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Nuclear Technology
ISSN: 0029-5450 (Print) 1943-7471 (Online) Journal homepage: http://www.tandfonline.com/loi/unct20
Monitoring Feedwater Flow Rate and Component
Thermal Performance of Pressurized Water
Reactors by Means of Artificial Neural Networks
Kadir Kavaklioglu & Belle R. Upadhyaya
To cite this article: Kadir Kavaklioglu & Belle R. Upadhyaya (1994) Monitoring Feedwater Flow
Rate and Component Thermal Performance of Pressurized Water Reactors by Means of Artificial
Neural Networks, Nuclear Technology, 107:1, 112-123, DOI: 10.13182/NT94-A35003
To link to this article: http://dx.doi.org/10.13182/NT94-A35003
Published online: 13 May 2017.
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Date: 25 October 2017, At: 05:32
MONITORING FEEDWATER FLOW
RATE AND COMPONENT THERMAL
PERFORMANCE OF PRESSURIZED
WATER REACTORS BY MEANS OF
ARTIFICIAL NEURAL NETWORKS
K A D I R K A V A K L I O G L U and B E L L E R.
REACTOR
CONTROL
KEYWORDS: feedwater
flow
rate, thermal performance, artificial neural networks
UPADHYAYA
The University of Tennessee, Department of Nuclear Engineering
Knoxville, Tennessee 37996-2300
Downloaded by [University of Florida] at 05:32 25 October 2017
Received July 22, 1993
Accepted for Publication January 12, 1994
e r a t o r w a t e r level r e g u l a t i o n i n pressurized w a t e r reactors ( P W R s ) . T h i s f l o w r a t e is m e a s u r e d b y installed
The fouling of venturi meters, used for steam generator feedwater flow rate measurement in pressurized
water reactors (PWRs), may result in unnecessary plant
power derating. On-line monitoring of these important
instrument channels and the thermal efficiencies of the
balance-of-plant components are addressed. The steam
generator feedwater flow rate and thermal efficiencies
of critical components in a P WR are estimated by means
of artificial neural networks. The physics of these systems and appropriate plant measurements are combined to establish robust neural network models for
on-line prediction offeedwater flow rate and thermal
efficiency of feedwater heaters in PWRs. A statistical
sensitivity analysis technique was developed to establish the performance of this
methodology.
v e n t u r i meters. T h e pressure d r o p across t h e v e n t u r i
t u b e , using pressure taps at t h e inlet a n d t h e t h r o a t , is
measured a n d is related t o the f l o w rate i n t h e p i p i n g . 1 ' 2
A l t h o u g h t h e use o f some c o r r e c t i o n f a c t o r s , such
as t h e t h e r m a l e x p a n s i o n f a c t o r a n d t h e a d i a b a t i c exp a n s i o n f a c t o r i n the pressure d r o p a n d mass f l o w r a t e
conversion equation, m i g h t introduce some errors, they
c a n be e l i m i n a t e d b y p r o p e r techniques such as instrument calibration. H o w e v e r , the most i m p o r t a n t probl e m i n f e e d w a t e r f l o w d e t e r m i n a t i o n is t h e d e p o s i t i o n
o f corrosion products o n the v e n t u r i converging section
a n d t h e t h r o a t over a p e r i o d o f t i m e . A s a result, t h e
measured f l o w rates are higher t h a n their actual values,
thus yielding artificially h i g h p l a n t t h e r m a l powers a n d
u n w a r r a n t e d p l a n t p o w e r deratings. 3 A 2 % p o w e r der a t i n g w o u l d cost 4 a b o u t $ 2 0 0 0 0 per d a y i n lost revenue f o r a n 8 0 0 - M W ( e l e c t r i c ) u n i t a t a u t i l i t y r a t e o f
$0.05/kWh.
Since v e n t u r i meters a r e used i n b o t h
P W R s a n d boiling water reactors ( B W R s ) , the t o t a l lost
INTRODUCTION
revenues c o u l d be v e r y large.
M o s t o f t h e previous w o r k p e r f o r m e d b y t h e u t i l i -
O n e o f t h e p r i m a r y objectives o f t h e p o w e r p l a n t
ties o r the vendors, related t o t h e d e t e r m i n a t i o n o f cor-
i n d u s t r y has l o n g b e e n t h e e f f i c i e n t o p e r a t i o n o f p l a n t
rect feedwater f l o w rates, has been m a i n l y recalibration
systems, thus reducing t h e cost o f electricity. Especially
o f v e n t u r i meters o r m o d i f i c a t i o n s o f t h e conversion
f o r nuclear g e n e r a t i n g stations, o p e r a t i n g t h e p l a n t at
equations b y some a n a l y t i c a l m e a n s . 5 O n e v e r y p o p u -
f u l l r a t e d p o w e r is e q u a l l y i m p o r t a n t . T h e o p e r a t i n g
l a r a n a l y t i c a l m e t h o d o f correcting t h e f l o w r a t e is t o
p o w e r o f a nuclear reactor is l i m i t e d b y t h e U . S . N u -
use the p r i m a r y a n d secondary t h e r m a l p o w e r balances.
