A multi-rate sensor fusion approach using information filters for estimating aero-engine performance degradation

Abstract

Gas-path performance estimation plays an important role in aero-engine health management, and Kalman Filter (KF) is a well-known technique to estimate performance degradation. In previous studies, it is assumed that different kinds of sensors are with the same sampling rate, and they are used for state estimation by the KF simultaneously. However, it is hard to achieve state estimation using various kinds of sensor measurements at the same sampling rate due to a complex network and physical characteristic differences between sensors, especially in an advanced multi-sensor architecture. For this purpose, a multi-rate sensor fusion using the information filtering approach is proposed based on the square-root cubature rule, which is called Multi-rate Square-root Cubature Information Filter (MSCIF) to track engine performance degradation. Soft measurement synchronization of the MSCIF is designed to provide a sensor fusion condition for multiple sampling rates of measurement, and a fault sensor is isolated by maximum likelihood validation before state estimation. The contribution of this paper is to supply a novel multi-rate information filter approach for sensor fault tolerant health estimation of an aero-engine in a multi-sensor system. Tests are conducted for aero-engine performance degradation estimation with multiple sampling rates of sensor measurement on both digital simulation and semi-physical experiment. Experimental results illustrate the superiority of the proposed algorithm in terms of degradation estimation accuracy and robustness to sensor failure in a multi-sensor system. Keywords: Aero-engine, Cubature information filter, Performance degradation, Sensor fusion, State estimation

Full text

A multi-rate sensor fusion approach using
information filters for estimating aero-engine
performance degradation
Feng LU
a
, Chunyu JIANG
a
, Jinquan HUANG
a,*
, Xiaojie QIU
b
a
Jiangsu Province Key Laboratory of Aerospace Power System, College of Energy and Power Engineering, Nanjing University
of Aeronautics and Astronautics, Nanjing 210016, China
b
Aviation Motor Control System Institute, Aviation Industry Corporation of China, Wuxi 214063, China
Received 13 September 2018; revised 4 December 2018; accepted 23 January 2019
Available online 29 May 2019
KEYWORDS
Aero-engine;
Cubature information filter;
Performance degradation;
Sensor fusion;
State estimation
Abstract Gas-path performance estimation plays an important role in aero-engine health manage-
ment, and Kalman Filter (KF) is a well-known technique to estimate performance degradation. In
previous studies, it is assumed that different kinds of sensors are with the same sampling rate, and
they are used for state estimation by the KF simultaneously. However, it is hard to achieve state
estimation using various kinds of sensor measurements at the same sampling rate due to a complex
network and physical characteristic differences between sensors, especially in an advanced multi-
sensor architecture. For this purpose, a multi-rate sensor fusion using the information filtering
approach is proposed based on the square-root cubature rule, which is called Multi-rate Square-
root Cubature Information Filter (MSCIF) to track engine performance degradation. Soft measure-
ment synchronization of the MSCIF is designed to provide a sensor fusion condition for multiple
sampling rates of measurement, and a fault sensor is isolated by maximum likelihood validation
before state estimation. The contribution of this paper is to supply a novel multi-rate information
filter approach for sensor fault tolerant health estimation of an aero-engine in a multi-sensor sys-
tem. Tests are conducted for aero-engine performance degradation estimation with multiple sam-
pling rates of sensor measurement on both digital simulation and semi-physical experiment.
Experimental results illustrate the superiority of the proposed algorithm in terms of degradation
estimation accuracy and robustness to sensor failure in a multi-sensor system.
Ó2019 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is
an open access article underthe CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
*Corresponding authors.
E-mail address: jhuang@nuaa.edu.cn (J. HUANG).
Peer review under responsibility of Editorial Committee of CJA.
Production and hosting by Elsevier
Chinese Journal of Aeronautics, (2019), 32(7): 1603–1617
Chinese Society of Aeronautics and Astronautics
& Beihang University
Chinese Journal of Aeronautics
cja@buaa.edu.cn
www.sciencedirect.com
https://doi.org/10.1016/j.cja.2019.04.024
1000-9361 Ó2019 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction
Condition-based maintenance has been widely promoted in the
field of aero-engine manufacturing, Maintenance, Repair, and
Overhaul (MRO) in recent years.
1,2
A maintenance schedule
formulated by current health condition brings improved oper-
ability and safety as well as reduced cost. The performance of
an aero-engine gradually deteriorates over time due to fouling,
corrosion, and erosion on major rotating components. Besides,
accidental events resulted from Foreign Object Damage
(FOD) or Domestic Object Damage (DOD) will impact a
quick degradation in gas path performance.
3,4
The ingestion
of birds and ice relates to the FOD, and the vane to ablate
or fracture relates to the DOD.
5
Health parameters are defined
by the changes of gas path component efficiencies and flow
capacities, and they are generally utilized to represent gradual
or abrupt performance degradation. Health parameters are
unmeasurable from engine sensors, and different kinds of sen-
sor measurements are introduced to calculate them.
6–8
A pre-
cise estimation of health parameters from available
measurements plays an important role in gas-path perfor-
mance analysis of Engine Health Management (EHM), and
it has received more attentions.
Some approaches have been developed to gain the engine
health condition from sensor measurements, such as weighted
least squares, Kalman Filter (KF), genetic algorithm, sparse
Bayesian, gray relation theory, neural networks, and sparse
kernel method.
9–15
The KF-based approach is one of the most
commonly used methods for estimating aero-engine degrada-
tion, since it relies on an engine physical performance model
from classical aero-thermodynamics principle.
16,17
More phys-
ical characteristics of engine components are contained in the
KF-based approach, and they are hardly interrupted by mea-
surement noise and little depend on prior samples of a degra-
dation dataset. Among these KFs, a linear KF is employed for
state estimation of a linear dynamic system, and extended to a
nonlinear dynamic system by the Extended KF (EKF),
Unscented KF (UKF), and Cubature KF (CKF).
18–20
The
EKF is with a first-order Taylor series expansion, while both
of the UKF and CKF with a second-order expansion. The
former nonlinear filtering algorithm produces more state esti-
mation errors than those of the latter two due to a missed
high-order term. The CKF has been developed in the last ten
years as the closest ever known direct approximation of a
Bayesian filter. Compared to the UKF, use of less state vari-
able points in the CKF leads to less computational consump-
tion without sacrificing accuracy. Hence, the CKF might be a
better candidate for estimating performance degradation of
aircraft engines.
The rapid development of sensor measurement technology
promotes more kinds of sensors used to estimate engine perfor-
mance degradation. Engine sensor measurements, like spool
speeds, gas path temperature, and pressure, are collected and
fused in various improved KF algorithms.
21,22
A bank of
hybrid KFs with multiple sensors improves performance
anomaly detection rates in EHM applications.
23,24
More sen-
sor measurements used will advance the reliability of perfor-
mance degradation estimation. However, some of the sensors
operate in different sampling rates, which inevitably leads to
a multi-rate state estimation issue in a sensor fusion process.
That is to say, the complication of health estimation increases
due to not only the number increase of sensor measurements
but also the filtering synchronization in a multi-sensor system.
Thus, a novel KF algorithm with data buffers was introduced
to gas path health estimation with different rates of sensor
acquisition.
20
The stability computation of the KF random
Riccati equation was proven with partly missed observation,
25
and the KF stability analysis was presented as Markov packet
losses.
26
An optimal sensor fusion state estimation method was
discussed for multi-sensor systems with disordered measure-
ments.
27
These studies presented the KF stability margin for
state estimation in a multi-sensor system with different sam-
pling rates, and mainly focused on the Linear Kalman Filter
(LKF) in a linear system.
Reliable sensor measurements are the key for a KF estima-
tor to calculate a state variable. However, it is hard to acquire
real engine performance degradation if one of the sensor mea-
surements deviates from the nominal value. It cannot ensure
that the involved sensors run normally all time for state esti-
mation, especially in the harsh operating circumstance of an
aircraft engine. To address this gap, a novel multi-rate nonlin-
ear filter methodology is proposed using sensor fusion and
square-root cubature rule from previous studies of KF algo-
rithms, which is named Multi-rate Square-root Cubature
Information Filter (MSCIF). An information filter is utilized
to describe state estimation with sensor fusion, since it brings
easier expressions of time update and measurement update in
a multi-sensor architecture. Multi-rate state estimation is
achieved in the MSCIF by the soft measurement synchronous,
and sensor measurements are divided into three subsets
depending on various kinds of speed, pressure, and tempera-
ture with their own sampling rates. A Maximum Likelihood
test combined to the MSCIF (ML-MSCIF) is designed to iso-
late an anomalous sensor by v2test running in each sensor sub-
set. Both digital simulations and semi-physical experiments are
carried out to evaluate the involved algorithms for abrupt and
gradual degradation estimation of aero-engine performance in
a multiple-sampling rate measurement system, besides the
combination of sensor fault tolerance is also addressed. Test
results indicate that the proposed algorithm owns a satisfac-
tory estimation accuracy with various sampling rates in a
multi-sensor system.
The rest of this paper is organized as follows. Section 2
raises the problem of aero-engine health estimation using a
state estimator based on sensor fusion with different sampling
rates. In Section 3, the ML-MSCIF algorithm is explained in
detail for multi-rate state estimation. Section 4 gives digital
simulations and semi-physical experiments on a turbofan
engine, followed by discussions are. Section 5 draws conclu-
sion remarks and gives suggestions for further work.
2. Problem formulation
A dual-spool turbofan engine is studied in this paper, which
includes an inlet, a fan, a compressor, a bypass, a combustor,
a High-Pressure Turbine (HPT), a Low-Pressure Turbine
(LPT), a mixer, and a nozzle. The inlet supplies airflow into
the fan, and then air is divided into two streams: one flowing
into the compressor and the other passing through the bypass.
Air leaving the compressor moves to the combustor, and fuel is
burnt to produce hot gas to drive turbines. The fan and the
compressor are driven by the LPT and the HPT, respectively.
1604 F. LU et al.

