chapter 3 modeling of deaerator and simulation of...
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CHAPTER 3
MODELING OF DEAERATOR AND SIMULATION OF
FAULTS
3.1 INTRODUCTION
Modeling plays an important role in the prediction and assessment
of plant performance. There are two ways of getting the model for any plant
i.e., theoretical model established by physical principles and behaviour model
derived from input and output data of the plant.
This chapter deals with simulation of the deaerator using
mathematical model. An analytical model for the deaerator is obtained in the
state space form based on fundamental physical laws. The model is linearised
around the operating point and the possible faults are simulated by varying the
system parameters using the linearised differential equations. The
mathematical model is validated by the parameters obtained through RLS
technique from the real time data obtained from the plant under normal
operating conditions.
3.2 OPERATION OF DEAERATOR
Modern power plants are operated at high pressure and
temperatures. The presence of oxygen in dissolved form in feed water results
in harmful corrosive attack. Of the many measures adopted to contain
corrosion in boilers and associated plant, removal of oxygen from feed water
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is the most important one. This removal of air or deaeration is done by
incorporating a deaerating unit in the feed system.
In addition to the function deaeration, the deaerator also serves for
the following purposes.
The deaerator functions as a surge tank of feed water
capable of meeting the variable demands of the plant.
The deaerator also forms part of the regenerative heating
system improving the temperature of condensate and
It also acts as a heat conversion unit.
The deaerator consists of a vertical deaerating tower and a
horizontal deaerating water storage tank as shown in Figure 3.1. The tower is
connected to the storage tank through two balance pipes. A safety valve is
provided at the top of the tower. In order to avoid buckling of tower due to
any possible vacuum, a vacuum breaker is also provided at the top.
The operation of the deaerator is based on the fact that the
solubility of gases in defined mass of liquid is inversely proportional to the
temperature of the liquid. Thus if water is heated up to the saturation
temperature and kept at this temperature for a sufficient time, all gases present
therein can be removed and vented to the atmosphere due to their reduced
solubility. In order to increase the deaerating efficiency, water is broken up
into small droplets through spray nozzles and perforated trays. There are four
perforated trays in the deaerating tower. The water enters the tower at the top
and gets divided into small droplets by means of spray nozzles. Then it is
distributed uniformly over the trays. The steam extracted from the turbine is
given out from the bottom of the tower.
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The deaerator is operated in the variable pressure mode. The
pressure in the deaerator is varied according to the operating status of the
turbine. Fourth extraction steam, the normal source, is feeding the steam to
deaerator at a pressure which is varying along with operating load on the
turbine. Since the load on the turbine is getting varied during normal
operation of the unit, the operating pressure of the deaerator will also vary and
it is maintained by pressure PID controller.
The water level in the deaerator storage tank is maintained by
regulating the make up water flow. The actual level is sensed by a level
transmitter and the deviation is fed to the level PI controller. Thus the
deaerator always responds to any change in operating conditions. For any
increase in incoming main water flow, there will be a corresponding increase
in the steam demand. For any decrease in incoming main water temperature
also, there will be a corresponding increase in the steam demand. For any
increase in steam pressure, there will be an increase in the deaerator water
temperature till the saturation temperature is reached.
3.3 MATHEMATICAL MODELING
The deaerator in general is a second order multivariable nonlinear
system. The model is developed in state space form based on the differential
equation considered by Abdennour et al (1993). The state variables
considered are pressure and enthalpy, the output variables are pressure and
water level and the manipulated variables are water valve and steam valve
positions.
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SP Setpoint PC Pressure Controller
LT Level Transmitter PS Level Controller
PT Pressure Transmitter
Figure 3.1 Schematic diagram of a deaerator
The state space representation of the deaerator model is given by
X k+1 = AX(k) + BU(k) (3.1)
Y k = CX k + DU k (3.2)
where X, U and Y are state, control and output vectors, respectively. In order
to obtain the state space model for the system, X(k) as 2×1 state vector, U(k)
as 2×1 input vector and Y(k) as 2×1 output vector are defined.
