e
WSSR e diag e






(26)
The variable
i

is the standard deviation of the
ith sensor subset, and is used to normalize the
fault indicator signals.

Int. J. Turbo Jet-Engines, Vol.xx(2013), pp.xxx-xxx Copyright © 2013 De Gruyter. DOI xx.xxxx/TJJ.2013.xxx
9
The FDD framework based on the nonlinear
integrated architecture is represented in Figure 3.
The functionality of the FDD system is
summarized in the following: When no sensor
or component fault happens, all fault indicator
signals retain low; When there is one sensor
fault, only one fault indicator signal with the
correct hypothesis retain low; When one
component fault, all fault indicator signals will
increase rapidly and violate their thresholds.
NBM
NRAPM
WSSR
Computation FDD
Logic
Component
abrupt faults
computation
No fault or the
sensor i fault
Component
fault
WSSK
y
y
WSSR
WSSR
1
m
hHealth
parameter
i shift
Figure 3. FDD framework based on the nonlinear
integrated architecture
The process of FDD framework includes
anomaly detection, sensor and component fault
diagnosis, and is completed by the fault
indicator signals with FDD logic. In the FDD
logic, the decision rules check for the fault
indicator signal violation of their thresholds,
which can be determined with the approach
used in the reference 33. If the WSSK exceeds
its threshold, anomaly is detected, and then all
WSSRi is checked. The sensor i fault is declared
when the corresponding WSSRi retains low and
the others violate their thresholds. If all WSSRi
exceeds their threshold, then no hypothesis is
correct and one component fault. The estimates
of performance parameter sudden shift by the
NRAPM are convinced, from which any
component fault is diagnosed.
4. Gas turbine engine model
The engine is a high bypass ratio gas turbine
engine, see Figure 4. A single inlet supplies
airflow to the fan. Air leaving the fan separates
into two streams: one stream passes through the
engine core, and the other stream passes through
the annular bypass duct and then leaves. The fan
is driven by the low pressure turbine. The air
passing through the engine core moves through
the compressor, which is driven by the high
pressure turbine. Fuel is injected in the
combustor and burned to produce hot gas for
driving the turbines. The air leaves the low
pressure turbine (LPT) through the nozzle,
which has a variable cross section area.
Compressor
Combustor HPT LPT Nozzle
1
Inlet
2 21
13
25
Bypass
3 4 41 42 795 8
Fan
Figure 4. Schematic representation of a gas turbine
engine
The engine model is a nonlinear
thermodynamic model, denoted as component
level model (CLM), including detailed
performance charts for the various engine
components. The CLM is written using C
language and packaged with dynamic link
library for using in Matlab environment [34-37].
The CLM balances and mass/energy equations
of the system is at a rate of 50 Hz.
The discretized time invariant equations that
model the gas turbine engine can be
summarized as equation 1.
x
is the 2-element
state vector,
u
is the 2-element control vector,
h
is the 7-element health parameter vector, and
y
is the 9-element measurement vector. The
noise terms and health parameter degradations
are added to the model for the problem studied
in the paper. The gradual deterioration is
injected into the performance parameters
simultaneously over time. Between
measurement times their deviations can be
approximated by the zero mean noise
,hk
w
. The
noise term
,xk
w
represents inaccuracies in the