Gas from the LPT and air from the bypass mix in the mixer,
and then leaves the engine through the nozzle. A mathematical
model of the engine is built on the basis of component-level
modeling theories,
20,28
and it is expressed as
_
xori tðÞ¼fxori tðÞ;utðÞ;cðtÞðÞ
ytðÞ¼gxori tðÞ;utðÞ;cðtÞðÞ
ð1Þ
where x
ori
(t), u(t), c(t), and y(t) are successively the engine orig-
inal state variables, input variables, atmosphere variables, and
sensor measurements. The input parameters of the engine
model are the fuel flow W
f
and the nozzle area A
8
, and the
original state variables include the low-pressure spool speed
N
L
and the high-pressure spool speed N
H
. The nonlinear func-
tion f(∙) is the engine state transition function, and g(∙) is the
measurement function. The sensor measurements for engine
degradation estimation are the fan outlet temperature T
22
,
the fan outlet pressure P
22
,the compressor outlet temperature
T
3
, the compressor outlet pressure P
3
, the HPT outlet temper-
ature T
43
, the HPT outlet pressure P
43
, the LPT outlet temper-
ature T
5
, and the LPT outlet pressure P
5
besides N
L
and N
H
.
The health parameter vector h= [SE
1
,SW
1
,SE
2
,SW
2
,
SE
3
,SW
3
,SE
4
,SW
4
]
T
is used to depict engine performance
degradation from an ideal condition, and its element is defined
by
SEi¼gi
g
i
;SWi¼Wi
W
i
i¼1;2;;4ð2Þ
where gi;Wiare the real component efficiency and flow capac-
ity, respectively, and g
i;W
iare their ideal values. SE
1
,SE
2
,
SE
3
, and SE
4
are the efficiency coefficients of the fan, the com-
pressor, the HPT, and the LPT, respectively, and SW
1
,SW
2
,
SW
3
, and SW
4
are separately their mass flow coefficients.
The variations of unmeasurable health parameters of interest
will result in sensor measurement changes. A Kalman filter is
employed to estimate state variables from sensor measure-
ments, so health parameters are added to the original state
variables to be estimated. Then augmented state variables
are rewritten by x=[x
ori
,h
T
]
T
=[N
L
,N
H
,SE
1
,SW
1
,SE
2
,
SW
2
,SE
3
,SW
3
,SE
4
,SW
4
]
T
.Fig. 1 gives a sensor distribution
diagram of an aero-engine
29
in a multi-sampling rates system.
In the multi-sensor system, the sensor measurements are
classified into Nsubsets by the sensor kinds. In this study,
engine physical parameters are normalized correction to stan-
dard atmosphere condition, and thus the atmosphere variable
cis not involved in the nonlinear engine expression. Provided
that the same sensor kind has a uniform sampling rate, the dis-
cretized equation of the engine model is summarized from
Eq. (1) as follows:
xkþ1ðÞ¼fxkðÞ;ukðÞðÞþwkðÞ
yikðÞ¼gixkðÞ;ukðÞðÞþvikðÞ
i¼1;2;;Nð3Þ
where kis time index, and subscript is the i-th sensor subsets.
y
i
(k) is the observation vector of the i-th sensor subset. The
process noise term w(k) and the measurement noise term
v
i
(k) are uncorrelated Gaussian white noises with
Eðwi;wjÞ¼Qdij, and Eðwi;vjÞ¼0, where dij ¼0i–jðÞ, other-
wise, dij ¼1; E() is the function for mathematical expectation
and Qis variance matrix of process noise.
Suppose that the sampling rate of the i-th sensor subset is
S
i
. For simplification and generality of sampling rate differ-
ences in various sensor subsets, Nsensor subsets sampling
rates follow
Si¼S1=Nii21;N½ ð4Þ
where Niis a known positive integer. An example of a multi-
sensor system with different sampling rates is illustrated in
Fig. 2, and there are totally three sensor measurement subsets.
Measurement data is collected in sensor subset 1 at each step,
sensor subset 2 every second step, and sensor subset 3 every
third step. That is to say, all sensor measurements are obtained
from three sensor subsets separately with sampling rates of
first step, second step, and third step, and it completes one glo-
bal sampling cycle using six steps.
Fig. 1 Aero-engine multiple-sensor distribution diagram for degradation estimation.
29
A multi-rate sensor fusion approach using information filters 1605

