fault detection for gas turbines based on long-term

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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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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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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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

=


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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


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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700 800 900 1000 1100 1200 1300 1400 1500 1600-40

-20

0

20

40

Testing Result

Time t


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


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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