clear R e g u l a t o r y C o m m i s s i o n ( N R C ) licensing require-
O n the other h a n d , some studies o n f e e d w a t e r f l o w es-
ments. Therefore, the t h e r m a l power o f the plant
t i m a t i o n o r system diagnostics using a r t i f i c i a l n e u r a l
should be d e t e r m i n e d v e r y accurately. C u r r e n t l y , clas-
n e t w o r k s d o n o t focus o n t h e v e n t u r i f o u l i n g p r o b -
sical t h e r m o d y n a m i c methods utilizing mass a n d energy
l e m . 6 , 7 A s a n alternative t o t h e existing approaches, a n
balances o n steam generators a r e used f o r t h e r m a l
a r t i f i c i a l n e u r a l n e t w o r k t r a i n e d w i t h reliable d a t a c a n
power calculation. T h e feedwater f l o w rate t o the steam
estimate t h e correct f l o w r a t e (used i n t h e r m a l p o w e r
generators is one o f t h e m a j o r quantities used i n deter-
calculations) regardless o f t h e changes i n t h e measure-
m i n i n g the t h e r m a l p o w e r . Feedwater f l o w signal is also
m e n t system o r the physical state o f the feedwater, since
one o f t h e i m p o r t a n t p a r a m e t e r s used f o r s t e a m gen-
n e u r a l n e t w o r k m o d e l s are based o n examples r a t h e r
t h a n the physical state and the geometry o f the system.
A sensitivity analysis m a y also be p e r f o r m e d f o r the
feedwater f l o w estimator networks in order to evaluate the i m p o r t a n t variables contributing to the f l o w
rate. Relative a n d statistical sensitivities m a y be used
as sensitivity measures.
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T h e efficient operation o f a power plant requires
the m o n i t o r i n g o f all critical process variables. 8 These
are the variables or parameters that contribute significantly to thermal power or heat rate. I n addition, when
there is a change in the performance o f the plant, it is
desirable to determine the cause and m a k e corrections
immediately. However, numerous components and subsystems are highly coupled in a nuclear generating stat i o n . This complexity makes the m o n i t o r i n g o f every
single component or signal by classical analytical or empirical methods a voluminous task.
Previous w o r k in P W R thermal performance m o n itoring primarily involves the use o f either classical thermodynamics or rule-based expert systems or both. O n e
o f the milestones i n t h e r m a l p e r f o r m a n c e diagnostics
using a rule-based approach is a report titled " T h e r m a l
P e r f o r m a n c e Diagnostics M a n u a l for Nuclear P o w e r
P l a n t s " by C o m b u s t i o n Engineering prepared f o r the
Electric Power Research Institute. 9 Its purpose was to
provide engineering personnel w o r k i n g at P W R s or
B W R s with a consistent way o f identifying thermal performance problems. L i k e the other studies in this field,
it provides a rule base f o r a n expert system to f i n d the
cause o f degradation. 1 0 ' 1 1 N e u r a l networks m a y also be
used for diagnostics o f the performance o f the plant.
A neural n e t w o r k can be trained for each component
o f the plant whose single output is the efficiency o f that
specific component. T h e n the outputs of these networks
can be treated as the inputs to another n e t w o r k whose
o u t p u t is the efficiency o f the overall system.
T h e overall efficiency o f a specific balance-of-plant
( B O P ) component was estimated as a means o f m o n i toring its behavior. Incipient problems may be detected
b y this simple application o f a neural n e t w o r k model.
T h e f o u r t h feedwater heater o f a Westinghouse-type
P W R plant was considered f o r this analysis.
This present study utilizes a multilayer perceptron
( M L P ) network that uses the backpropagation ( B P ) alg o r i t h m for training. T h e ability o f the B P a l g o r i t h m
to learn any a r b i t r a r y nonlinear m a p p i n g f r o m inputs
to outputs and the fault-tolerant property o f a m u l t i layer n e t w o r k have a variety o f applications in the
power plant industry. 1 2 T h e study also includes a statistical sensitivity analysis for establishing the performance o f neural networks.
T h e mapping is performed using a multilayer, fully
connected, heteroassociative n e t w o r k . T h e n e t w o r k is
said to be heteroassociative when the input and .the output layers are not identical. T h e B P algorithm computes
the weights between pairs o f processing elements so that
the difference between the actual output a n d the netw o r k output is m i n i m i z e d in a least-squares sense. T h e
output layer, in general, consists o f several elements,
but i f the goal is to predict one variable as a function
o f the others, then the output w i l l be a single element.
I n general, the M L P is capable o f performing arbitrary mapping between inputs and the outputs without
k n o w i n g the complete system specifications. I n f o r m a t i o n about the system is incorporated into the network
during the training phase. I t is also possible for neural networks to update the models by renewing the connection weights.
T h e m a j o r accomplishment o f this research is the
design and i m p l e m e n t a t i o n o f a neural n e t w o r k methodology as a n o f f - l i n e and on-line feedwater f l o w rate
a n d component thermal performance m o n i t o r i n g t o o l
for a P W R plant. A n o t h e r important accomplishment
is that actual plant data f r o m t w o P W R s were used in
all the analyses.
FEEDWATER FLOW MONITORING
Since the operating t h e r m a l power o f a nuclear
power plant is limited by N R C licensing requirements,
it is very beneficial to evaluate the t h e r m a l power accurately. 1 2 ' 1 3 I n plant terminology, plant thermal power
(QTH) is the power calculated f r o m the secondary side
(Fig. 1) a n d is given by the following:
Qth = Qs +
QVM
~ Qfw
,
(1)
where
Qth
= thermal power transferred to the secondary
side
Qs = t h e r m a l power transferred to the steam
Qvbd
~ thermal power transferred to the blowdown
flow
Q f W = t h e r m a l power lost by feedwater.