Int. J. Turbo Jet-Engines, Vol.xx(2013), pp.xxx-xxx Copyright © 2013 De Gruyter. DOI xx.xxxx/TJJ.2013.xxx
10
system model, and
k
v
represents measurement
noise. The EKF is used to estimate the augment
state vector
,aug k
x
.
The two state variables are low pressure rotor
speed
Nl
, and high pressure rotor speed
Nh
.
The controls, health parameters, and
measurements are summarized in Table 1-3,
along with their values at the design operating
point considered in this paper, which is at cruise
(
10700 , 0.84H m Ma
). Table 3 also shows
typical standard deviations for the
measurements, based on experience. Sensor
dynamics are assumed to be high enough
bandwidth that they can be ignored in the
dynamic equations.
Table 1. Gas turbine CLM controls and nominal values
Control
Acronyms
Nominal values
Fuel flow
Wf
2.5 kg/s
Variable nozzle area
8
A
0.54 m2
Table 2. Turbofan engine CLM health parameter, operating point, standard deviation and degeneration maximum
Augment state
Acronyms
Operating point
Standard deviation
Deteriorate
maximum (%)
Fan efficiency
1
SE
1
0.0005
-2.85
Fan airflow capacity
1
SW
1
0.0005
-3.65
HPC efficiency
2
SE
1
0.0005
-9.4
HPC airflow capacity
2
SW
1
0.0005
-14.1
HPT efficiency
3
SE
1
0.0005
-3.81
HPT airflow capacity
3
SW
1
0.0005
2.57
LPT efficiency
4
SE
1
0.0005
-1.08
Table 3. Turbofan engine CLM measurements at the cruise
Variables
Acronyms
Operating points
Standard deviation
Fuel flow
Wf
2.5 kg/s
Variable nozzle area
8
A
0.54 m2
Low pressure rotor speed
nL
3799 RPM
0.0015
High pressure rotor speed
nH
11341 RPM
0.0015
Fan exit pressure
P13
175677 Pa
0.0015
HPC inlet pressure
P25
321039 Pa
0.0015
HPC inlet temperature
T25
698 K
0.002
HPC exit pressure
P3
3266005 Pa
0.0015
HPC exit temperature
T3
1122 K
0.002
LPT exit pressure
P5
181377 Pa
0.0015
LPT exit temperature
T5
1053 K
0.002
5. Simulations and analysis
The gas turbine engine CLM experiences the
gradual deterioration to represent the
performance degradation with the usage that
exists in the real environment. The SSR-UKF in
the NRAPM tracks the engine health status at

Int. J. Turbo Jet-Engines, Vol.xx(2013), pp.xxx-xxx Copyright © 2013 De Gruyter. DOI xx.xxxx/TJJ.2013.xxx
11
each sample point. The estimated engine
performance is then used to update the NBM
periodically. The FDD system based on the
nonlinear integrated architecture fulfills the
decision of gas path faults. The simulations and
analysis are carried out in the following sections.
The NRAPM with the SSR-UKF computational
consume of each step is less than 20ms under
both steady and dynamic condition, and
measurement step equals 20ms.
5. 1 Gradual deterioration real time tracking
The normal operating parameters of the gas
turbine engine are depicted in Tables 1, and 3.
Gaussian noise whose magnitude is specified in
Table 3 is added to the clean simulated
measurements to make them representative of
real data. Gradual deterioration is injected into
all seven engine performance parameters by
quadratic function drifting, and the deterioration
profile that the engine model will undergo is
starting from their nominal values and with the
following degradation at the end of the sequence
(6000 cycle number): -2.85% on SE1, -3.65% on
SW1, -9.4% on SE2, -14.1% on SW2, -3.81% on
SE3, 2.57% on SW3, -1.08% on SE4. The
deterioration profile specifies a unique health
condition at each sample point. At each cycle
point, the engine model is run in the cruise
steady state.
Figure 5 shows the actual and estimated
performance parameters over 6000 cycles, and
every 400 cycles the performance parameters
are depicted. The estimated parameters were on-
line generated by the state estimators. The
improvement in estimation accuracy can be
gained by applying the NRAPM versus the
conventional RTAPM [24] in figure 5. In each
plot the black square points denotes actual
performance deterioration, the red round points
denotes the LKF estimate of performance
deterioration, and the green triangle points
denotes the SSR-UKF estimate of performance
deterioration. As can be seen from figure 5, The
SSR-UKF is able to follow the degradation
profile quite well for all seven performance
parameters, while the LKF is only for SW1 and
SW2. Applying the NRAPM helps to
significantly improve performance track
accuracy during the whole lifetime.
01000 2000 3000 4000 5000 6000
-6
-5
-4
-3
-2
-1
0
SE1%
Cycle
Actural degraded value
LKF estimate
SSR-UKF estimate
(a)
01000 2000 3000 4000 5000 6000
-5
-4
-3
-2
-1
0
Cycle
Actural degraded value
LKF estimate
SSR-UKF estimate
SW1%
(b)
01000 2000 3000 4000 5000 6000
-10
-8
-6
-4
-2
0
Actural degraded value
LKF estimate
SSR-UKF estimate
SE2%
Cycle
(c)