1
2
x k pX k = =
hx k
(3.3)
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Tc sU k = y y (3.4)
TY k = p L (3.5)
The real time plant data obtained from 110 Atm deaerator supplied
by M/s Thermax Pune for Madras Fertilizers Limited, Chennai is used for
obtaining the model shown in Figure 3.2. The nominal values of the variables
of the deaerator are p = 1.2kg/cm2, h = 277kJ/kg, yc = 55.41 % open,
ys = 79.64 % open, and L = 1.62m. The water valve is normally in a closed
condition and in Figure 3.2 it represents the percentage of opening. The steam
valve is normally of open type and in Figure 3.2 it represents the percentage
of closure. The height of the deaerator tank is 2m and in Figure 3.2 it is
represented in terms of percentage.
Figure 3.2 Real time plant data1
1 p: pressure (kg/cm2), L: level (in %), h: enthalpy (kJ/kg), ys: steam valve position (% of closure), yc: water valve position (% of opening)
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3.4 PARAMETER ESTIMATION USING RLS TECHNIQUE
In this section, the system identification technique is used for
developing an alternative model for the deaerator. The RLS method is used
for parameter estimation. The multivariable discrete data system is described
by
X k = A X k -1 + B U k -1
n×1 n×n n×n n×m m×1 (3.6)
The problem of identifying the matrices A and B of the system
from knowledge of the sequence X() and U()was taken as a type of
adaptive identification problem. The following notations are used for
obtaining RLS model.
ψ A B (3.7)
ˆ ˆψ k A k B k (3.8)
T T TY k X k U k (3.9)
X k = ψ k Y k-1 (3.10)
ˆX k = ψ k Y k-1
(3.11)
e k = X k -X k
(3.12)
Thus the algorithm
T
T
e k+1 Y k P kˆ ˆψ k+1 = ψ k +1+Y k P k Y k
(3.13)
gives a stable estimate of the sequence ψ() for ψ, where the symmetric
positive definite matrix │P│ = 1. The stability of the scheme is provided by
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Janakiraman et al (1981). Thus the recursive parameter estimation algorithm
for the deaerator is formulated in which the new estimate is given by the old
estimate plus a correction term based on the error e(k+1), P(k) and the
observation vector Y(k). Figure 3.3 shows the block diagram of the
generalised RLS. The computational algorithm comprises the following steps
(Renganathan 2003).
Figure 3.3 Block diagram representation of RLS technique
1. Set initial values at time index k = 0, ψ (k) = 0, P (k) = α × I,
where α is a large number and I is the identity matrix.
2. Obtain measurement Y(k).
3. Estimate state vector X(k-1) = ψ(k) Y(k)
4. Compute error in state estimate e(k+1) = X(k+1) - X(k+1)
5. Perform recursive parameter estimation
T
T
e k+1 Y k P kˆ ˆψ k+1 = ψ k +1+Y k P k Y k
6. Compute covariance matrix of error in estimate recursively
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T
T
P k Y k Y k P kP k+1 = P k
1+Y k P k Y k
7. Continue from step 2 for next sampling instant k =1.
The same procedure is used for obtaining C matrix. The parameters
matrices A, B, C are obtained by RLS technique and its convergence plot is
shown in Figure 3.4 for a given operating condition. The results are given in
Equations (3.14) and (3.15).
1 1 1
2 2 2
x (k+1) x (k) u (k)5.611e-05 5.645e-03 2.6865e-03 3.6456e-03x (k+1) x (k) u (k)6.044e-03 6.081e-01 2.8941e-01 3.9272e-01
(3.14)
1 1
2 2
y (k) x (k)5.5986e-05 1.480e-005y (k) x (k)8.0214e-05 2.110e-005
(3.15)
From Equations (3.14) and (3.15) it is inferred that the obtained
parameters of the state matrix for the deaerator model indicate instability.
Hence, a state feedback control system based on the pole placement technique
is employed to make the system open loop-stable. The closed loop poles of
the system using pole placement controller are {0, -0.5}. The K-state feed
back gain matrix is obtained as
0.0147 10.6815
K0.0 0.1462
(3.16)
The control input U(k) of the pole placement controller is
U(k) = - K X(k) (3.17)
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The control system performance of the deaerator is obtained using
Matlab / Simulink package with change in setpoint and load disturbance. A
PID controller with KP = 0.795, Ti = 1.75, Td = 0.028 is used for the pressure
control loop and a PI controller with KP = 0.6 and Ti = 3 is employed for the
level control loop. The block diagrams of two control loops are shown in
Figure 3.5.
