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7/27/2019 Fault Detection for Gas Turbines Based on Long-term
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Proceedings of the Sixth International Conference on Machine Learning and Cybernetics, Hong Kong, 19-22 August 2007
FAULT DETECTION FOR GAS TURBINES BASED ON LONG-TERMPREDICTION USING SELF-ORGANIZING FUZZY NEURAL NETWORKS
YONG-JIE ZHAI1,2
, XUE-WU DAI2,3
, QIAN ZHOU1
1 Department of Automation, North China Electric Power University, Baoding 071003, China2 Control Systems Centre, Manchester University, Manchester, M60 1QD
3Southwest University, Chongqing, ChinaE-MAIL: [email protected]
Abstract:
For real-time condition monitoring and fault detection of
dual-lane controlled systems, reduced order models and
long-term prediction are required. In this paper fault
detection of reduced order model of nonlinear systems based
on long-term prediction is proposed by using self-organizing
fuzzy neural network (SOFNN). The main advantages of
SOFNN are that, firstly, it is very user friendly as it can
automatically determine the model structure and identify the
model parameters without requiring the in-depth knowledge
about fuzzy systems and neural networks; secondly, it
provides the excellent modeling accuracy.
Data gathered at an aero engine test-bed serve as the test
vehicle to demonstrate the long-term prediction. A faultdetection system is designed by using SOFNN. SOFNN is
trained and used to simulate system dynamic characteristic.
The simulation result is compared with actual output, and
then fault error is drawn. The simulation result shows that,
SOFNN can simulate the system more accurately, thus the
change of residual error is easy to be detected. This assures the
validity of this fault detection system.
Keywords:Self-organizing fuzzy neural network (SOFNN); Fault
detection; Gas turbines
1. Introduction
Gas turbines are widely used in aerospace, marine and
power industries. Their safety requirement and associatedmaintenance costs are quite high. Condition monitoring andfault detection of gas turbine engines is extremelyimportant in aircraft operation, which strongly depends onthe health of the engine and its sensors and controllers.
In recent years, many model-based approaches have
been applied in real time model identification, conditionmonitoring and fault detection. Time-domain methods areused to build a reduced order linear model and use GeneticAlgorithms to optimize the prediction in [1], [2]. Spectral
estimation methods in frequency-domain are used toimprove the identification accuracy of FRF(Frequency-response function) in [2][4]. In stochasticdomain methods[5, 6], Markov models and neural networksare used. In [7, 8], applications of reduced order models forcondition monitoring are studied. In [2,4], RPLDM
(Real-time Piecewise Linear Dynamic Model) and LDM(Linear Dynamic Model) are applied for real-timemodelling.
This study is motivated by the challenges ofdeveloping modeling algorithms for long-term prediction.
And a reduced order model is needed for real-time
application. Furthermore, in the case of dual-lane controller,a long-term prediction model is required for fault detectionand the problem of prediction errors dependency [9] has tobe resolved.
This paper is organized as follows. Model-based
condition monitoring in dual-lane engine control isintroduced in section 2. Section 3 formulates the long-termprediction model and describes the problem of predictionerrors dependency. Section 4 introduces the algorithm ofSOFNN. Finally, section 5 contains the results ofexperimental application of this method using actual data
collected from an engine test-bed .
2. Gas Turbine Engine Condition Monitoring
In modern aero engines, control systems are usuallyorganized as dual-lane systems with two sets of parallelsensors and controllers. One lane works as primary lane toissue the control signal, another lane is waiting in hotback-up. When the primary lane fails, the spare lanecomes online immediately. An information redundancy
exists by using such two sets of duplicated hardware, asshown in Figure. 1. Therefore, the detection of lane failuresis possible by comparing the measurement differencebetween two channels.
1-4244-0973-X/07/$25.00 2007 IEEE
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Proceedings of the Sixth International Conference on Machine Learning and Cybernetics, Hong Kong, 19-22 August 2007
However, it is possible neither to decide which lane isin failure nor to detect a fault in an engine itself. It isnecessary to introduce a third lane and perform a majority
vote scheme. Unfortunately, having three or more hardwarelanes would be very expensive and could increase aircraftweight significantly. Furthermore, hardware redundancydoes not provide sufficient information to detect faults inthe engine itself.
Figure 1. Dual-lane Control of Gas Turbines. ControllerC1 and sensor S1 compose the primary lane. Controller C2and sensor S2 compose the second lane. The model worksas the third virtual lane.
A long-term prediction model, a sort of mathematicredundancy, is used to solve this problem. Such a model
runs autonomously as the third virtual lane to detect thefaults in two physical lanes. A general scheme, presented inFigure. 1, shows the use of on-board engine modeling incondition monitoring of a dual-lane control system [1]. The
monitor unit compares the values of high pressure shaftspeed n1, n2 measured by sensor in two hardware lanerespectively and n3, the value of model prediction. Theswitches are controlled by the monitor unit using majorityvote mechanism, as shown in Fig. 2. The 1st lane is theprimary lane which controls the engine when the
differences between the measurements of three lanes are
smaller than the tolerance . If they are significantly
different, then the majority vote is carried out and the
control tasks are rescheduled onto the healthy lanes:
|n1-n2|
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Proceedings of the Sixth International Conference on Machine Learning and Cybernetics, Hong Kong, 19-22 August 2007
modeling accuracy.