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12
01000 2000 3000 4000 5000 6000
-16
-14
-12
-10
-8
-6
-4
-2
0
SW2%
Cycle
Actural degraded value
LKF estimate
SSR-UKF estimate
(d)
01000 2000 3000 4000 5000 6000
-7
-6
-5
-4
-3
-2
-1
0
Cycle
Actural degraded value
LKF estimate
SSR-UKF estimate
SE3%
(e)
01000 2000 3000 4000 5000 6000
0
1
2
3
4
Cycle
Actural degraded value
LKF estimate
SSR-UKF estimate
SW3%
(f)
01000 2000 3000 4000 5000 6000
-1.5
-1.0
-0.5
0.0
Actural degraded value
LKF estimate
SSR-UKF estimate
Cycle
SE4%
(g)
Figure 5. Actual and estimated health deterioration over the engine’s lifetime. (a) Fan efficiency; (b) Fan airflow
capacity; (c) Compressor efficiency; (d) Compressor airflow capacity; (e) HPT efficiency; (f) HPT airflow capacity;
(g) LPT efficiency.
5. 2 Performance update to the NBM
As discussed in section 3, the on-line gas
path fault diagnostics will eventually lose its
effectiveness as the engine is normally
deteriorated over time. This happens because
the baseline model outputs will not reflect the
sensed engine outputs. To maintain diagnostic
effectiveness, the performance parameters of the
NBM must be updated from the feeding of the
performance buffer. This update is implemented
only when the following two conditions
satisfied: the performance update switch turned
on, and no faults detected.
The results of this nonlinear on-board
baseline model outputs with different update
strategies are represented in figure 6 where, over
its lifetime of 6000 cycles, the gas turbine
engine is subject to the specific health
deterioration profile shown in figure 6. In the
experiment, the averages of performance
estimates in the performance buffer at 20s after
operating in cruise steady state each cycle are
used to update the health status of the baseline.
In figure 6, the black line denotes the engine
actual sensed output, the red line denotes the
output of nonlinear baseline model with no
update, the blue line denotes the output of linear
baseline model with off-line update each cycle
(the PBM), and the pink line denotes the output
of the nonlinear baseline model output with the
above strategy (the NBM). As can be seen from
the figure 6, if the baseline is not updated from
the nominal condition, the residuals between the
baseline and the actual engine measurements
will increase with the operational cycle. The
different updated baselines produced the outputs
that could track the engine actual sensed outputs.

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13
However, compared to the PBM, the NBM has
less estimated output errors.
Measurement
Nonupdate model output
The PBM output
The NBM output
01000 2000 3000 4000 5000 6000
0.92
0.93
0.94
0.95
0.96
0.97
Cycle
nL
nL 1
(a) nL
Measurement
Non update model output
The PBM output
The NBM output
01000 2000 3000 4000 5000 6000
0.80
0.82
0.84
0.86
0.88
0.90
0.92
P3
Cycle
(b) P3
Measurement
Non update model output
The PBM output
The NBM output
01000 2000 3000 4000 5000 6000
1.00
1.02
1.04
1.06
1.08
1.10
1.12
T5
Cycle
(c) T5
Figure 6. The baseline model outputs with the
performance deterioration over the cycle.
5. 3 On-line gas path fault diagnostics
In order to verify the capability of the
nonlinear integrated architecture to diagnose the
faults, experiments on the sensor fault and the
component fault are carried out. According to
the FDD logic, whether fault happens is firstly
determined by the fault indicator signal WSSK.
Then all the WSSR are used to discriminate the
component or sensor fault, and further to
determine which sensor fault. If the component
fault is declared, the estimates of performance
parameter shift by the RTAPM are reliable.
There are 9 fault indicator signals WSSR
because of 9 sensors used for gas path analysis
as seen in Table 3, and the WSSRi is sequentially
corresponding to the correct hypothesis of no
fault in sensor i. The thresholds of each fault
indicator signal are calculated as the same
method as reference [33], including the
knowledge of the modeling errors and standard
deviation. Table 4 represents the thresholds in
the steady state of the 3000 cycles at cruise
point.
Table 4. The fault indicator signal thresholds at the steady state of the 3000 cycles
WSSK
WSSR1
WSSR2
WSSR3
WSSR4
WSSR5
WSSR6
WSSR7
WSSR8
WSSR9
81.63
72.59
72.79
72.63
72.57
72.59
72.54
72.51
72.39
72.43
Figure 7 shows the fault indicator signal
WSSK in the normal condition at cruise point
after the 3000 cycles. In the figure 7, black line
is the WSSK, and red line is its threshold (equals
to 81.63). We can see that the WSSK keeps
lower than its threshold, and then no fault is
obtained by the FDD logic. The diagnostic