T h e feedwater f l o w rate to the steam generators is
one o f the m a j o r signals used in determining the therm a l power. This flow rate is measured by installed vent u r i meters (Fig. 2). There are alternative methods o f
measuring this f l o w rate, such as the use o f ultrasonic
flowmeters. H o w e v e r , most power plants do not have
ultrasonic flowmeters as an on-line measurement syst e m . T h e system is used as a precision test equipment
whenever the feedwater f l o w values f r o m the venturi
meter measurement become highly inconsistent with the
heat balance calculations. T h e results are sometimes
used to recalibrate the venturi meter.
The Venturi Meter
T h e venturi meter (Fig. 2) combines a short constricted portion between two tapered sections into a single unit a n d is usually inserted between t w o flanges in
a pipe. Its purpose is to accelerate the f l u i d a n d temporarily lower its static pressure. Suitable pressure connections are provided f o r observing the difference in
Kavaklioglu and Upadhyaya
MONITORING FEEDWATER FLOW
Main Steam : (s)
Qrw
Steam
Generator
Hot Leg
Feedwater: (fw)
Feedwater
Inlet
Vessel Blowdown
Aow : (vbd)
Cold
Leg
Hot Leg
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Cold leg
Fig. 1. Schematic of a steam generator.
Conical Diffuser Section
Fig. 2. Schematic of a venturi meter.
pressures between the inlet and the constricted portion,
or throat. Pressure drop across the venturi throat is
measured and is related to the flow across the venturi.
Venturi Fouling
Venturi fouling, or precipitation fouling in technical
terms, may be defined as the phenomenon of solid-layer
deposition on the venturi converging section arising primarily from the presence of corrosion products such as
iron oxides or iron hydroxides in the feed water, which
exhibit supersaturation under process conditions. 14 An
increase in the roughness of the converging or throat
sections induces a lowering of the discharge coefficient.15 Since the discharge coefficient used in the conversion equations is higher than the actual coefficient,
114
the measured feedwater flow rates become higher than
the actual values. The effect of roughness on the convergent cone and the throat may be strikingly high.
However, accounting for the roughness change requires
a knowledge of the height, spacing, configuration, and
the geometrical shape of the roughness elements, which
is almost impossible to evaluate. 16
THERMAL PERFORMANCE MONITORING
In recent years, considerable effort has been expended in the development of tools to assist plant operators in identifying and correcting thermal performance
problems. These tools include various performance diagnostic guides, in the form of both logic and decision
NUCLEAR TECHNOLOGY
VOL. 107
JULY 1994
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trees, which can be used as tools for identifying the root
causes of power plant thermal performance problems. 9
These trees represent a compilation of expert knowledge
of the relationships between the behavior of observable
process parameters and the underlying problems that
affect heat rate in power plants. They provide valuable
guidance in the techniques and steps to be used in troubleshooting performance problems at typical nuclear
and fossil plants. However, in their present form, they
can be difficult to interpret, to use, or to maintain.
An expert system approach is required to implement these trees. Expert systems can give the user substantial insight into the problem through the rule base
constructed from logic trees. The expert system can easily be modified for a new rule, and it can be connected
to the current data acquisition system to provide online diagnostics information.
On the other hand, application of a heat rate diagnostics expert system to a particular power plant requires the modifications specific to the plant since the
trees mentioned earlier are generated for generic fossil or nuclear power plants. It is not easy or economical for utilities to have their own expert advisors.
In this paper, an artificial neural network (ANN)
methodology was proposed for identifying the component of the plant causing the degradation and then applied to a sample component —one of the feedwater
heaters of an operating P W R power plant. The idea is
to design a neural network whose output is a measure
of the thermal efficiency for each component of a
power plant. Then these networks can be used in diagnosing degradation of heat rates caused by one or more
components. The heat given by the extraction steam
and the heat received by the feedwater can be used to
determine the thermal performance of the system. A
schematic of the fourth feedwater heater of a typical
P W R is given in Fig. 3. Referring to this figure, an efficiency measure can be defined mathematically as
where
e = efficiency of the component
Qfw = heat that is transferred to the main feedwater
Qs = heat that extraction steam loses.
Combining Eq. (2) with the steam properties, the
thermal performance of the component can be determined and monitored. Another technique for determining the thermal performance is to use neural networks
for estimating the desired parameter. The main purpose
of using a neural network for monitoring thermal performance is to obtain a fast estimate. The thermal performance of the fourth feedwater heater of a typical
P W R was studied using the measurements related to
this subsystem.
THE METHODOLOGY
The M L P network 1 7 ' 1 8 is one of the most important historical developments in neural network technology. It is a powerful mapping network that has been
successfully applied to problems from financial analysis to signal processing. The M L P is a multilayer, feedf o r w a r d A N N (Fig. 4). The capabilities of these
networks come from the nonlinear transfer functions
used on the processing elements. It is a well-known fact
that a three-layer perceptron (counting the input layer)
forms half-plane decision regions, and a four-layer perceptron can classify any convex region in the input
space. 19
Extraction Steam (s)
Drain Flows (d)
Fig. 3. Schematic of a typical feedwater heater.
Kavaklioglu and Upadhyaya
MONITORING FEEDWATER FLOW
Outputs
Output Layer
Other Hidden Layers
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First Hidden Layer
Input Layer
Inputs
Fig. 4. General topology of an MLP network.