Figure 3.4 Parameter estimation using RLS technique
The variations of deaerator output such as pressure and level are
plotted in Figure 3.6a and 3.6b for a positive and negative step change in level
and pressure respectively introduced at 2500th instant. It is evident that the
controllers are able to track the changes.
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Figure 3.5 Block diagram representation of deaerator control loops
Figure 3.6a System output for 10% positive and negative step change in
level setpoint
Figure 3.6b System output for 10% positive and negative step change in
pressure setpoint
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3.5 SIMULATION OF FAULTS
3.5.1 Introduction
The introduction of fault in a real healthy system may not be
acceptable. But the same fault can be easily simulated in a simulation
environment. The possible faults in the deaerator are simulated using a
linearised mathematical model. The occurrence of fault will alter the
parameters of the system namely A, B and C. Since A and B parameters are
affected more than C parameter, the variations in A and B parameters are
considered for fault diagnosis. The simulation of fault in deaerator is carried
out through the following steps:
i. a fault and its magnitude is specified,
ii. the effect of this fault on the process variables is determined,
iii. the variations in A and B parameters for the above fault is
obtained using the linearised mathematical model (discussed
in 3.5.2) with the changed process variables, and
iv. the specified fault is simulated by using A B parameters as
determined above.
The model obtained by the RLS technique using the real time data
cannot be used to find the change in A and B parameters for different faults,
as the introduction of the faults in real system is not feasible. Hence, efforts
are made to obtain a mathematical model using fundamental laws and the
model is then employed to simulate fault.
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3.5.2 Linearised mathematical model
An analytical model proposed by Abdennour (1993) for the
deaerator is considered for fault simulation in state space form. As the
introduction of faults in the nonlinear model is very difficult, the model is
linearised around the operating point and then used for fault simulation. The
analytical model is given by Equations (3.18) and (3.19).
e l
t
w - w1 ρh = pρ 3600v ph
(3.18)
e l e e l l
t
p(w - w ) + h - w h - w hρhp =
ρρ144p3600v +ρ 778
h
(3.19)
where
e c sw = w +w
cc q c cw = c ρ p - p
ss v s s
19w = c ρ p - p30
c
c c
q
2 2v p
1c = 1 1
c c
s
3v s max
c = Ysvc
c
3v c max
c = Ycvc
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The variables are defined as follows p: Pressure (kg/cm2), w: flow
rate (T/hr), h: enthalpy (kJ/kg), L: level (m), y: valve position (in %), : bulk
density over the entire vessel(kg/m3), we: flow rate entering feed
water + steam (T/hr), wl: flow rate leaving (T/hr), he: enthalpy of fluid
entering the vessel (kJ/kg), hf: enthalpy of fluid leaving the vessel (kJ/kg),
vt: total volume of deaerating and storage tank (m3), cv: valve conduction,
cp: pipe conduction. The subscript c stands for water and s stands for steam.
The process variables in the deaerator and their nominal values are given in
Table 3.1.
Table 3.1 Process variables of the deaerator
Sl.No. Process Variables Unit Nominal
Value
1. p pressure in the deaerator kg/cm2 1.2
2. h enthalpy in the deaerator kJ/kg 495
3. yc water inlet valve position (opening) % 60
4. ys steam valve position (opening) % 75
5. wl water flow rate leaving T/hr 80
6. he enthalpy of fluid entering the vessel kJ/kg 255
7. c density of water in the deaerator kg/m3 954
8. s density of steam in the deaerator kg/m3 0.7
9. pc inlet water pressure kg/cm2 1.3
10. ps inlet steam pressure kg/cm2 3.5
The Equations (3.18) and (3.19) are linearised around the
equilibrium point (setpoint) as the same values considered in the real time
system. The linearisation depends on five variables namely, pressure,
enthalpy, feed water level, water valve position and steam valve position. The
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linearised differential equations that govern the operation of deaerator are
expressed in Equations (3.20) and (3.21).