3. Multi-rate information filter algorithms
The state-space formulation of a state estimator is from the
engine component level model, which is developed from a vir-
tual turbofan engine from General Gas Turbine Simulation
(GGTS).
30
It is programmed using C language, and packaged
by a dynamic link library to be called by MATLAB software.
Thus, the state-space formulation of the KF estimator is non-
linear. The computer hardware used for the simulation is CPU
i5-3470 @ 3.20 GHz and RAM 4 GB. The sampling time of
the examined engine is 0.02 s.
An information filter is presented in the terms of an inverse
information covariance matrix of a plain KF algorithm, and it
is the mathematical equivalence to the plain-state estima-
tor.
20,31
The information variables and covariance of the infor-
mation filters bring easier expressions of time update and
measurement update in the multi-sensor fusion system. An
Extended Information Filter (EIF) and a Cubature Informa-
tion Filter (CIF) are presented in this study, and a soft mea-
surement synchronization is designed and combined with the
involved information filter algorithms to perform degradation
estimation for aircraft engines.
3.1. Multi-rate extended information filter
The EIF algorithm is derived from the plain EKF for state
estimation of the nonlinear system in a multi-sensor system.
The EIF is interested in the information state vector ^
xFkjkðÞ
and the information matrix PFkjkðÞrather than the state esti-
mate ^
xkjk
ðÞ
and the error covariance Pkjk
ðÞ
in the EKF. The
detailed EIF algorithm is as follows.
The prior information state vector ^
xFkjk1ðÞand the
prior information matrix PFkjk1
ðÞ
are given as
^
xFkjk1ðÞ¼PFkjk1ðÞ
^
xkjk1ðÞ
PFkjk1
ðÞ
¼P1kjk1
ðÞ
¼ukðÞPk1jk1ðÞuTkðÞþQk1ðÞ½
1
8
>
<
>
:ð5Þ
where Pkjk1ðÞis the prior error covariance, and ukðÞis the
Jacobian expression of the nonlinear process equation in
Eq. (3) at k, i.e., ukðÞ¼
@fðxkðÞ;ukðÞÞ
@xkðÞ .Pk1jk1ðÞis the
posterior error covariance, and Q(k1) is the process noise
covariance at k1. The prior state variable ^
xkjk1ðÞis
obtained by ^
xkjk1ðÞ¼f^
xk1jk1ðÞ;uk1ðÞðÞ.
The posterior information state vector ^
xFkjkðÞand the
information matrix PFkjkðÞare updated as
^
xFkjkðÞ¼
^
xFkjk1ðÞþikðÞ
PFkjkðÞ¼PFkjk1ðÞþIkðÞ
(ð6Þ
where ikðÞis the information state modification, and IkðÞis the
associated information contribution matrix, defined by
ikðÞ¼HTkðÞR1kðÞtkðÞþHkðÞ
^
xkjk1ðÞ½
IkðÞ¼HTkðÞR1kðÞHkðÞ
(ð7Þ
where tkðÞ is the innovation vector,
tk
ðÞ
¼yk
ðÞ
g^
xkjk1
ðÞ
;uk
ðÞðÞ
,R(k) is the covariance
matrix of measurement noise at time k, and HkðÞis the Jaco-
bian matrix of the nonlinear measurement equation,
HkðÞ¼
@g^
xkjk1ðÞ;ukðÞðÞ
@x.
Consider sensor fusion with different sampling rates during
EIF state estimation, a soft measurement synchronization is
designed and combined into the Multi-rate EIF (MEIF). When
three sensor subsets are used to stream measurements for state
estimation in the multi-sensor system as given in Fig. 1, the
posterior information variables of MEIF with the soft mea-
surement synchronization are rewritten by
Fig. 2 Multi-sensor system of three sensor subsets with different
sampling rates.
^
xFkjkðÞ¼
^
xFkjk1ðÞþi1kðÞif mod k;N2
ðÞ–0&mod k;N3
ðÞ–0
^
xFkjk1ðÞþi1kðÞþi2kðÞif mod k;N2
ðÞ¼0&mod k;N3
ðÞ–0
^
xFkjk1ðÞþi1kðÞþi3kðÞif mod k;N2
ðÞ–0&mod k;N3
ðÞ¼0
^
xFkjk1ðÞþi1kðÞþi2kðÞþi3kðÞif mod k;N2
ðÞ¼0&mod k;N3
ðÞ¼0
8
>
>
>
<
>
>
>
:
PFkjkðÞ¼
PFkjk1ðÞþI1kðÞif mod k;N2
ðÞ–0&mod k;N3
ðÞ–0
PFkjk1ðÞþI1kðÞþI2kðÞif mod k;N2
ðÞ¼0&mod k;N3
ðÞ–0
PFkjk1ðÞþI1kðÞþI3kðÞif mod k;N2
ðÞ–0&mod k;N3
ðÞ¼0
PFkjk1
ðÞ
þI1k
ðÞ
þI2k
ðÞ
þI3k
ðÞif mod k;N2
ðÞ
¼0&mod k;N3
ðÞ
¼0
8
>
>
>
<
>
>
>
:
8
>
>
>
>
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
>
>
>
>
:
ð8Þ
1606 F. LU et al.

where mod k;Ni
ðÞ¼0 denotes kdivided by Niwith no
remainder, and mod k;Ni
ðÞ–0 denotes that kcannot be com-
pletely divided by Ni.
3.2. Multi-rate square-root cubature information filter
As was mentioned earlier, the CKF is a state-of-the-art nonlin-
ear filtering algorithm, and there are 2ncubature points to be
calculated for state estimation in the CKF at each step. Less
computational efforts are paid by the CKF without estimation
accuracy sacrifice compared to the UKF. The MSCIF is devel-
oped from the conventional CKF, and it deals with state esti-
mation using multiple-sampling rate sensor measurement
fusion. Square-root processing of the information contribution
matrix in the MSCIF is to preserve the matrix positive defini-
tiveness, and symmetry to improve the numerical stability dur-
ing filtering iteration behavior. In addition, the MSCIF
algorithm combined with a sensor fault tolerant criterion is
discussed, and it is presented in detail in the following section.
In the MSCIF algorithm, the parameter of interest is the
square-root of the information matrix SFkjkðÞrather than
the information matrix itself. SFkjkðÞis derived from the fac-
torization of the information matrix as
PFk1jk1ðÞ