The BP algorithm utilizes a generalization of the
least-mean-squares algorithm. 19 •20 It uses a gradient
descent technique to minimize the cost function, which
is the mean square difference between the desired and
the actual network outputs. This gradient descent technique may find a local minimum in the cost function
instead of the global minimum. Using extra hidden
nodes, lowering the gain term used in connection
weights, adding momentum, and restarting training with
a different set of initial weights are some of the remedies used to avoid being trapped at a local minimum.
The success of using ANNs for any application depends highly on the data handling before or during network operation. For each of the applications presented
in this paper, the governing physical phenomenon o(
the problem was taken into consideration to establish
the process signals to be used as inputs to a given network for estimating a related parameter. In the case of
feedwater flow rate analysis, a macroscopic heat and
Data preprocessing was found to be a very important issue in applying neural networks. This was used
to discard sample values that deviated from a normal
range. Column-wise normalization was applied to overcome the saturation effect of sigmoidal transfer functions. In the most general case, the minimum and the
maximum of each signal were calculated and used to
transform linearly all values of that signal into a small
interval such as [0.1, 0.9]. However, it was found that
for some studies requiring extrapolation of data beyond
the original input domain or output range, a smaller
normalization interval, such as [0.2, 0.8] was used. This
facilitates the ability of the network to extrapolate beyond the training domain.
Selection of training data has a vital role in the performance of a supervised neural network. In general,
for good recall performance, one should provide training
patterns that fully span the range of input and output
signals. However, it should always be emphasized that
the training patterns that carry _the input-output relationship for the system should be as accurate as possible. In a nuclear power plant, the most precise data are
mass balance analysis on the steam generator was used
expected to be recorded during the first weeks after re-
to determine the signals that can be used to evaluate
feedwater flow rate. The input signals determining the
thermal efficiency of the system were determined from
the analytical calculation of the component's thermal
efficiency.
fueling because a very intense maintenance program is
instituted during the refueling outage. Almost all components, control systems, and measurement systems are
inspected, and corrective actions are taken if necessary.
Especially for feedwater flow estimation, it is very
Data Preparation
116
NUCLEAR TECHNOLOGY
VOL. 107
JULY 1994
i m p o r t a n t to acquire the feedwater flow measurements
early i n the fuel cycle because o f the fouling p r o b l e m
o f the venturi, which is the on-line measurement system. Because venturi meters are inspected, cleaned, and
recalibrated during plant outage, the data t a k e n at the
beginning o f the fuel cycle must be very precise.
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Another subject in data processing that must be emphasized is the difference between the approach used
in this paper and in most o f the previous neural network
applications to power plant operations. M o s t o f the
previous applications used instantaneous d a t a w i t h a
small sampling interval, which can deal w i t h fast and
moderate t i m e dynamics o f the system. I n the studies
presented i n this paper, h o u r l y or daily averaged signals were used and the long-term behavior o f the syst e m was analyzed.
T h e m a j o r drawback of using averaged values is the
possible problems that could occur in the n o r m a l i z a t i o n process. Because o f averaging, the effects due to
fast transients are eliminated, and the input a n d output d a t a ranges become very small compared to their
m e a n values. T h e r e f o r e , a visual analysis o f the input
and the output signals was performed to make sure that
the system does not have a pattern that is t o o high or
t o o l o w w i t h respect to the average value o f the corresponding signal. These types o f patterns were removed
during d a t a preparation.
Network Parameters
A l t h o u g h it was believed that increasing the n u m ber o f hidden layers is necessary f o r i m p r o v i n g the
training performance, the same goal can be achieved
by keeping the number o f layers at three (one hidden
layer) and adjusting the number o f processing elements
in the hidden layer. I t has been shown that a three-layer
B P neural n e t w o r k exists that can a p p r o x i m a t e any
square-integrable function to within a sufficiently small
mean-squared error accuracy. 1 8 I n most o f the networks implemented in this paper, three-layer networks
were used.
A trial-and-error approach was used to determine
the n u m b e r o f hidden layer processing elements, starting w i t h a l o w n u m b e r o f hidden units a n d increasing
this n u m b e r as learning problems occur. T h e transfer
function used in all the applications is the standard sigm o i d function. Another critical parameter in B P learning is the speed o f convergence, which is determined by
the learning coefficient. I n general, it is desirable to
have fast learning, but not so fast as to cause instability o f learning iterations. I t is well k n o w n that starting
w i t h a large learning coefficient a n d reducing it as the
learning process proceeds results in b o t h fast learning
and stable iterations. This learning strategy was applied
in the networks designed for the specific tasks. T h e m o m e n t u m coefficients were also set according to a schedule similar to the one f o r the learning coefficients.
C u m u l a t i v e update o f the weights option was also used
for increasing the learning performance.
Network Sensitivity Analysis
T h e i n p u t / o u t p u t ( I / O ) model by a neural network
m a y be used to determine the sensitivity o f the output
to any o f the input variables. These sensitivities m a y
then be used to establish the choice o f signals for estimating the network output. D i f f e r e n t i a l and statistical
sensitivity measures were applied to the neural networks
developed for feedwater f l o w rate estimation. A n analytical derivation 2 1 shows that the differential sensitivity is a first-order a p p r o x i m a t i o n to the statistical
sensitivity.