c c s c s sle c e s
t t t
0.01 ρ p 0.1 ρ p +0.213 ρ pwp = - p + h y -h y3600 v 3600 v 3600 v
(3.20)
c c s c s sle c e s
t t t
0.02 ρ p 0.2 ρ p + 0.426 ρ p2 wh = - h + h y -h y3600 v 3600 v 3600 v
(3.21)
By substituting the steady state values in Equations (3.22) and
(3.23) the state model is obtained as follows:
1 1 1
2 2 2
x (k+1) x (k) u (k)-2.1930e-03 0 8.9999e-04 -9.8320e-04x (k+1) x (k) u (k)-1.0965e-03 0 6.2092e-04 -4.9160e-04
(3.22)
1 1
2 2
y (k) x (k)5.5986e-05 1.480e-005y (k) x (k)8.0214e-05 2.110e-005
(3.23)
In general, the dynamics of the system is influenced in a larger
measure by the state matrix (A) and input matrix (B). Hence, for simulation,
the output matrix (C) for the mathematical model is considered from the
estimated model. The variations of deaerator output such as pressure and level
are plotted in Figure 3.7a and 3.7b for a positive and negative step change in
level and pressure respectively introduced at 2500th instant. It is evident that
the controllers are able to track the changes.
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Figure 3.7a System output for 10% positive and negative step change in
level setpoint in linearised model
Figure 3.7b System output for 10% positive and negative step change in
pressure setpoint in linearised model
By comparing the deaerator responses plotted in Figures 3.6a and
3.6b to Figures3.7a and 3.7b respectively, it may be observed that both
models (model obtained using RLS technique and analytical linearised model)
give almost same output responses.
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3.5.3 Simulation of faults using linearised model
There are many reasons for the appearance of faults, like ageing,
corrosion, wear during normal operation, wrong operation, improper
maintenance and so on. They may appear suddenly with a large size or in
steps with smaller size or slow like a drift. In this work the large step size
fault are simulated using the Matlab / Simulink. Eight important faults that
occur in the deaerator are given below:
1. Leakage in tank
2. Sedimentation deposit
3. Positive bias in the inlet water valve
4. Negative bias in the inlet water valve
5. Positive bias in the inlet steam valve
6. Negative bias in the inlet steam valve
7. Decrease in inlet water temperature and
8. Steam mixing with water in preheater.
Fault 1: The simulation of fault, water leakage in the tank is shown
in Figure 3.8. This is simulated by increasing the outlet flow by 10% at 2000th
instant. It can be seen from the graph that as level decreases the pressure also
decreases. For example if a11 and a21 is increased by 10% from their nominal
value and b11, b12, b21, b22 are normal, then the fault is water leakage in the
tank and the magnitude of leakage is 10%. The inference is as follows. An
excess of outlet flow in the outlet pipe from its nominal value can be assumed
as leakage in the tank. Equations (3.20) and (3.21) are used to obtain the
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modified values of plant parameters (a11, a21, b11, b12, b21, b22) due to 10%
increase in output flow rate. The change in plant parameters thus determined
is +10% for a11 and a21 and 0% for b11, b12, b21 and b22.
Fault 2: A decrease in outflow is the result of the sedimentation
deposit in the water outlet pipe. This is simulated by decreasing the outlet
flow by 10% at 3500th instant. It can be seen from the graph that as level
increases the pressure also increases. The fault is represented in Figure 3.8.
For example, if a11 and a21 is decreased by 10% from their nominal value and
b11, b12, b21, b22 are normal then the fault is ‘sedimentation deposit’ and the
magnitude of leakage is 10%. This inference is as follows. When
sedimentation gets deposited in the outlet water pipe, the water outlet flow
gets reduced by 10%. Equations (3.20) and (3.21) are used to obtain the
modified values of plant parameters (a11, a21, b11, b12, b21, b22) due to 10%
increase in output flow rate. The change in plant parameters thus determined
is -10% for a11 and a21 and 0% for b11, b12, b21 and b22. Similarly, the outflow
is assumed as 99% to 90% of normal flow when the fault sedimentation
deposit has a severity of 1% to 10%. Thus the change in A and B parameters
for the faults with severity of 1% to 10% is determined.