1¼SFk1jk1ðÞSFk1jk1ðÞ

T
ð9Þ
The number of cubature points is 2nas nstate variables to
be estimated. The l-th posterior cubature point X(l;k1|
k1) at k1 and the l-th prior cubature point X(l;k|k1)
at current step kare computed as
Xl;k1jk1ðÞ¼Sk1jk1ðÞnlþ^
xk1jk1ðÞ
Xl;kjk1ðÞ¼fXl;k1jk1ðÞ;uk1ðÞðÞ
l¼1;2;;2n
ð10Þ
where the square-root factor of the error covariance is
obtained from Sk1jk1ðÞ¼SFk1jk1ðÞ

T. The
cubature operator nl¼ffiffiffi
n
p1½
l, wherein 1½
lis the l-th column
of the points set 1½, which equals to
1
0

;0
1

;1
0

;0
1

as 1½2R2.
The predicted cubature state and its square-root of the
error covariance are given as
^
xkjk1ðÞ¼
1
2nP2n
l¼1Xl;kjk1ðÞ
Skjk1ðÞ¼Tria Xskjk1ðÞ;SQk1ðÞ
½
(ð11Þ
where Tria ðÞdenotes the QR decomposition of the matrix,
while SQk1ðÞis a square-root factor of Qk1ðÞ, and
Qk1ðÞ¼SQk1ðÞSQk1ðÞ

T. The weighted cubature
state matrix is defined by
Xskjk1ðÞ¼
1
ffiffiffiffiffi
2n
pX1;kjk1ðÞ
^
xkjk1ðÞ;X2;kjk1ðÞ½
^
xkjk1ðÞ; ;X2n;kjk1ðÞ
^
xkjk1ðÞ
ð12Þ
Yskjk1
ðÞ
¼1
ffiffiffiffiffi
2n
pY1;kjk1
ðÞ
^
ykjk1
ðÞ
;Y2;kjk1
ðÞ½
^
ykjk1ðÞ; ;Y2n;kjk1ðÞ
^
ykjk1ðÞ
ð13Þ
Similar to the corporation of EIF measurement equations
in Eq. (3), a pseudo measurement matrix HskðÞis introduced
to MSCIF as
HT
skðÞ¼P1kjk1ðÞPxy kjk1ðÞ ð14Þ
where the information covariance P
xy
(k|k1) is calculated
from the weighted cubature state matrix Xskjk1ðÞand the
measurement matrix Yskjk1ðÞ. With the help of the pseudo
measurement matrix HskðÞ, the information state modification
i(k) and its information contribution matrix I(k) are expressed as
ikðÞ¼HT
skðÞR1kðÞtkðÞþHskðÞ
^
xkjk1ðÞðÞ
Ik
ðÞ
¼HT
sk
ðÞ
R1k
ðÞ
Hsk
ðÞ
(ð15Þ
The information contribution matrix is factorized as
IkðÞ¼SIkðÞSIkðÞðÞ
T. Thus, the square-root factor SIkðÞof
the information contribution matrix is expressed as
SIkðÞ¼HT
skðÞSRkðÞ
¼P1kjk1ðÞPxy kjk1ðÞSRkðÞ
¼SFkjk1ðÞSFkjk1ðÞ

TXskjk1ðÞYskjk1ðÞðÞ
TSRkðÞð16Þ
where SRkðÞdenotes a square-root factor of R1kðÞso that
R1kðÞ¼SRkðÞSRkðÞðÞ
T. Then, the updated cubature informa-
tion state at step kis rewritten as
ikðÞ¼ HT
skðÞR1kðÞtkðÞþHskðÞ
^
xkjk1ðÞðÞ
¼HT
skðÞSRkðÞSRkðÞðÞ
TtkðÞ
þHT
sk
ðÞ
SRk
ðÞHT
sk
ðÞ
SRk
ðÞ

T^
xkjk1
ðÞ
¼SIkðÞSRkðÞtkðÞþSIkðÞSIkðÞðÞ
T^
xkjk1ðÞ
ð17Þ
The updated information matrix is factorized at step kas
follows:
PFkjkðÞ¼PFkjk1ðÞþIkðÞ
¼SFkjk1ðÞSFkjk1ðÞ

TþSIkðÞSIkðÞðÞ
T
¼SFkjk1ðÞ;SIkðÞ

SFkjk1ðÞ;SIkðÞ

T
ð18Þ
The square-root matrix of the updated information is
obtained by
SFkjkðÞ¼Tria SFkjk1ðÞ;SIkðÞ

ð19Þ
In order to make the square-root CIF algorithm to achieve
state estimation using different sampling rates measurement
for the multi-sensor system, the calculation of soft measure-
ment synchronization is also used to form the MSCIF. That
is to say, the MSCIF algorithm is developed from the
square-root CIF, and further extended to the applications of
multi-rate state estimation in a sensor fusion configuration
with information feedback. The posterior information vari-
ables of MSCIF with soft measurement synchronization are
rewritten in three subsets of the multi-sensor system by
A multi-rate sensor fusion approach using information filters 1607

The MSCIF algorithm for sensor fusion of multiple sam-
pling rates includes three parts: local information filtering esti-
mation, soft synchronization module, and master information
filter. The former one implements in the local field, and the lat-
ter two run in the fusion center. As three sensor subsets are
involved, the speed sensor measurements are denoted by subset
1, pressure by subset 2, and temperature by subset 3. Each
local information relates to one sensor subset, and measure-
ments are collected in local information filters in different sam-
pling rates. The local information variables are matched by the
sampling rate, and streamed by the i-th channel triggered in
soft synchronization. The local information state vectors and
information contribution matrices are calculated real-time in
the local field, and then transmitted to the fusion center for
fusion calculation.
In the fusion center, the estimated local information vari-
ables are used in fusion calculation of the master information
filter only when the measurement update completes in the local
field. The master information filter produces global state esti-
mates by time update and prediction steps, and it runs at the
highest sampling step. The predicted information variables
play the roles of the prior states in both the local field and
the fusion center. The global information variables are feed-
back to each local information filter at the same time for the
local estimates at the next step. The sensor fusion framework
of the MSCIF algorithm is illustrated for a multi-sensor net-
work in Fig. 3.
Since the failure probability of a multi-sensor system
increases as more sensors are utilized for state estimation, sen-
sor fault detection and isolation capacity are critical to cut
anomalous sensor data for improving the reliability of sensor
fusion filtering estimation. Maximum likelihood validation is
introduced and combined to check whether the sensed data
fault or not for the MSCIF, and it is defined by the ML-
MSCIF. It is achieved by comparing the real to the predicted
measurement, and accepting only those lie within a predeter-
mined bound. The statistical v2test is expressed by
kikðÞ¼
tT
ikðÞPi;ykjk1ðÞ