4. Algorithm of SOFNN
4.1. Structure of SOFNN
The structure of the self-organizing fuzzy neuralnetwork (SOFNN) is a five-layer fuzzy neural networkshown in Figure. 1. The five layers are the input layer, theellipsoidal basis function (EBF) layer, the normalized layer,the weighted layer, and the output layer.
The detailed mathematical description of the structure
of the SOFNN is given as follows:
Figure 3. Self-organizing fuzzy neural network.
Layer 1 is the input layer. Each neuron in this layerrepresents an input variable, , 1, 2,...,ix i r= .
Layer 2 is the EBF layer. Each neuron in this layerrepresents an if-part (or premise) of a fuzzy rule. Choosing
the MFs to be Gaussian functions and the outputs of EBFneurons as the products of the grades of MFs function, thejth neuron can be represented as
2
21
( )( ) exp , 1, 2,...,
2
ri ij
j
i ij
x cX
=
= =
j u (1)
where is the input vector,
is the vector of centre in the j-th EBF
neuron, and
),...,( 1 rxxX =
),...,( 1 rjjj xcc =
),...,( 1 rjjj = is the vector of widths in
thej-th neuron.Layer 3 is the normalized layer. The output of the j-th
neuron in this layer is2
21
2
121
1
( )exp
2
( )exp
2
1, 2,...,
ri ij
i ijj
j ur
u i ijjjj
i ij
x c
x c
j u
=
=
==
= =
=
(2)
Layer 4 is the weighted layer. Each neuron in this layerhas two inputs and the product of these inputs as its output.One of the inputs is the output of the related neuron in the
layer 3 and the other is the weighted bias2 j
w . For the
Mamdani fuzzy system,2 j
w is a constant. For
Takagi-Sugeno(TS)fuzzy system,2 jw is a linear function
as follows:
2 0
1
, 1, 2,...,r
j j ij i
i
w a a x j=
= + = u (3)
If choosing andjA B in Figure.1 as
, for Mamdani fuzzysystem, and for Takagi-Sugeno (TS)
fuzzy system, then
],...,,[ 10 rjjjj aaaA=
]0,...,0,1[=
BT
rxxB ],...,,1[ 1=
2, 1, 2,...,
j jw A B j= = u (4)
which is the then-part (or consequent) of the jth fuzzy ruleof the fuzzy model. The output of each neuron at this layer
is ),...,2,1(2 ujwf jjj == .
Layer 5 is the output layer. Each neuron in this layerrepresents an output variable as the summation of incoming
signals from the layer 4. Therefore, the output of a neuronin the layer 5 is
2
1 1
( )
u u
j j
j j
y F X f w = =
= = = 2
21
2 21
211
( )exp
2
( )exp
2
ri ij
ui ij
jr
j u i ij
ji ij
x c
wx c
=
=
==
=
(5)
where is the output value of fuzzy system .y )(XF
4.2. LEARNING ALGORITHM OF SOFNN
The learning process of the SOFNN includes bothparameter learning and structure learning. The parameterlearning makes the network converge quickly through an
on-line recursive least squares algorithm. The structurelearning attempts to achieve an economical network sizewith a new self-organizing approach. The most importantadvantage of the proposed structure learning algorithm isthat it can automatically identify the number of the neuronsneeded rather than the trial and error approach used by mostexisting neural network and fuzzy neural learning methods.