Fault 3 and 4: The inlet water valve to the deaerator is normally of
closed type. The positive and negative bias in the inlet water valve will cause
an increase and decrease in flow rate respectively. The negative bias to the
valve is introduced by increasing the upstream pressure, the pressure
upstream to the water inlet valve, and the positive bias is simulated by
decreasing the same. The positive bias is simulated at 2000th instant, which
causes an increase in level and pressure in the deaerator. The negative bias
will create a decrease in flow rate, which will cause a decrease in level and
pressure in the deaerator, which is simulated at 3500th instant. Both the faults
are represented in Figure 3.9 and the severity of the faults is 10%.
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Fault 5 and 6: The inlet steam valve to the deaerator is normally of
open type. The positive and negative bias in the inlet steam valve will cause
an increase and decrease in flow rate respectively. The negative bias to the
valve is introduced by increasing the upsteam pressure by 10% at 2000th
instant, the pressure upstream to the steam inlet valve, and the positive bias is
simulated by decreasing the steam pressure by 10% at 3500th instant. Both the
faults are represented in Figure 3.10.
Fault 7: The decrease in temperature of the inlet water to the
deaerator is represented by decreasing the enthalpy of inlet water by 10% at
3500th instant. The response is given in Figure 3.11.
Fault 8: The mixing of steam with water in the preheater will
increase the temperature of the inlet water. This causes an increase in pressure
and level in the deaerator tank. The simulation is done, by increasing the
enthalpy of the inlet water by 10% at 2000th instant. The response is shown in
Figure 3.11.
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(a)
(b)
Figure 3.8 Simulation of tank leakage and sedimentation deposit by
increasing/decreasing the outflow (a) pressure variation
(b) level variation
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(a)
(b)
Figure 3.9 Simulation of positive and negative bias of inlet water valve
by increasing/decreasing upstream water pressure
(a) pressure variation (b) level variation
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(a)
(b)
Figure 3.10 Simulation of positive and negative bias of inlet steam valve
by decreasing/increasing upstream steam pressure
(a) pressure variation (b) level variation
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(a)
(b)
Figure 3.11 Simulation of steam mixing with water in preheater and
decrease in inlet water temperature by increasing/
decreasing the temperature of the inlet water
(a) pressure variation (b) level variation
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The values of A and B parameters for the fault leakage in tank of
severity ranging from 0% to 10% in steps of 1% are given in
Table 3.2. Similarly the changes in A and B parameters for the other seven
faults with severity ranging from 1% to 10% in steps of 1% is also
determined. The parameters values are given in Table 3.3 to Table 3.9. The
ranges for the occurrence of double fault are a11 [-1.8525×10-3
–2.7166×10-3], a12 [0 0], a21 [-9.523×10-4 –1.707×10-3], a22 [0 0],
b11 [7.897×10-4 1.453×10-4], b12 [-8.2488×10-4 -1.1151×10-3],
b21 [5.1883×10-4 7.8301×10-4] and b22 [-3.7480×10-4 -5.9076×10-4].
3.6 PARAMETER IDENTIFICATION USING ANN
In this section an attempt is made to use a single layer neural
network for identifying the parameters of the linear deaerator system. The
RLS algorithms have been used to train the single layer back propagation
linear neural network. Given a training set of input-output pair which defines
a function, such a network is considered to learn the function. The learning
process involves the determination of the weights, which is nothing but the
parameters of the system.