1tikðÞ
ni
i¼1;2;3ð21Þ
Pi;ykjk1ðÞ¼
1
2nX
2n
l¼1
Yil;kjk1ðÞ
^
yikjk1ðÞðÞ½
Yil;kjk1ðÞ
^
yikjk1ðÞðÞ
TiþRikðÞ ð22Þ
where R
i
(k) is the measurement noise covariance related to i-th
sensor subset, kikðÞis the i-th sensor subset fault indicator, and
niis the innovation vector dimension of the i-th local filter. The
anomalous threshold of sensor measurement ki;max is empiri-
cally selected by the statistical characteristics of sensor mea-
surement noise. The sensor data is rejected as kik
ðÞ
>ki;max
for successively three steps, and kikðÞ;ki;max are dimensionless
parameters. As we know, the sensor measurements are
Fig. 3 Framework of MSCIF algorithm for a distributed multi-rate sensor network.
^
xFkjkðÞ¼
^
xFkjk1ðÞþi1kðÞif mod k;N2
ðÞ–0&mod k;N3
ðÞ–0
^
xFkjk1ðÞþi1kðÞþi2kðÞif mod k;N2
ðÞ¼0&mod k;N3
ðÞ–0
^
xFkjk1ðÞþi1kðÞþi3kðÞif mod k;N2
ðÞ–0&mod k;N3
ðÞ¼0
^
xFkjk1ðÞþi1kðÞþi2kðÞþi3kðÞif mod k;N2
ðÞ¼0&mod k;N3
ðÞ¼0
8
>
>
>
<
>
>
>
:
SFkjkðÞ¼
Tria SFkjk1ðÞ;SI;1kðÞ

if mod k;N2
ðÞ–0&mod k;N3
ðÞ–0
Tria SFkjk1ðÞ;SI;1kðÞ;SI;2kðÞ

if mod k;N2
ðÞ¼0&mod k;N3
ðÞ–0
Tria SFkjk1ðÞ;SI;1kðÞ;SI;3kðÞ

if mod k;N2
ðÞ–0&mod k;N3
ðÞ¼0
Tria SFkjk1ðÞ;SI;1kðÞ;SI;2kðÞ;SI;3kðÞ

if mod k;N2
ðÞ¼0&mod k;N3
ðÞ¼0
8
>
>
>
<
>
>
>
:
8
>
>
>
>
>
>
>
>
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
>
>
>
>
>
>
:
ð20Þ
1608 F. LU et al.

redundant for the engine Full Authority Digital Electronic
Control (FADEC), and there are usually dual-channel struc-
tures to ensure the system reliability. The redundant channel
of sensor measurement runs in hot standby. In this paper,
we assume that the sensor measurements in channel A are nor-
mally used for performance degradation estimation, and the
measurements in channel B will work as sensor anomaly
recognized.
4. Experiments and discussion
4.1. Comparison of degradation estimation accuracy
The proposed methodology is assessed by systematical experi-
ments using multi-rate sensor fusion for gas path degradation
estimation of aircraft engines. Three physical sensor kinds are
employed for engine performance estimation, and denoted by
a speed sensor subset y1¼½NL;NH, a pressure sensor subset
y2¼½P22 ;P3;P43;P5, and a temperature sensor subset
y3¼½T22 ;T3;T43;T5. Sensor measurements of various physi-
cal kinds own different sampling rates, and sensor faulty like
anomaly bias is considered in the network. The MSCIF with
a maximum likelihood test achieves to detect the combination
anomaly of performance degradation and sensor faulty. Pro-
vided that subset 1 has a sampling rate S
1
= 20 ms, the rest
two sensor subsets have S
2
= 40 ms and S
3
= 60 ms. The
covariance matrices of measurement noise in different sensor
subsets follow R1¼0:00152I22,R2¼0:00152I44, and
R3¼0:0022I44.
Monte Carlo simulation of ten tries is performed to test
gradual degradation and abrupt degradation of gas turbine
engine performance. Root Mean Square Error (RMSE) and
Root Mean Square Deviation (RMSD) are used as perfor-
mance indicators to illustrate estimation accuracy of the pro-
posed algorithms, and they are separately defined as
RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
NpNqX
Np
j¼1X
Nq
k¼1
^
hjkðÞhjkðÞ
hi
v
u
u
tð23Þ
RMSD ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
NpNqX
Np
j¼1X
Nq
k¼1
^
hjkðÞh
j
kðÞ

v
u
u
tð24Þ
where N
q
is the data series length of one test, and N
p
is the
health parameter number of sensor subset. ^
hjkðÞ,hjkðÞ, and
h
j
kðÞare the estimated value, true value, and estimated average
value of health parameters at time kin the j-th simulation run,
respectively.
Engine performance gradual degradation is expressed by
health parameters generally deviated from their nominal val-
ues in the course of its lifetime. The engine is health when every
element of health parameter vector equals to 1. The health
parameters are dimensionless. The health parameters start
from 1 at t= 0 s, and move to the magnitudes at the end
t= 10 s as: 2.18% on SE
1
,2.85% on SW
1
,6.71% on
SE
2
,8.99% on SW
2
,3.22% on SE
3
, +2.17% on SW
3
,
0.808% on SE
4
, and +0.3047% on SW
4
.
20
Four typical
abrupt degradations are involved: fan degradation (2% on
SE
1
and 2% on SW
1
), compressor degradation (2% on
SE
2
and 2% on SW
2
), HPT degradation (2% on SE
3
and +2% on SW
3
), and LPT degradation (2% on SE
4
and
+2% on SW
4
). The deviations of health parameters are
injected at t= 2 s to simulate abrupt degradation.
The RMSEs by the MEIF with synchronous sampling of
40 ms and multi-rate sensor fusion are separately 0.0342 and
0.0311, and those by the MCIF are 0.0250 and 0.0231 in the
case of gradual deterioration affecting all major components
at the same time. Besides, typical operating points are selected
to evaluate the proposed methodology in a flight envelope in
cases of abrupt degradation, and they are labelled Point 1,
Point 2, and Point 3. Operating Point 1 is at ground (Height
H= 0, Mach number Ma =0, W
f
= 2.48 kg/s), and it owns
the corrected N
L
100%. Operating Point 2 is also at ground
(H=0, Ma =0, W
f
= 1.95 kg/s), but its corrected N
L
is
90%. Operating Point 3 is at the cruise condition
(H= 10000 m, Ma = 0.7, W
f
= 1.13 kg/s), and its corrected
N
L
is 100%. Comparison results of estimation accuracy by
the MEIF and the MSCIF are presented in Table 1, and
RMSEs and RMSDs are involved in the cases of abrupt degra-
dation and gradual degradation.
As seen from Table 1, RMSEs and RMSDs of the MSCIF
are lower than those of the MEIF no matter which type of
abrupt fault modes is examined at the three flight operating
conditions. Likewise, the MSCIF has lower RMSEs than those
of the MEIF during gradual deterioration simulations. Since
Table 1 Comparison results of estimation accuracy by MEIF and MSCIF at typical operations.
Degradation type Algorithm Operating point 1 Operating point 2 Operating point 3
RMSE RMSD RMSE RMSD RMSE RMSD
Gradual
deterioration
MEIF 0.0227 0.0189 0.0253 0.0208 0.0268 0.0202
MSCIF 0.0205 0.0166 0.0227 0.0196 0.0231 0.0195
Fan MEIF 0.0268 0.0205 0.0274 0.0230 0.0326 0.0249
MSCIF 0.0211 0.0188 0.0229 0.0205 0.0286 0.0222
Compressor MEIF 0.0241 0.0208 0.0264 0.0242 0.0298 0.0239
MSCIF 0.0213 0.0188 0.0235 0.0214 0.0262 0.0228
HPT MEIF 0.0254 0.0213 0.0275 0.0224 0.0338 0.0254
MSCIF 0.0226 0.0197 0.0253 0.0221 0.0281 0.0225
LPT MEIF 0.0284 0.0210 0.0269 0.0231 0.0341 0.0247
MSCIF 0.0218 0.0191 0.0236 0.0211 0.0254 0.0222
A multi-rate sensor fusion approach using information filters 1609