I n system theory, the m o d e l sensitivity is defined
as the p a r t i a l derivative o f the output w i t h respect to
an input or a related parameter o f interest. T h e output
sensitivity o f a single-output, two-layer neural network
w i t h a differentiable transfer function, wiht respect to
any o f its inputs, m a y be given as the f o l l o w i n g :
S(y°,xh
=
dy°
(3)
dx!"
(4)
where
xf
= output o f z'th node at p'th
layer
wfj = connection weight f r o m / ' t h node at ( p layer to the y ' t h node at p'th layer
l)'th
I f = weighted sum to the y ' t h node o n layer p
in = input layer
h = hidden layer
o = output layer
/ = transfer function.
T h e statistical sensitivity o f output to input is the
ratio between the standard deviation o f the output and
the standard deviation o f the input. 2 2 ' 2 3 T h e statistical
sensitivity is defined as
o\ 21)1/2
S{y°,xf)
= lim
1Z
-0 O r
{E[(y° y°)1})
irt\ 2 n > 1/2
.0
[E[(xr-x'ts")'])
lim
(5)
where y° a n d xj" are the averages o f the output and
the input signals, respectively.
For the sensitivity studies in this paper, experiment a l evaluation o f sensitivities was p e r f o r m e d for b o t h
d i f f e r e n t i a l a n d statistical measures, and they were
f o u n d to be very close. F o r the d i f f e r e n t i a l sensitivity,
different perturbations were applied to the i n p u t , and
the change o f the output was evaluated t h r o u g h netw o r k recall. T h e ratio o f the t w o as the input perturbation goes to zero gives the differential sensitivity. For
the statistical sensitivity, different Gaussian sequences
w i t h zero m e a n and k n o w n standard deviations were
applied to the input, and the standard deviation o f the
o u t p u t was calculated using t h e results o f n e t w o r k re-
ing patterns. T h e n u m b e r o f t r a i n i n g patterns is 15 f o r
call. T h e r a t i o o f the t w o as the i n p u t s t a n d a r d devia-
the first u n i t a n d 10 f o r t h e second u n i t .
t i o n goes t o zero gives t h e statistical sensitivity o f the
B o t h networks were trained up to a learning rootmean-square (rms) error o f 1 0 " 3 i n the n o r m a l i z e d do-
output to that particular input.
m a i n a n d t h e n used f o r recall. T h e results c o m p a r i n g
the m e a s u r e d a n d the estimated f e e d w a t e r f l o w rates
RESULTS AND DISCUSSION
are given i n Figs. 5 a n d 6 f o r the first a n d t h e second
T h e M L P , w h i c h uses t h e B P l e a r n i n g a l g o r i t h m ,
was a p p l i e d i n some o f t h e i m p o r t a n t areas o f nuclear
units o f the p l a n t , respectively. T h e learning a n d recall
rms errors are presented i n T a b l e I I .
power plant p e r f o r m a n c e m o n i t o r i n g w i t h the focus o n
W h i l e there is n o a p p a r e n t p a t t e r n b e t w e e n the
the B O P system. T h e applications presented i n this pa-
m e a s u r e d a n d the estimated f e e d w a t e r f l o w rates f o r
per are feedwater f l o w rate e s t i m a t i o n a n d c o m p o n e n t
the first u n i t , t h e m e a s u r e d rates are generally higher
thermal performance estimation.
t h a n the estimated values f o r t h e second u n i t , f o r t h e
T h e analyses were p e r f o r m e d w i t h actual d a t a f r o m
t w o different operating P W R s . A c o m m e r c i a l software
recall phase. H o w e v e r , t h e t r e n d is so c o m p l e x t h a t it
does n o t y i e l d a n y clear conclusions.
package called N W O R K S ® was used f o r b u i l d i n g neu-
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r a l networks i n all the studies presented i n this paper. 2 4
T o achieve h i g h confidence i n the estimation accuracy,
it is necessary t o validate the signals that are used as inputs t o the n e t w o r k . T h i s section presents t h e results
o b t a i n e d f r o m these studies.
Sensitivity Analysis
T h e sensitivity o f a n I / O m o d e l m a y be used t o det e r m i n e t h e most i m p o r t a n t i n p u t signals c o n t r i b u t i n g
to the output. Feedwater f l o w estimator networks for
t h e f o u r - l o o p Westinghouse-type P W R w e r e used as
n e t w o r k models f o r the sensitivity analysis. A n a r b i -
A Four-Loop Pressurized Water Reactor
t r a r y training pattern was selected f o r each n e t w o r k f o r
T h i s p a r t o f the feedwater f l o w estimation analysis
involves t h e use o f o p e r a t i o n a l d a t a f r o m t w o f o u r l o o p , 1 1 4 0 - M W ( e l e c t r i c ) Westinghouse P W R s . C a l c u l a t i o n s a r e p e r f o r m e d f o r each u n i t s e p a r a t e l y .
t h e first a n d t h e second units o f t h e p l a n t .
First, the differential sensitivities were evaluated exp e r i m e n t a l l y using the f o l l o w i n g :
A
three-layer neural n e t w o r k was developed f o r each unit
t o estimate t h e f e e d w a t e r f l o w r a t e as a f u n c t i o n o f
seven variables. T h e i n p u t signals are given i n T a b l e I
a n d w e r e selected b y considering heat a n d mass b a l ances f o r the steam generators as explained previously.
T h e n u m b e r o f hidden layer nodes is 2 0 for the first unit
a n d 16 f o r t h e second u n i t .