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Table 3.2 Values of A and B parameters for the fault leakage in tank
Sl. No. Severity of fault a11 a21 b11 b12 b21 b22
1 0% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
2 1% -2.1711E-03 -1.0855E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
3 2% -2.1491E-03 -1.0746E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
4 3% -2.1272E-03 -1.0636E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
5 4% -2.1053E-03 -1.0526E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
6 5% -2.0833E-03 -1.0417E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
7 6% -2.0614E-03 -1.0307E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
8 7% -2.0395E-03 -1.0197E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
9 8% -2.0175E-03 -1.0088E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
10 9% -1.9956E-03 -9.9781E-04 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
11 10% -1.9737E-03 -9.8684E-04 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
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Table 3.3 Values of A and B parameters for the fault sedimentation deposit
Sl. No. Severity of fault a11 a21 b11 b12 b21 b22
1 1% -2.2149E-03 -1.1075E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
2 2% -2.2368E-03 -1.1184E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
3 3% -2.2588E-03 -1.1294E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
4 4% -2.2807E-03 -1.1404E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
5 5% -2.3026E-03 -1.1513E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
6 6% -2.3246E-03 -1.1623E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
7 7% -2.3465E-03 -1.1732E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
8 8% -2.3684E-03 -1.1842E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
9 9% -2.3904E-03 -1.1952E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
10 10% -2.4123E-03 -1.2061E-03 8.9999E-04 -9.8320E-04 6.2092E-04 -4.9160E-04
52
Table 3.4 Values of A and B parameters for the fault positive bias in water valve
Sl. No. Severity of fault a11 a21 b11 b12 b21 b22
1 1% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.8484E-04 6.2402E-04 -4.9242E-04
2 2% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.8647E-04 6.2710E-04 -4.9324E-04
3 3% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.8809E-04 6.3017E-04 -4.9405E-04
4 4% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.8971E-04 6.3322E-04 -4.9485E-04
5 5% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.9131E-04 6.3626E-04 -4.9566E-04
6 6% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.9291E-04 6.3928E-04 -4.9646E-04
7 7% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.9451E-04 6.4229E-04 -4.9725E-04
8 8% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.9609E-04 6.4528E-04 -4.9805E-04
9 9% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.9767E-04 6.4826E-04 -4.9883E-04
10 10% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.9924E-04 6.5123E-04 -4.9962E-04
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Table 3.5 Values of A and B parameters for the fault negative bias in water valve
Sl. No. Severity of fault a11 a21 b11 b12 b21 b22
1 1% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.8155E-04 6.1781E-04 -4.9078E-04
2 2% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.7990E-04 6.1468E-04 -4.8995E-04
3 3% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.7824E-04 6.1154E-04 -4.8912E-04
4 4% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.7656E-04 6.0838E-04 -4.8828E-04
5 5% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.7488E-04 6.0520E-04 -4.8744E-04
6 6% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.7319E-04 6.0201E-04 -4.8660E-04
7 7% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.7149E-04 5.9880E-04 -4.8575E-04
8 8% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.6978E-04 5.9557E-04 -4.8489E-04
9 9% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.6807E-04 5.9232E-04 -4.8403E-04
10 10% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.6634E-04 5.8906E-04 -4.8317E-04
54
Table 3.6 Values of A and B parameters for the fault positive bias in steam valve
Sl. No. Severity of fault a11 a21 b11 b12 b21 b22
1 1% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.8647E-04 6.2092E-04 -4.9323E-04
2 2% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.8972E-04 6.2092E-04 -4.9486E-04
3 3% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.9295E-04 6.2092E-04 -4.9647E-04
4 4% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.9617E-04 6.2092E-04 -4.9808E-04