gradual deterioration impacts all components while abrupt
degradation impacts one (at most two) component at a time,
the former degradation estimation produces higher RMSEs
than those of the latter one. It indicates that the MSCIF pro-
vides better health estimation accuracy and is less fluctuant
around the real degradation compared to the MEIF. Hence,
only the MSCIF is chosen and further assessed to state estima-
tion performance with regard to sensor fault tolerance in dig-
ital simulations.
4.2. Sensor-fault-tolerant degradation estimation
The health parameter tracked by the MSCIFs is discussed
under gradual deterioration with one sensor faulty during sen-
sor fusion in a multi-sampling system. As was mentioned ear-
lier, k
1
,k
2
, and k
3
refer to the fault indicators of the speed,
pressure, and temperature subsets, and fault thresholds of
the three engine sensor subsets are selected by statistical mea-
surement noise.
32
The fault thresholds of the three subsets are
k
1,max
= 7.5, k
2,max
= 5, and k
3,max
= 5. The total cycle num-
ber is 2000 in the simulation. A magnitude 1.5% of sensor bias
fault is injected to the LPT outlet pressure sensor P
5
during
1000–1400 cycles, and the remaining sensors run normally.
The same bias magnitude is given to sensor N
L
, and it means
that the sensor subset of the spool speed fails. Fig. 4 depicts
health performance estimation by MSCIF algorithms during
gradual deterioration, and estimated and real values of health
parameters are separately depicted by solid and dotted lines.
Four estimated health parameters SW
2
,SE
3
,SW
3
, and SW
4
by the MSCIF have rapid changes and deviate from their nor-
mal values as sensor P
5
fault injection at 1000 cycles under
gradual deterioration in Fig. 4(a). From Fig. 4(c), the esti-
mated fan flow capacity SW
1
drops obviously from 98.5% to
96.2%, and the rest health parameters change a little as sensor
N
L
bias occurs. Some deviation of sensor measurements will
pollute the health parameters estimates of the MSCIF, and
these estimates are no longer suitable for engine performance
monitoring. Fig. 4(b) and 4(d) give the health estimation by
the MSCIF with the maximum likelihood test during gradual
degradation, and the fault indicators kof the three sensor sub-
sets in the ML-MSCIF are given in Fig. 5(a) and 5(b).
From Fig. 5(a), the fault indicators of spool speed and tem-
perature sensor subsets k
1
and k
3
move smoothly, while k
2
sud-
denly exceeds the fault threshold value (k
2,max
= 5) from 1000
cycles to 1400 cycles. The sensor P
5
breakdown only leads to a
clear change on the fault indicator of the pressure sensor sub-
set, and no effect on the other fault indicators. Fault indicator
k
1
violates its threshold, and the rest indicators k
2
and k
3
are
below their thresholds during the sensor N
L
bias in Fig. 5(b).
As was mentioned earlier, the fault sensor will be isolated,
and the corresponding sensor signal in Channel B will be trig-
gered for state estimation when the sensor failure of a subset in
Fig. 4 Health estimation with one sensor faulty under gradual deterioration by MSCIFs.
1610 F. LU et al.

Fig. 6 Health estimation under abrupt degradation combined with sensor faulty.
Fig. 5 ML-MSCIF fault indicators of sensor subsets combined with gradual degradation.
A multi-rate sensor fusion approach using information filters 1611