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14
result is consistent with the actual condition of
the gas turbine engine.
050 100 150 200
0
50
100
WSSK
t/s
Figure 7. The WSSK in the cruise steady state of the 3000
cycles with no faults
In order to validate the capability of sensor
fault diagnosis, the magnitude of 2% step fault
is injected into the sensor P3 at 50s in the steady
state of the 3000 cycles, as shown is Figure 8.
The WSSK increases rapidly after the 50s, then
anomaly is declared and other fault indicator
signals should be checked. From the rest 9
graphs in Figure 8, we can see that all WSSR
violate their thresholds except the WSSR7.
Therefore, the hypothesis of the sensor P3 no
fault, corresponding to the WSSR7, is wrong and
then the sensor P3 fault is diagnosed.
050 100 150 200
0
100
200
050 100 150 200
0
100
200
050 100 150 200
0
100
200
050 100 150 200
0
100
200
050 100 150 200
0
100
200
WSSR1
WSSK
WSSR4
WSSR3
WSSR2
t/s
050 100 150 200
0
100
200
050 100 150 200
0
100
200
050 100 150 200
0
100
200
050 100 150 200
0
100
200
050 100 150 200
0
100
200
WSSR9
WSSR8
WSSR7
WSSR6
t/s
WSSR5
Figure 8. The fault indicator signals in the steady state of
the 3000 cycles with 2% step fault of sensor P3
Component performance abrupt shift
sometimes will result in serious failure, and it
needs to be diagnosed in time for the engine
health management. Then the simulation of
component sudden fault diagnostics is carried
out, and 2% degradation of the SE3 is introduced
at 50s to the gas turbine engine CLM when the
engine has experienced the 3000 cycle. The
fault indicator signals are represented in Figure
9, all of them exceed their thresholds and then
the component fault is determined by the FDD
logic. Then the component health parameters
estimated by the spherical SR-UKF in flight are
credible, and the shifts of the parameters from
the performance buffer in the NRAPM represent
the component abrupt faults.

Int. J. Turbo Jet-Engines, Vol.xx(2013), pp.xxx-xxx Copyright © 2013 De Gruyter. DOI xx.xxxx/TJJ.2013.xxx
15
050 100 150 200
0
300
600
050 100 150 200
0
300
600
050 100 150 200
0
300
600
050 100 150 200
0
300
600
050 100 150 200
0
300
600
t/s
WSSR4
WSSR3
WSSR2
WSSR1
WSSK
050 100 150 200
0
300
600
050 100 150 200
0
300
600
050 100 150 200
0
300
600
050 100 150 200
0
300
600
050 100 150 200
0
300
600
t/s
WSSR9
WSSR8
WSSR7
WSSR6
WSSR5
Figure 9. The fault indicator signals in the cruise state of
the 3000 cycles with 2% SE3 degradation
The comparisons of performance parameter
shift estimate by the two integrated approaches
in the cruise steady state of the 3000 cycles with
2% degradation of the SE3 are depicted in
Figure 10. The black bar denotes the actual
performance abrupt shift introduced to the
engine, the red one denotes performance
parameter shift estimates by the conventional
integrated architecture (labeled as I), and the
blue one denotes the estimates by the nonlinear
integrated architecture with the FDD logic
(labeled as II). As can be seen from the Figure
10, the shift estimates of seven performance
parameters by the approach I are separately
about 0.84%, 0.12%, 0.65%, -0.45%, -1.76%,
0.09%, -0.19%, while the estimates by the
approach II are about 0.05%, -0.01%, 0.02%, -
0.02%, -2.05%, -0.02%, 0.01%. Therefore, the
estimates of approach II are obviously more
consistent with the actual condition that all
performance parameters no degraded except the
SE3 -2% jumps.
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
SE4
SW1
h%
SE1
Actual shift
Estimated by the I
Estimated by the II
SW2
SE2 SW3
SE3
Figure 10. The estimates of performance
parameter shift in the steady state of the 3000
cycles with 2% SE3 degradation
The performance of the nonlinear integrated
architecture is evaluated under multiple
component fault scenarios in the steady state of
the 3000 cycles. To capture a range of expected
component faults, the seven scenarios, with
performance parameter jump magnitude as
follows: SE1 (-2%), SW1 (-3%), SE2 (-6%), SW2
(-10%), SE3 (-2%), SW3 (+3%), SE4 (-3%),
separately labeled as the scenario 1 to 7, are
investigated. These shifts to the performance
parameter, representing abrupt component fault
due to foreign object damage, are injected as
step changes. The absolute estimate errors and
square sum error under each scenario by the two
methods are shown in Table 5. The performance
errors under all seven scenarios by the method II