5 5% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.9937E-04 6.2092E-04 -4.9968E-04
6 6% -2.1930E-03 -1.0965E-03 8.9999E-04 -1.0026E-03 6.2092E-04 -5.0128E-04
7 7% -2.1930E-03 -1.0965E-03 8.9999E-04 -1.0057E-03 6.2092E-04 -5.0286E-04
8 8% -2.1930E-03 -1.0965E-03 8.9999E-04 -1.0089E-03 6.2092E-04 -5.0444E-04
9 9% -2.1930E-03 -1.0965E-03 8.9999E-04 -1.0120E-03 6.2092E-04 -5.0601E-04
10 10% -2.1930E-03 -1.0965E-03 8.9999E-04 -1.0152E-03 6.2092E-04 -5.0758E-04
55
Table 3.7 Values of A and B parameters for the fault negative bias in steam valve
Sl. No. Severity of fault a11 a21 b11 b12 b21 b22
1 1% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.7992E-04 6.2092E-04 -4.8996E-04
2 2% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.7662E-04 6.2092E-04 -4.8831E-04
3 3% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.7331E-04 6.2092E-04 -4.8665E-04
4 4% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.6997E-04 6.2092E-04 -4.8499E-04
5 5% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.6663E-04 6.2092E-04 -4.8331E-04
6 6% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.6326E-04 6.2092E-04 -4.8163E-04
7 7% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.5987E-04 6.2092E-04 -4.7994E-04
8 8% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.5647E-04 6.2092E-04 -4.7823E-04
9 9% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.5305E-04 6.2092E-04 -4.7652E-04
10 10% -2.1930E-03 -1.0965E-03 8.9999E-04 -9.4961E-04 6.2092E-04 -4.7480E-04
56
Table 3.8 Values of A and B parameters for the fault decrease in inlet water temperature
Sl. No. Severity of fault a11 a21 b11 b12 b21 b22
1 1% -2.1930E-03 -1.0965E-03 8.9099E-04 -9.7337E-04 6.1472E-04 -4.8668E-04
2 2% -2.1930E-03 -1.0965E-03 8.8199E-04 -9.6354E-04 6.0851E-04 -4.8177E-04
3 3% -2.1930E-03 -1.0965E-03 8.7299E-04 -9.5371E-04 6.0230E-04 -4.7685E-04
4 4% -2.1930E-03 -1.0965E-03 8.6399E-04 -9.4387E-04 5.9609E-04 -4.7194E-04
5 5% -2.1930E-03 -1.0965E-03 8.5499E-04 -9.3404E-04 5.8988E-04 -4.6702E-04
6 6% -2.1930E-03 -1.0965E-03 8.4599E-04 -9.2421E-04 5.8367E-04 -4.6210E-04
7 7% -2.1930E-03 -1.0965E-03 8.3699E-04 -9.1438E-04 5.7746E-04 -4.5719E-04
8 8% -2.1930E-03 -1.0965E-03 8.2799E-04 -9.0455E-04 5.7125E-04 -4.5227E-04
9 9% -2.1930E-03 -1.0965E-03 8.1899E-04 -8.9471E-04 5.6504E-04 -4.4736E-04
10 10% -2.1930E-03 -1.0965E-03 8.0999E-04 -8.8488E-04 5.5883E-04 -4.4244E-04
57
Table 3.9 Values of A and B parameters for the fault steam mixing with water in preheater
Sl. No. Severity of fault a11 a21 b11 b12 b21 b22
1 1% -2.1930E-03 -1.0965E-03 9.0899E-04 -9.9303E-04 6.2713E-04 -4.9652E-04
2 2% -2.1930E-03 -1.0965E-03 9.1799E-04 -1.0029E-03 6.3334E-04 -5.0143E-04
3 3% -2.1930E-03 -1.0965E-03 9.2699E-04 -1.0127E-03 6.3955E-04 -5.0635E-04
4 4% -2.1930E-03 -1.0965E-03 9.3598E-04 -1.0225E-03 6.4576E-04 -5.1126E-04
5 5% -2.1930E-03 -1.0965E-03 9.4498E-04 -1.0324E-03 6.5197E-04 -5.1618E-04
6 6% -2.1930E-03 -1.0965E-03 9.5398E-04 -1.0422E-03 6.5818E-04 -5.2110E-04
7 7% -2.1930E-03 -1.0965E-03 9.6298E-04 -1.0520E-03 6.6439E-04 -5.2601E-04
8 8% -2.1930E-03 -1.0965E-03 9.7198E-04 -1.0619E-03 6.7060E-04 -5.3093E-04
9 9% -2.1930E-03 -1.0965E-03 9.8098E-04 -1.0717E-03 6.7681E-04 -5.3584E-04
10 10% -2.1930E-03 -1.0965E-03 9.8998E-04 -1.0815E-03 6.8302E-04 -5.4076E-04
58
3.6.1 Architecture of the neural network
A single layer neural network used to identify the parameters of the
deaerator is shown in Figure 3.12. The learning process involves the
determination of the weights which directly indicate the parameters of the
system. The number of input neurons is equal to the number of input and state
variables and the number of output neurons is equal to the number of
predicted states. In the deaerator, there are four inputs namely enthalpy,
pressure, steam valve position and water valve position and the two output
variables are the predicted state variables. The weight associated with each
neuron represents the adaptable weight corresponding to one of the system
parameters to be estimated (say a11). The estimation algorithm trains the
network weights with sequential updates. Whenever the parameters of the
deaerator changes, it is reflected as an error in the predicted state variable
value X̂ k+1 . The predicted value of state variable X̂ k and actual value of
state variable X k+1 are different and this difference is utilised by the
algorithm to change the weights (parameters) till convergence take place. The
neural network thus trained with a set of data corresponding to normal and
fault conditions gets converged and the parameters thus obtained are used for
detecting the faults by different types of neural network.