Channel A is detected. Then the estimates of engine health
parameters are calculated by the ML-MSCIF on the basis of
the measurement without sensor bias pollution.
When it comes to abrupt performance degradation, a sim-
ulation test of the MSCIFs on fan abrupt degradation and
HPT abrupt degradation combined with sensor bias is carried
out. The total simulation time is 10 s. The abrupt degradation
of components occurs at t= 2 s, and a 2% bias of sensor T
43
and N
H
are injected from 5 s to 7 s. Comparisons of engine
health estimation between the MSCIF and the ML-MSCIF
are shown in Fig. 6. From Fig. 6(a), the estimates of health
parameters obviously deviate from their real values between
5 s and 7 s, especially the LPT efficiency suddenly shifts to
109%. It is obtained that the sensor bias results in a deviation
of health parameter estimates by the MSCIF without maxi-
mum likelihood validation. Similar results can be obtained in
Fig. 6(c), and some health parameter estimates by the MSCIF
clearly deviate from their real magnitudes as sensor N
H
fault.
The fault indicators kof the three sensor subsets in the ML-
MSCIF are shown in component abrupt degradation in Fig. 7.
From Fig. 7(a), the fault indicators of speed and temperature
sensor subsets k
2
and k
3
exceed their thresholds at 2 s, and
immediately move back. Only k
3
runs above its threshold from
5 s to 7 s. The fault indicators k
2
and k
3
jump over their thresh-
olds at 2 s, which is resulted from a component performance
abrupt change. These indicators rapidly move below the
thresholds after 2 s. Based on the maximum likelihood test
of the ML-MSCIF, it is not sensor anomaly at 2 s since these
fault indicators are not above their thresholds for three succes-
sive steps. Hence, the sensor measurement in Channel A will
still work for engine health estimation by the ML-MSCIF,
and no need of redundant measurements in Channel B. Since
the overrun of fault indicator k
3
successively occurs during
5 s and 7 s, an anomaly of the temperature sensor subset is
detected. Then, the fault sensor subset is isolated, and its
redundant sensor subset of temperature is triggered for state
estimation. As seen from Fig. 6(b), the estimates of health
parameters are around 1 before 2 s, and then SE
1
and SW
1
move to 0.98, and the rest health parameters are still around
1 after 2 s. In Fig. 6(d), SE
3
moves to around 0.98, SW
3
to
1.02, and the remaining health parameters are about 1 after
2 s, which indicates that HPT abrupt degradation is reached
and tolerant to sensor N
H
faulty. Therefore, the ML-MSCIF
yields a correct health condition of the aircraft engine in the
scenarios of fan and HPT abrupt degradation with one sensor
faulty.
The simulation results from Fig. 4 to Fig. 7 reveal that the
health parameters estimates can well track to their real changes
of health condition under fan abrupt degradation with sensor
T
43
fault and HPT abrupt degradation with sensor N
H
fault. In
order to comprehensively evaluate the health estimation per-
formance of the ML-MSCIF in a multi-sensor system, tests
in various combinations of component degradation with faulty
sensors are performed at ground design operation. The magni-
tudes of sensor bias in speed, pressure, and temperature are
1.5%, 1.5%, and 2%, respectively. Table 2 shows the RMSEs
and RMSDs of the ML-MSCIF in cases of four rotating com-
ponents with one sensor deviation from its normal value.
The maximum RMSEs of fan, compressor, HPT, and LPT
degradation are respectively 0.0229, 0.0231, 0.0235, and 0.0221
from Table 2, which indicate that health parameter estimates
by the ML-MSCIF algorithm could give a good tracking accu-
racy in the examined component performance abrupt degrada-
tion. The RMSDs of four abrupt degradations are all below
0.0217, so the ML-MSCIF estimation results are relatively
steady around the real health status. From the simulations
above, we conclude that the ML-MSCIF algorithm can pro-
vide a satisfactory performance of health estimation in both
gradual deterioration and abrupt degradation combined with
sensor faulty.
Fig. 7 ML-MSCIF fault indicators of sensor subsets under component abrupt degradation.
1612 F. LU et al.

4.3. Semi-physical experiment and analysis
In order to further verify the health estimation performance of
the proposed algorithm using sensor fusion with different sam-
pling rates, tests are performed in a semi-physical experimental
system of aircraft engine rotating component health monitor-
ing. This experimental system is developed from an engine
health monitoring rapid prototype system,
33
and the hardware
equipment and block diagram for the engine degradation esti-
mation semi-physical experiment are presented in Fig. 8. The
semi-physical experimental system contains an aircraft engine
simulator, a controller rapid prototype, real I/O interfaces, a
fuel servo system, and a health estimation module.
A virtual aircraft engine model regarded as a real engine
runs in the engine simulator in real time on the National
Instrument (NI) PXIe module, and the sampling frequencies
of various sensors are set as digital simulation. One hardware
NI CompactRIO (CRIO) plays the role of health estimation
unit to track component performance and sensor fault
isolation in real time. Another NI CRIO is used as a controller
Fig. 8 Semi-physical experiment platform for engine health estimation.
Table 2 RMSEs and RMSDs of ML-MSCIF under various combinations of component degradation with one sensor faulty.
Sensor Fan Compressor HPT LPT
RMSE RMSD RMSE RMSD RMSE RMSD RMSE RMSD
N
L
0.0212 0.0187 0.0223 0.0186 0.0227 0.0193 0.0215 0.0192
N
H
0.0207 0.0190 0.0229 0.0198 0.0231 0.0194 0.0211 0.0187
P
22
0.0223 0.0210 0.0229 0.0194 0.0232 0.0204 0.0220 0.0200
P
3
0.0221 0.0195 0.0225 0.0199 0.0233 0.0200 0.0220 0.0194
P
43
0.0224 0.0194 0.0231 0.0195 0.0230 0.0201 0.0221 0.0187
P
5
0.0222 0.0187 0.0223 0.0194 0.0233 0.0200 0.0221 0.0196
T
22
0.0229 0.0217 0.0225 0.0195 0.0235 0.0203 0.0212 0.0184
T
3
0.0213 0.0199 0.0224 0.0195 0.0230 0.0196 0.0220 0.0193
T
43
0.0216 0.0188 0.0228 0.0199 0.0231 0.0202 0.0221 0.0186
T
5
0.0225 0.0200 0.0225 0.0199 0.0227 0.0200 0.0221 0.0186
A multi-rate sensor fusion approach using information filters 1613

rapid prototype to calculate fuel flow from the residuals of the
command and sensor measurement. The actuator of the exam-
ined system is achieved by an electro-hydraulic servo module,
which is driven by a small inertia motor simulating the engine
Low-Pressure (LP) spool.
The analog signal of engine fuel consumption sensed by a
turbine flowmeter with a sampling rate of 20 ms is transformed
to a digital signal, and it is then sent into the engine simulator
for engine model computation. The digital signal of the LP
rotor speed is transformed to an analog signal to make a small
inertial motor follow this spool speed, and it drives the fuel
pump to supply fuel for the control system by a power shaft
at the same time. The rotating speed is measured by a speed
sensor installed on the motor, and transformed to a digital sig-
nal to stream into both of the controller and the health estima-
tion module.
Gradual degradation and abrupt degradation of gas path
performance are tested on the semi-physical experimental plat-
form, with a closed-loop control of the LP rotor speed at the
design operation.
33,34
The data sampling rates are 20 ms,
Fig. 9 Health estimation of ML-MSCIF under gradual deterioration on semi-physical experiment platform.
Fig. 10 Health estimation of ML-MSCIF in abrupt degradation on semi-physical experiment platform.
1614 F. LU et al.