As shown in the last section, the output of the SOFNNmodel is linearly dependent on the weighting parameters,therefore the SOFNN model could be written as a special
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Proceedings of the Sixth International Conference on Machine Learning and Cybernetics, Hong Kong, 19-22 August 2007
case of a linear regression model: (see[9],[10] for details)
1
( ) ( ) ( )M
i i
i
d t p t t =
= + (6)
where, is the desired output ; are the regressors
which are some fixed functions of input vector
,.i.e., ; are the linear
parameters; is the error signal;
( )d t ( )i
p t
1 2( ...t t t r X x x x= )t p t p X = i( ) ( )i i t
( )t is the dimension
of the parameters, .( 1)M u r= +
Rewrite in matrix form for time ,t n=( ) ( ) ( ) ( )D n P n n E n= + (7)
where
( ) [ (1) (2)... ( )] ;T nD n d d d n R=
( ) [ (1) (2)... ( )]T T T T T nP n p p p n R = = M
M
,
here,
1 2( ) [ ( ) ( )... ( )],1T
Mp i p i p i p i i n= ;
2 1 2( ) [ ... ]T T
Mn W R = = ;
( ) [ (1) (2)... ( )]T nE n n = R ;
Based on the recursive least squares algorithm (RLS),at time t, an on-line weight learning algorithm for the
SOFNN has been developed as
( ) ( ) ( )L t Q t p t= 1( 1) ( )[1 ( ) ( 1) ( )]TQ t p t p t Q t p t = + ,(8)
( ) [ ( ) ( )] ( 1)T
Q t I L t p t Q t = , (9)
( ) ( 1) ( )[ ( ) ( ) ( 1)]Tt t L t d t p t t
= + , (10)
1, ( ) ( )
0, ( ) ( )
e t t
e t t
=
7/27/2019 Fault Detection for Gas Turbines Based on Long-term
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Proceedings of the Sixth International Conference on Machine Learning and Cybernetics, Hong Kong, 19-22 August 2007
5.2. Definition of the performance criterion
Mean Squared Error(MSE) is defined as follows:
=
=
n
i
iiyy
nMSE
1
2)(1
(14)
Normalized Mean Square Error (NMSE) is defined asfollows:
=
=
=n
i
i
n
i
ii
yy
yy
NMSE
1
1
(15)
Where and are the actual and prediction value ofthe sample point,
iy iyith y is the average actual value of the
sample points, is the number of the sample points.n
5.3. Implementation and Results
1) Training and long-term predictionThe results of training and long-term prediction are
shown in Figure5 and Figure.6. In these figures, the bluesolid line is the actual data and the red-dash line is theprediction data. The results of train and predictionperformance criteria are shown in Tables I.
Table 1. Accuracy of training
MSE NMSE
training 6.1125e-006 0.0010419
prediction 6.1495 0.032432
0 100 200 300 400 500 600 700 800-0.3
-0.2
-0.1
0
0.1
0.2Training Result
TargetandtrainingOutput
0 100 200 300 400 500 600 700 800-0.01
-0.005
0
0.005
0.01
Time t
Error
Figure 5. The Result of Training
700 800 900 1000 1100 1200 1300 1400 1500 1600-40
-20
0
20
40Testing Result
TargetandTestingOutput
700 800 900 1000 1100 1200 1300 1400 1500 1600-5
0
5
10
Erroroftest
Time t
Figure 6. The Result of Long-term Prediction
For the long-term prediction, as mentioned before, theinput of SOFNN is include the last prediction value. So the
error of prediction is larger than the training and theone-step-ahead prediction. The performance of training isexcellent and the performance of long-term prediction ispromising.2) Fault Detection
The residual error is the difference between the
prediction output value and the actual output value. The
residual error under different fault conditions of the outputsensor is shown in Figure7.
700 800 900 1000 1100 1200 1300 1400 1500 1600-40
-20
0
20
40
60Testing Result
Time t
TargetandTestingOutput
700 800 900 1000 1100 1200 1300 1400 1500 1600-30
-20
-10
0
10
20
Time t
error
Figure 7. (a) Residual Error of Sensor Gain Fault at t=1200s
From Figure.7 it can be concluded that when the faultof output sensor is occurred , the residual error will be
changed obviously. So, the fault can be detected based onthe change of residual error and the time of fault occurredcan be obtained.
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Proceedings of the Sixth International Conference on Machine Learning and Cybernetics, Hong Kong, 19-22 August 2007
700 800 900 1000 1100 1200 1300 1400 1500 1600-40
-20
0
20
40
Testing Result
Time t
TargetandTestingOutput
700 800 900 1000 1100 1200 1300 1400 1500 1600-20
-15
-10
-5
0
5
Time t
error
Figure 7. (b) Residual Error of Sensor Bias Fault at t=1200s
700 800 900 1000 1100 1200 1300 1400 1500 1600-40
-20
0
20
40Testing Result
Time t
TargetandTestingOutput
700 800 900 1000 1100 1200 1300 1400 1500 1600
-20
-15
-10
-5
0
5
Time t
error
Figure 7. (c) Residual Error of Sensor Spike Fault att=1200s
6. Conclusions
The SOFNN model is a very simple and effectiveapproach, which generates a fuzzy neural model with highaccuracy and compact structure [15]. In this paper, thisapproach is proposed to be applied to the long-termprediction and fault detection of the gas turbines system.
The experiments demonstrate that the application is very
successful with very promising results.This approach is developed for modeling of reducedorder linear model, although the system considered isnonlinear. It is considered important for real-time conditionmonitoring to avoid the complexities that would otherwise
be inevitable when nonlinear models are used. Furthermore,as a plant usually runs at an expected point of operation,order reduction is reasonable and linear models are stillvery valid.
Finally, although this is an application study based ona gas turbine, the principles and methods used here are
applicable to a broad class of industrial system withdynamic behaviour.
Acknowledgements
This paper is supported by the research projects fundfunded for the doctoral teachers of North China Electric
Power University. The item number is 200512014.The authors wish to acknowledge Dr. Tim Breikin, who
is with the University of Manchester, for provision of theexperimental data and technical support.
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