27

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

28

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.

29

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.

30

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)

31

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)

32

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

33

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

34

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)

35

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.

36

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

37

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.

38

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

39

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

40

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.

41

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.

42

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

43

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%.

44

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.

45

(a)

(b)

Figure 3.8 Simulation of tank leakage and sedimentation deposit by

increasing/decreasing the outflow (a) pressure variation

(b) level variation

46

(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

47

(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

48

(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

49

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.

50

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

51

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

53

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.