F o r each o f t h e seven signals given i n T a b l e I , the i n p u t signal is p e r t u r b e d i n a small a m o u n t a p p r o a c h i n g
z e r o , a n d t h e resulting o u t p u t d e v i a t i o n was f o u n d b y
using n e t w o r k recall. T h e o u t p u t is the feedwater f l o w
rate.
T h e d a t a f o r this analysis w e r e t a k e n f r o m t h e
Second, a n e x p e r i m e n t a l e v a l u a t i o n o f t h e statisti-
weekly turbine cycle performance report files o f the t w o
cal sensitivity o f the output t o any o f the inputs was per-
o p e r a t i n g f o u r - l o o p Westinghouse P W R s . A l l t h e sig-
f o r m e d . F o r each o f the inputs, t e n d i f f e r e n t ( d i f f e r e n t
nals used i n t h e n e t w o r k w e r e n o r m a l i z e d i n t o t h e in-
s t a n d a r d deviations) G a u s s i a n sequences o f 100 ele-
t e r v a l [ 0 . 2 , 0 . 8 ] . T h e r e w e r e a t o t a l o f 4 1 patterns f o r
ments w i t h m e a n zero w e r e created a n d a d d e d t o the
the first unit a n d 2 2 f o r the second u n i t . F o r b o t h units,
i n p u t signal. These p e r t u r b e d inputs were presented t o
the patterns close t o the beginning o f the cycle a n d w i t h
the n e t w o r k a n d the o u t p u t deviations w e r e evaluated.
fewer u n a c c o u n t e d heat losses w e r e used as the t r a i n -
T a b l e I I I presents the order o f i m p o r t a n c e o f i n p u t signals a c c o r d i n g t o t h e n e u r a l n e t w o r k m o d e l s .
Results h a v e s h o w n t h a t d i f f e r e n t sensitivity m e a -
TABLE I
sures y i e l d similar results f o r the o u t p u t sensitivity.
List of Signals Used for Feedwater Flow Analysis
of a Four-Loop PWR
Number
1
2
3
4
5
6
7
TABLE II
Signal
Feedwater temperature
Learning and Recall rms Errors for
Feedwater Flow Estimation
R C S pressure
Cold-leg temperature
Hot-leg temperature
Vessel blowdown flow
Feedwater pressure
Steam generator pressure
Unit 1
Unit 2
Learning
(kg/s)
Recall
(kg/s)
0.07
0.03
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1
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16
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21
estimated
1
31
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41
Pattern #
Fig. 5. Measured versus estimated feedwater flow rates for Unit 1.
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Fig. 6. Measured versus estimated feedwater flow rates for Unit 2.
On the other hand, the sensitivities of feedwater flow
to inputs were not very close for different units. However, for both units, the hot-leg temperature was found
to be the most important signal, whereas the vessel
blowdown flow was the least important. In general,
temperatures are more important than the pressures for
estimating the flow rate. A final point that must be
made is that all the sensitivities depend on the input pattern. Any deviation in these patterns will affect the order of importance of the signals.
A Six-Loop Pressurized Water Reactor
The data for this analysis were acquired from a 450MW(electric), six-loop P W R plant. The data consisted
of the daily averages of various signals for a period of
1 yr. In addition to the input signals used for the fourloop P W R , primary loop pressure was also used as an
input variable to the neural networks developed for this
reactor. All the analyses were carried out for each of
the six loops separately.
TABLE III
T h e neural networks were trained to give an rms error o f 1 0 - 2 in the normalized domain. T h e trained networks were used to estimate the feedwater flow rate for
the remaining data. T h e results for the first and the seco n d loops are given i n Figs. 7 a n d 8. T a b l e I V summarizes the learning a n d overall rms error between the
estimated and the measured feedwater f l o w rate. Feedwater flow rate estimation analysis was p e r f o r m e d for
each o f the six loops, but the results are presented f o r
loops 1 and 2. T h e results f o r the first loop are similar
to the results f o r the t h i r d and the f i f t h loops, and the
results for the second loop are similar to the results for
the f o u r t h and the sixth loops.
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Order of Importance of Inputs for
Feedwater Flow Rate
Order
Unit 1
Unit 2
1
2
3
4
5
6
7
Hot-leg temperature
Cold-leg temperature
Feedwater temperature
Steam generator pressure
RCS pressure
Feedwater pressure
Vessel btowdown flow
Hot-leg temperature
Feedwater temperature
RCS pressure
Cold-leg temperature
Feedwater pressure
Steam generator pressure
Vessel blowdown flow
T h e estimations o f feedwater f l o w rate by the neural networks are lower than the measured flow rates for
loops 1 , 3 , a n d 5; whereas the estimates roughly agree
w i t h the measurements for loops 2, 4, a n d 6. T h e reason for the deviations seen in the estimations for loops
1 , 3 , and 5 may be due to venturi fouling or some other
a n o m a l y . A change in the system such as a p u m p or
valve might have changed the interrelationship a m o n g
the signals. T h e use o f erroneous learning patterns
might have also been a reason f o r the observed d i f f e r ence in the recall phase.
F o r each loop o f the p l a n t , a neural n e t w o r k was
built w i t h eight input and one output layer processing
elements. T h e output processing element is the feedwater flow rate. Since it was believed that the data for
the first 2 weeks were accurate enough, the first 14 patterns were used to train the neural networks for the six
loops.