40 ms, and 60 ms in the speed sensor subset, pressure sensor
subset, and temperature sensor subset using a dual-channel
mode. The control variables and sensor measurements are nor-
malization and dimensionless before filtering calculation. The
change rule of the engine health parameters is the same as that
during gradual degradation in the digital simulation above,
and sensor P
5
in Channel A is failed with a 2% bias from
500 to 700 cycles. Fig. 9 presents the system parameters of
engine health estimation during gradual deterioration on the
semi-physical experimental platform. The control variable W
f
and the plant output N
L
are given in Fig. 9(a), and the esti-
mates of engine health parameters are shown in Fig. 9(b).
As seen from Fig. 9(a), fuel flow measured by the sensor of
the turbine flowmeter increases slowly along with performance
gradual deterioration, while parameter N
L
is almost not chan-
ged. More fuel is consumed to make actual N
L
to follow the
control command as the component performance degradation.
From Fig. 9(b), the actual change rules of health parameters
follow the dot lines, which are similar to those in Fig. 4(b).
The estimated health parameters move around the dot lines,
and the maximum deviation of health parameters by the
ML-MSCIF is below 0.9%. The standard deviations in the
digital test are less than those in the semi-physical test due to
the higher noise level and the fuel actuator included in the lat-
ter test. Consequently, the ML-MSCIF yields the estimated
health parameters well tracking real degraded magnitudes of
gas path performance using sensor fusion with different sam-
pling rates.
The abrupt performance degradations of four rotating
components by the ML-MSCIF are tested combined with a
2% bias on sensor N
H
using an asynchronous sample of sensor
measurements. An abrupt degradation on components occurs
at 2 s, and the sensor bias from 5 s to 7 s. Anomaly tracking
results are shown in Fig. 10, wherein health parameters esti-
mates in the cases of fan degradation in Fig. 10(a), compressor
degradation in Fig. 10(b), HPT degradation in Fig. 10(c), and
LPT degradation in Fig. 10(d).
The estimates of health parameters SE
1
and SW
1
by the
ML-MSCIF begin to deviate 2% from 1 at 2 s, and each
health parameter follows its real value change denoted by a
dot line in Fig. 10(a). Fan degradation is then recognized from
Fig. 10(a) at 2 s since 2% on both SE
1
and SW
1
relates to fan
degradation. The estimates of health parameters SE
3
and SW
3
deviate 2% and 2% from 1 at 2 s, and the rest estimates track
their real parameters well in the whole 10 s in Fig. 10(c). From
Fig. 10(b) and Fig. 10 (d), we can separately find compressor
degradation and LPT degradation from 2 s, which indicates
that the ML-MSCIF could give accurate estimates of gas path
performance changes. The effect of health parameters on the
control variables is extended to the semi-physical experiment
in the N
L
close-loop system, and Fig. 11 gives examined
parameters results by the ML-MSCIF under single fan health
parameter degradation.
The engine runs at the design operation, and a deviation of
3% on SE
1
occurs at 4.5 s. From Fig. 11(b), all health
parameter estimates move around 1.00, and only the SE
1
Fig. 11 Semi-physical experimental results of ML-MSCIF health estimation under single health parameter degradation.
A multi-rate sensor fusion approach using information filters 1615

estimate has a sharply shift to 0.97 from 4.5 s. Since the fan
efficiency decreases, the fuel flow increases to about 1.04 to
maintain N
L
in Fig. 11(a). Fig. 11(c) and 11(d) show the effect
of the fan mass flow coefficient SW
1
on the fuel flow in the N
L
close-loop system. The SW
1
estimate steps to about 0.98 at
2.5 s and tracks its actual value from Fig. 11(d). It illustrates
that SW
1
degradation in the fan leads to less fuel consumption
for a given N
L
. Although N
L
can still be maintained, the power
reduces due to a decrease of the air mass flow. That is to say,
performance degradation in any of the components does not
always result in more fuel consumption for a given N
L
, and
a given N
L
is only one of the key factors to reflect the power
requirement.
In order to further evaluate the health estimation perfor-
mance of the ML-MSCIF on multiple-component degrada-
tions, one typical abrupt degradation on double components
is carried out combined with sensor N
H
bias using an asyn-
chronous sample of sensor measurements. This combination
of component degradation is fan-plus-HPT abrupt degrada-
tion, in which the fan degrades at t= 2 s and the HPT at
t= 6 s successively. A bias magnitude of 2% on sensor N
H
occurs from 8 s, and semi-physical experiment results by the
ML-MSCIF are shown in Fig. 12.
The fuel flow W
f
decreases a little from 2 s and then clearly
increases from 6 s in Fig. 12(a). Fan degradation leads to a
decrease of power consumption in the LP spool, and an air
mass flow coefficient reduction plays the dominant role for
the fuel flow decrease after 2 s. Although a fan efficiency reduc-
tion will increase the fuel flow, a fan flow capacity reduction
will more obviously decrease the fuel flow from the previous
simulation and discussion. The power driving the spool to
rotate will reduce as HPT degradation. Compared to fan
degradation, HPT degradation dominates the power change
with the same degradation magnitudes on efficiency and flow
capacity. Hence, more fuel will be consumed to maintain the
spool speed unchanged as the combination degradation on
fan and HPT from 6 s. Although the LP spool speed N
L
fluc-
tuates at about 2 s and 6 s as component degradation, it can
move back and along 1.00 in the whole 10 s in Fig. 12(a).
The health parameter estimates follow the desired deviation
of gas path health performance by the ML-MSCIF from
Fig. 12(b). In a word, the health estimation performance of
the ML-MSCIF is validated using sensor fusion with multiple
sampling rates from the semi-physical experiment, and it
acquires similar results achieved by digital simulations.
5. Conclusions
This paper has proposed a new multi-rate state estimation
method based on information filters for aero-engine degrada-
tion estimation. The novelty of this methodology lies in the
development of ML-MSCIF algorithms using sensor subsets
fusion with asynchronous measurement, and the maximum
likelihood validation strategy to address the issues of combina-
tion anomaly detection of component degradation and one-
sensor faulty. The methodology is evaluated on a dual-spool
turbofan engine for gas path abrupt and gradual degradation
estimations by digital simulation and semi-physical experi-
ment. Experimental results show that the involved information
filters with soft measurement synchronization can achieve
multi-rate state estimation by sensor fusion. The MSCIF has
better state tracking performances than those of the MEIF
at typical operations in a flight envelope from systematic com-
parisons. Besides, sensor fault tolerant health estimation is
completed by the ML-MSCIF using maximum likelihood val-
idation, and it provides satisfactory accuracy of health
estimation.
This research introduces a novel multi-rate filtering algo-
rithm for aero-engine health estimation with asynchronous
measurement. There are several important topics for future
research that are related to this work. The information filtering
methodology developed in this paper runs in a partly sensor
fusion structure, and the same kinds of sensor are classified
into one sensor subset. Further studies can extend to a compre-
hensive sensor fusion system, and sensors of the same kind in
one subset could own different sampling rates. In addition, the
evaluation of the proposed methodology is limited to digital
simulation and semi-physical experiment, and it will be of
more practical significance to examine these involved algo-
rithms on a rig test of an aero-engine at more typical opera-
tions in a full flight envelope.
Acknowledgements
We are grateful for the financial supports of the National
Natural Science Foundation of China (No. 61304113), the
Fig. 12 Semi-physical experimental results of ML-MSCIF health estimation under fan+ HPT abrupt degradation.
1616 F. LU et al.

Fundamental Research Funds for the Central Universities,
China (No. NS2018018), and Qinglan Project of Jiangsu
Province.
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