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Neural Network Approach for
Predicting Drum Pressure and Level
in a Coal-fired Subcritical Power Plant
Eni OKO and Meihong Wang Process and Energy Systems Research Group, School of Engineering
University of Hull HU6 7RX, United Kingdom
10th European Conference on Coal Research and its Applications Sept 15-17, 2014, University of Hull, UK
Outline
Background
Boiler Drum Data
NARX Model
NARX Model Training
Results
Conclusion and Future Work
Outline
Background
Boiler Drum Data
NARX Model
NARX Model Training
Results
Conclusion and Future Work
Background
Layout of Coal-fired Subcritical Power Plant1
Background
Boiler Drum is a critical component of a coal-fired subcritical
power plant:
acts as energy reservoir in the plant enabling it to cope
with short term load changes
dictates overall plant dynamics due to the slower
dynamics compared to the steam turbine dynamics
Due to tightening regulations, deserves study of the
dynamics for operation and control purposes
Data-based approach such as neural networks less
laborious than physical modelling
Outline
Background
Boiler Drum Data
NARX Model
NARX Model Training
Results
Conclusion and Future Work
Boiler Drum Process
Represented by a detailed first principle model
according to Åström and Bell [3] using gPROMS tool.
Inputs: Feedwater flowrate, Steam flowrate and heat
energy input
Outputs: Drum pressure and drum water level
Thermodynamic properties of water/steam were
obtained using IAPWS-95 formulation in Aspen Properties
via COThermo interface.
Thermodynamic property derivatives were obtained using
polynomial approximations of steam table calculations from NIST REFPROP V9.1.
Boiler Drum Process
Global Conservation Equations Downcomer-Riser Dynamics
Drum Dynamics
stfwwtwsts mmVVdt
d ][
stsfwfwsatpttwtwwstss mhmhQTCMpVVhVhdt
d ][
rdcrvwrvs mmVVdt
d ])1([
rwwsrwdc
satprrrvwwrvss
mhhhhmQ
TCMpVVhVhdt
d
))((
])1([
)]1()ρ(ρα
ρ[1
ρρ
ρα
swr
s
sw
wv
s
swrIn
VVV wtst
k
VAgm swrdcvw
dc
)(2
cdsdrrsds mmmVdt
d
])([1
dt
dTCm
dt
dpVV
dt
dhV
dt
dhV
hhhh
hhmm sat
pdwdsdw
wdws
sds
wsws
fww
fwcd
)()( 0
rdcrdcrsdsd
d
ssd mmmVV
Tm
d
sdwdd
A
VVL
rvdcwtwd VVVV )1(
Boiler Drum Data
Data obtained at open loop conditions using the developed
model
The system is excited by perturbing the inputs in
succession with a series of step changes in no particular
order
Perturbation in each input is sustained for an hour resulting
to a total test period of 3 hours (10800 seconds).
Other inputs are maintained at their equilibrium value while
perturbing the other.
Boiler Drum Data
40
50
60
70
80
90
100
110
120
130
140
0 500 1000 1500 2000 2500 3000 3500
Fee
dw
ate
r Fl
ow
(kg
/s)
Time (s)
40
50
60
70
80
90
100
110
120
130
140
3500 4500 5500 6500
Ste
am F
low
(kg
/s)
Time (s)
1.20E+08
1.30E+08
1.40E+08
1.50E+08
1.60E+08
1.70E+08
1.80E+08
1.90E+08
2.00E+08
2.10E+08
7100 8100 9100 10100
He
at In
pu
t (W
)
Time (s)
Boiler Drum Data
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0 2000 4000 6000 8000 10000
Dru
m w
ate
r le
vel (
m)
Time (s)
8.5E+06
9.0E+06
9.5E+06
1.0E+07
1.1E+07
1.1E+07
1.2E+07
1.2E+07
1.3E+07
0 2000 4000 6000 8000 10000
Dru
m P
ress
ure
(P
a)
Time (s)
Outline
Background
Boiler Drum Data
NARX Model
NARX Model Training
Results
Conclusion and Future Work
Neural Networks (NNs)
Computational paradigm inspired from the structure of
biological neural networks and their way of encoding and
solving problems.
Able to identify underlying highly complex relationships
based on input-output data only.
Neural Networks (NNs)
NN model capable of reproducing time-dependent
(dynamic) data takes into account the time variable by
means of a memory process.
This is done using NN architectures with feedback
connections among neurones and time delay lines (TDL)
NARX NN is a typical NN with feedback connections
enclosing several layers of the network and a TDL.
NARX Model
NARX Model is defined by the Equation:
y(t) = f[y(t-1),y(t-2),...,y(t-ny),u(t-1),u(t-2),...,u(t-nu)]
Where:
(y(t))=Current value of predicted output signal expressed
(y(t-1),y(t-2),...,y(t-ny))= Previous values of the output signal
(u(t-1),u(t-2),...,u(t-nu)) = Previous values of an independent
(exogenous) input signal.
For NARX NN, the previous values are recorded using the
TDL and the nonlinear polynomial function (f)
approximated using a feedforward NN
Outline
Background
Boiler Drum Data
NARX Model
NARX Model Training
Results
Conclusion and Future Work
NARX Model Training
Training complicated due to the feedback loop; ideally
dynamic training algorithm which is complex is needed
y(t)
Feedforward
Network
T
D
L
T
D
L ŷ(t)
u(t)
ŷ(t)
Feedforward
Network
T
D
L
T
D
L
u(t)
(a) Parallel Architecture
(Standard NARX Architecture)
(b) Series-Parallel Architecture
With (b), less complex static training algorithm is used for
training.