A l l the networks used in this study were three-layer
networks with 12 processing elements in their single hidden layer. Starting f r o m a high value f o r the hidden
layer elements, this n u m b e r was decreased until the
same learning rms error was established. T h e n this
n u m b e r was used for all the networks. T h e interval
[0.2 0.8] was used as the n o r m a l i z a t i o n interval. T h e
learning and m o m e n t u m coefficients were given high
values at the beginning o f learning and were decreased
as the learning proceeded. T h e sigmoid was used as the
transfer function.
Thermal Performance Monitoring
T h e detection o f degradation in a component o f the
power plant is important for isolating the causes o f degr a d a t i o n in the overall plant p e r f o r m a n c e , such as the
heat rate. Properly trained neural networks can detect
the changes in the behavior o f i n d i v i d u a l systems. A
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151
181
211
241
Pattern #
Fig. 7. Measured (M) versus estimated (E) feedwater flow rates for loop 1.
271
Kavaklioglu and Upadhyaya
MONITORING FEEDWATER FLOW
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ti.
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#
Fig. 8. Measured (M) versus estimated (E) feedwater flow rates for loop 2.
Learning
(kg/ s)
Recall
(kg/ s)
thermal performance diagnostics purposes. This specific example indicates that a change in the performance
of the feed water heater may be detected by a neural network (in this case, a small decrease in the efficiency).
On-line implementation of this monitoring is being considered for a commercial plant.
0.0955
0.0634
0.6677
0.3652
CONCLUSIONS
TABLE IV
Learning and Recall rms Errors for
Feedwater Flow Estimation
Loop 1
Loop 2
feedwater heater was chosen to be the sample component for this analysis. A C code was written to calculate the efficiency of the component based on the first
law of thermodynamics and the steam tables. A singleoutput three-layer network was built to estimate the
efficiency of the component. Twelve signals that are
necessary to determine the thermal efficiency of the
heater are used as the input signals for this mapping.
The number of hidden layer processing elements is 12.
The data for this analysis were hourly averages of
the archived data of the 12 signals. There were a total
of 110 patterns, and 30 of them were used as training
patterns. The efficiency was first calculated analytically. These values were used to train the network. The
normalization interval was [0.2, 0.8].
The network was trained up to a learning rms error of w- 3 in the normalized domain, and used for recall. The results are presented in Fig. 9. The results have
shown the feasibility of applying neural networks for
NUCLEAR TECHNOLOGY
VOL. 107
JULY 1994
The results obtained from the studies in this paper
have shown that the feedwater flow rate to the steam
generators can be monitored using ANNs. These network models may also be used to detect the fouling of
feed water venturi meters . However, accurate quantification of the effect of venturi fouling may not be possible by neural networks. The reason for this could be
the possibility of using slightly fouled venturi meter
readings as network training patterns.
The sensitivity analysis based on neural network
models has shown that the most important signal that
contributes to feedwater flow rate is the hot-leg temperature, and the least important signal is the vessel
blowdown flow. However, it should be emphasized that
these sensitivities depend not only on the network connection weights, but also on the input pattern used for
evaluating them. Therefore, there may be slight changes
in the order of importance of input variables for different input patterns, as well as for different networks.
The results have also shown that neural networks
can be applied successfully to diagnose the degradations
121
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Downloaded by [University of Florida] at 05:32 25 October 2017
95.5
40
time (hour)
Fig. 9. Calculated versus estimated feedwater heater efficiencies.
in the thermal performance of components of a power
plant. Small changes in the thermal efficiency of a feedwater heater were detected precisely by a network. The
methodology can be extended to the whole power plant.
If a neural network is developed for each component
of the system whose single output is a measure of the
thermal efficiency of the related component, then, by
combining these networks, the cause of an overall plant
heat rate degradation problem can be localized to the
component that is the source of the problem.
On the other hand, there are some drawbacks in the
application of neural networks to power plant thermal
performance problems. Data preprocessing was found
to have a very important role in the performance of
neural network models. The ranges in which the input
and output signals can vary should be determined very
carefully. The normalization interval should be well
suited to the specific application.
Since there is no obligation to include or exclude
a process variable as a model input for neural networks
in contrast to physical models, determining the input
signals for estimating a given variable depends on the
analyst. Using a small number of inputs may result in
the network's inability to perform the desired mapping,
whereas using too many signals as inputs may introduce
unnecessary complexities and erroneous results.
A disadvantage of neural network models is the
need for updating the model, especially for on-line applications when there is a design change, component replacement, or some similar change in the power plant.
Neural networks are sample-based models and the
training samples must cover the dynamic range over
which the recall occurs. Neural networks also cannot
provide physical insight into the problem unless they
are designed to function so. In other words, they cannot generate reasons for producing a certain output.
Therefore, the analyst should develop the methodology
such that it allows diagnostic-type conclusions based on
the results.
ACKNOWLEDGMENTS
This research was sponsored by a grant to the University of Tennessee by the Tennessee Valley Authority (TVA)
Resource Group, Research and Development. The authors
gratefully acknowledge the assistance provided by the TVA
personnel at the Sequoyah Nuclear Plant and at the TVA offices in Chattanooga, Tennessee. The authors appreciate the
constructive remarks by the reviewers.
REFERENCES
1. "Fluid Meters, Their Theory and Application," ASME
Report, p. 43, Research Committee on Fluid Meters, New
York (1959).
2. E. O. DOEBELIN, Measurement Systems Applications
and Design, p. 528, McGraw-Hill, New York (1983).