Int. J. Turbo Jet-Engines, Vol.xx(2013), pp.xxx-xxx Copyright © 2013 De Gruyter. DOI xx.xxxx/TJJ.2013.xxx
16
are largely less than the method I, as shown in
Table 5. The bold values in the table are the
estimate errors, just the degraded performance
parameters.
Table 5. The performance errors under different operation
scenarios （×10-2)
Scen-
ario
Met-
hod
SE1
SW1
SE2
SW2
SE3
SW3
SE4
SSE
1
I
0.94
0.26
0.10
0.18
0.32
0.09
0.16
1.13
II
0.03
0.15
0.01
0.09
0.16
0.07
0.07
0.07
2
I
0.09
0.52
0.11
0.19
0.44
0.06
0.40
5.04
II
0.28
0.17
0.01
0.01
0.13
0.03
0.06
0.13
3
I
1.05
0.24
0.85
1.07
0.23
0.39
0.13
3.25
II
0.14
0.01
0.01
0.06
0.07
0.01
0.08
0.04
4
I
0.15
0.14
1.26
1.52
0.41
0.70
0.25
4.66
II
0.44
0.18
0.07
0.05
0.21
0.10
0.02
0.29
5
I
0.84
0.12
0.65
0.45
0.24
0.09
0.19
1.45
II
0.05
0.01
0.02
0.02
0.05
0.02
0.01
0.01
6
I
0.53
0.05
0.35
0.45
0.29
0.28
0.12
0.78
II
0.02
0.01
0.01
0.02
0.03
0.01
0.01
0.01
7
I
1.21
0.42
0.26
0.42
0.69
0.24
0.27
2.48
II
0.29
0.15
0.03
0.10
0.22
0.05
0.03
0.17
6. Conclusions
An on-line nonlinear integrated architecture
has been proposed to improve the capability of
gas path fault diagnosis for gas turbine engine
by exploiting the available engine sensor data.
The architecture is mainly including two
independent on-board nonlinear models, and the
FDD system. One engine model, named as the
nonlinear real-time adaptive performance model
(NRAPM) based on the SSR-UKF, produces
streaming estimates of performance parameters.
The other one, nonlinear baseline model (NBM)
updated its performance by the piecewise health
predictor every cycle, provides the degradation-
free estimates of engine sensor measurements.
The simulation has validated that compared to
the linear approach the NBM tracks the actual
engine sensed values with better accuracy in the
whole lifetime, therefore, it can be used as the
reference for gas path fault diagnosis.
In the nonlinear integrated architecture, the
FDD system is designed to anomaly detection,
sensor fault diagnosis, and component fault
diagnosis. The two groups of fault indicator
signals, the WSSK and the WSSR, used for the
FDD logic, are calculated from the residuals of
the actual measurements and the NBM
corresponding outputs. Whether the gas turbine
engine operates normally can be obtained with
the WSSK firstly, while all the WSSR are used
for discriminating sensor or component fault,
further the sensor i fault. The estimate of the
performance parameters jumps by the NRAPM
is only convince when all the WSSR violate their
thresholds. The effects of gas path fault
diagnosis by the proposed approach are
evaluated on the gas turbine engine CLM, and
the diagnostic results are consistent with the
actual condition well.
The performance update period for the NBM
is influenced to the matching accuracy between
the engine model and the real engine over time.
In this study, in order to verify the effectiveness
of the proposed approach, the performance
update is implemented at 20s after operating in
the cruise steady state. However, in future the
update period is need to be determined by
weighting and considering balance of the
computational efforts and fault diagnostic
capacity in practice. The FDD logic is designed
and validated with the assumption of one sensor
fault or one component fault at one time, the
further implementation of the integrated
architecture is to increase the function of gas
path fault diagnosis in the case of multiple
sensor or component simultaneous faults.
Acknowledgments
We are grateful for the financial support of
the National Nature Science Foundation of
China (51276087, and 61304133), China
Postdoctoral Science Foundation
(2013M530256), Jiangsu Province Nature
Science Foundation (BK20130802), and Jiangsu

Int. J. Turbo Jet-Engines, Vol.xx(2013), pp.xxx-xxx Copyright © 2013 De Gruyter. DOI xx.xxxx/TJJ.2013.xxx
17
Province Key Laboratory of Aerospace Power
Systems (APS201303).
Received: xx, 2013. Accepted: xx, 2013.
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