The activation function ‘purelin’ is used for this neural network.
The computer used for this work is pentium IV intel 3.4 GHz CPU. And
504MB RAM. A sampling period of once again has been used in all the
computer wok (and graphs) reported in this thesis .
59
Figure 3.12 Single layer neural network used for parameter estimation
3.6.2 Fault simulation by single layer neural network
Fault simulation essentially means introduction of fault (by varying
the appropriate system parameters) through a simulated process. This exercise
is required in order to carry out fault diagnosis in the simulated deaerator. The
changes of the system parameters (A and B) due to occurrence of eight faults
have been determined using the linear model of deaerator (section 3.5.2).
These changes are effected (one set of changes at a given time) in the single
layer neural network, which is equivalent to introducing a fault and this is
termed as fault simulation.
For example, various steps involved in the simulation of fault,
leakage in tank are given below:
i. The values of A and B parameters during fault leakage in
tank are noted down
60
ii. The fault is introduced (Matlab program) by effecting the
changes in system parameters at the 500th sampling instant in
the Equations (3.20) and (3.21)
iii. The input and state variables which are continuously fed to
the single layer neural network are subjected to changes at
the 500th sampling instant (after the introduction of the
fault). These changes lead to the changes of the weights of
the neural network (which are nothing but the system
parameters).
iv. The steady state values of the parameters as determined by
the single layer neural network is then fed to the next stage
for fault diagnosis.
v. The above fault is with drawn at 750th sampling instant and
another fault sedimentation deposit is introduced from 1000th
to 1250th sampling instant. Figure 3.13 gives the variation of
system parameters as determined by single layer neural
network due to the introduction of above two faults.
vi. Similarly the simulation for two faults positive bias in water
valve (from 500th to 750th) and negative bias in water valve
(from1000th to 1250th) are illustrated in Figure 3.14.
Figure 3.15 illustrate the fault simulation for the faults
positive bias in steam valve and negative bias in steam
valve. Figure 3.16 illustrate the fault steam mixing with
water in preheater and decrease in inlet water temperature.
61
Figure 3.13 Simulation of faults leakage in tank and sedimentation
deposit (variation in a11 and a21)
Figure 3.14 Simulation of faults positive bias in water valve and negative
bias in water valve (variation in b12, b21 and b22)
62
Figure 3.15 Simulation of faults positive bias in steam valve and negative
bias in steam valve (variation in b12 and b22)
Figure 3.16 Simulation of faults steam mixing with water in preheater
and decrease in inlet water temperature (variation in
b11, b12, b21 and b22)
63
3.7 SUMMARY
This chapter describes the procedure used for identifying the
parameters of the deaerator plant using RLS algorithm utilising the plant data.
The method described is recursive in nature and suitable for both on-line and
off-line implementation. As the model is unstable it was stabilized using pole
placement technique. As the simulation of fault using RLS model is not
feasible, a linearised mathematical model using fundamental laws was
developed. A PI controller is used for level loop and PID controller is used for
pressure loop. The closed-loop responses obtained with both models are
almost same. Eight different faults are simulated (in closed-loop conditions)
by varying A and B parameters of the deaerator and the responses during
faulty conditions are also plotted. It is lasso observed that the ANN takes
about 200s for estimating parameters (weights) initially. Any further change
in parameter (due to fault) in estimated in a very short time, ie. 1s.