3. "Feedwater Flow Measurement in U.S. Nuclear Power
Generation Stations," TR-101388, Electric Power Research
Institute (Nov. 1992).
4. "Flowrate Measurement Causes Unneeded Derating,"
Nucl. News, 36, 2, 39 (Feb. 1993).
and Testing Symp., Knoxville, Tennessee, May 1992, Vol.
2, p. 87.01 (1992).
5. "Technical Instruction TI-2.1, Calorimetric Calculation
for Unit-1," Sequoyah Nuclear Power Plant, Tennessee Valley Authority (June 1990).
14. D. HASSON, "Precipitation FoulingFouling of Heat
Transfer Equipment, p. 527, Hemisphere, New York (1981).
6. J. E. MOTT and P. BLANCH, "Feedwater Flow Estimation via Sample Based Modeling," Proc. 8th Power Plant
Dynamics Control and Testing Symp., Knoxville, Tennessee, May 1992, Vol. 2, p. 85.01, The University of Tennessee (1992).
Downloaded by [University of Florida] at 05:32 25 October 2017
7. M. KHADEM, F. J. ALEXANDRA, and R. W. COLLEY, "Sensor Validation in Power Plants Using Neural Networks," International Neural Network Society, Summer
Workshop on Neural Network Computing for the Electric
Power Industry, Stanford University, August 1992, Electric
Power Research Institute.
8. K. BOOTH, "On-Line Monitoring Energizes Power
Plant Performance," INTECH, Applying Technology, p. 44
(Oct. 1991).
9. "Thermal Performance Diagnostics Manual for Nuclear
Power Plants," NP-4990, Vols. 1-3, Electric Power Research
Institute (Apr. 1987).
10. D. M. SOPOCY, R. E. HENRY, S. M. GEHL, and
S. M. DIVAKARUNI, "Development of an On-Line Expert
System: Heat Rate Degradation Expert System Advisor,"
Proc. Expert Systems Applications for the Electric Power Industry, Orlando, Florida, June 5-8, 1989, Vol. 2, p. 911
(1989).
11. M. MCLINTOCK, R. METZINGER, and N.
HIROTA, "Thermal Performance Advisor Expert System
Development," Proc. Expert Systems Applications for the
Electric Power Industry, Orlando, Florida, June 5-8, 1989,
Vol. 2, p. 1193 (1989).
15. A. SCHLAG, "Survey of Studies of Classical Venturi
Meters at the University of Liege," Proc. Flow Measurement
in Closed Conduits Symp., Edinburgh, Scotland, September I960, Vol. 1, p. 269.
16. F. V. A. ENGEL, "How to Improve Flow Measurement
Accuracy of Orifices, Nozzles, and Venturi Meters," Proc.
Flow Measurement in Closed Conduits Symp., Edinburgh,
Scotland, September 1960, Vol. 1, p. 317.
17. P. K. SIMPSON, Artificial Neural Systems, Pergamon
Press, New York (1990).
18. R. HECHT-NIELSEN, Neurocomputing,
Wesley, Reading, Massachusetts (1990).
Addison-
19. R. P. LIPPMANN, "An Introduction to Computing
with Neural Nets," IEEE ASSPMagazine, 4, 4 (Apr. 1987).
20. D. R. HUSH and B. G. HORNE, "Progress in Supervised Neural Networks," IEEE Signal Proc. Magazine, 8
(Jan. 1993).
21. K. KAVAKLIOGLU, "Performance Monitoring of
Pressurized Water Reactors Using Artificial Neural Networks," MS Thesis, The University of Tennessee (May
1993).
22. J. Y. CHOI and C. CHOI, "Sensitivity Analysis of
Multi-Layer Perceptron with Differentiable Activation
Functions," IEEE Trans. Neural Networks, 3,1, 101 (Jan.
1992).
12. R. E. UHRIG, "Applications of Neural Networks to the
Operation of Nuclear Power Plants," Proc. SMORN VI,
Gatlinburg, Tennessee, May 1991, Vol. 2, p. 55.01 (1991).
23. M. IWATSUKI, M. KAWAMATA, and T. HIGUCHI,
"Statistical Sensitivity and Minimum Sensitivity Structures
with Fewer Coefficients in Discrete Time Linear Systems,"
IEEE Trans. Circuits Syst., 37, 1, 72 (Jan. 1988).
13. K. KAVAKLIOGLU, B. R. UPADHYAYA, and E.
ERYUREK, "Neural Networks for Feedwater Flow Estimation in PWRs," Proc. 8th Power Plant Dynamics Control
24. "NeuralWorks Professional II/Plus and NeuralWorks
Explorer," NeuralWare Inc., Pittsburgh, Pennsylvania
(1991).
Kadir Kavaklioglu (BS, nuclear engineering, Hacettepe University, T u r key, 1989; M S , nuclear engineering, T h e University o f Tennessee, 1993) is currently a graduate student pursuing a P h D in nuclear engineering at the
University o f Tennessee. H i s research interest is nuclear power plant t h e r m a l
p e r f o r m a n c e m o n i t o r i n g a n d diagnostics.
Belle R. Upadhyaya ( P h D , University o f C a l i f o r n i a , San D i e g o ) is a professor o f nuclear engineering at the University o f Tennessee and the director
o f the Preventive M a i n t e n a n c e Engineering L a b o r a t o r y . H i s research interests include digital signal processing, power plant dynamics a n d control, preventive maintenance technology, and artificial neural networks.
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