NARX Model Training
lD
pD mFW NARX NN
mST
Q
Training with simulated data from the detailed physical model.
Early stopping technique used to avoid overfitting: Data
divided into training (70%), validation (15%) and testing
(15%) data.
Levenberg-Marquardt training algorithm used (trainlm) with
mean squared error (MSE) performance function.
100 neurones in the hidden layer each with a sigmoid
transfer function
NARX Model Training
0 50 100 150 200 250 300
10-6
10-4
10-2
100
102
Best Validation Performance is 4.8725e-07 at epoch 300M
ea
n S
qu
are
d E
rro
r (
ms
e)
306 Epochs
Train
Validation
Test
Best
Outline
Background
Boiler Drum Data
NARX Model
NARX Model Training
Results
Conclusion and Future Work
Results
-20 -15 -10 -5 0 5 10 15 20
0
0.5
1
1.5
2
2.5
3
x 10 6
Lag
Correlations
Zero Correlation
Confidence Limit
Co
rrela
tio
n
-20 -15 -10 -5 0 5 10 15 20
0
1
2
3
4
5
6
7
x 10 -11
Lag
Correlations
Zero Correlation
Confidence Limit
Error Autocorrelation Plot
Drum Pressure Prediction Error
Autocorrelation Plot
Drum Level Prediction Error
Autocorrelation Plot
The plots show reliable estimate of the network
parameters, weights and biases
Results
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25x 10
7
Dru
m P
res
su
re (
Pa
)
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000-4
-2
0
2
4x 10
4
Err
or
Time (s)
Training Targets
Training Outputs
Validation Targets
Validation Outputs
Test Targets
Test Outputs
Errors
Response
Targets - Outputs
0.015
0.02
0.025
0.03
0.035
0.04
0.045
Dru
m L
ev
el (m
)
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000-2
0
2
4x 10
-4
Err
or
Time (s)
Training Targets
Training Outputs
Validation Targets
Validation Outputs
Test Targets
Test Outputs
Errors
Response
Targets - Outputs
Output/Target Comparison (Drum Pressure) Output/Target Comparison (Drum Level)
Results
Step Change Test: Performed on one input at a time
while other inputs remain unchanged
+30 kg/s step change in feedwater flowrate
0.035
0.036
0.037
0.038
0.039
0.04
0.041
0.042
0 50 100 150 200
Dru
m L
eve
l (m
)
Time (s)
Actual NARX
9.80000E+06
9.90000E+06
1.00000E+07
1.01000E+07
1.02000E+07
1.03000E+07
1.04000E+07
1.05000E+07
1.06000E+07
1.07000E+07
0 50 100 150 200
Dru
m P
ress
ure
(P
a)
Time (s)
Actual NARX
Results
+10 MW step change in Heat Input
0.0325
0.033
0.0335
0.034
0.0345
0.035
0.0355
0.036
0.0365
0 50 100 150 200 250
Dru
m L
eve
l (m
)
Time (s)
Actual NARX
1.04000E+07
1.06000E+07
1.08000E+07
1.10000E+07
1.12000E+07
1.14000E+07
1.16000E+07
0 50 100 150 200 250
Dru
m P
ress
ure
(P
a)
Time (s)
Actual NARX
Results
0.035
0.036
0.037
0.038
0.039
0.04
0.041
0.042
0.043
0 50 100 150 200 250
Dru
m L
eve
l (m
)
Time (s)
Actual NARX
+10 kg/s step change in Steam Flowrate
9.20000E+06
9.40000E+06
9.60000E+06
9.80000E+06
1.00000E+07
1.02000E+07
1.04000E+07
1.06000E+07
1.08000E+07
0 50 100 150 200 250D
rum
Pre
ssu
re (
Pa)
Time (s)
Actual NARX
Outline
Background
Boiler Drum Data
NARX Model
NARX Model Training
Results
Conclusion and Future Work
Conclusion and Future Work NARX NN can be used to obtain reliable dynamic model
of a boiler drum from the plant input-output operating
data only.
Use of NARX NN avoids the rigours of reliable parameter
estimation often needed in modelling from first principle.
As it is the case with all empirical models, NARX NN
models are only reliable when they are used within the
conditions that they were trained.
The NARX NN model developed in this study is subject to
the inherent deficiencies in Åström and Bell [3] model
which was used to obtain the training data.
Development of model predictive control (MPC) of the
boiler drum based on the NARX NN model is on-going.
References
1) Illustrations and text are taken from the Spirax Sarco website 'Steam Engineering Tutorials' at
http://www.spiraxsarco.com/resources/steam-engineering-tutorials.asp. Illustrations and text are
copyright, remains
the intellectual property of Spirax Sarco, and have been used with their full permission
2) Åström, K.J. and Bell, R.D. Drum-boiler dynamics. Automatica 2000; 36: 363-378.
Acknowledgement
Natural Environment Research Council (NERC), UK
EU FP7 Marie Curie
Multiphase Flow Measurement Research Group,
South East University, Nanjing, China
Questions???
Contact:
Dr Meihong Wang
Process and Energy Systems Engineering Group,
School of Engineering, University of Hull HU6 7RX
Tel.: +44 1482 466688. E-mail address: [email protected]
Thank you for your Attention!