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ELIMINATION OF CROSS SENSITIVITY IN ADMITTANCE

TYPE LEVEL MEASUREMENT USING FUZZY BASED

LINEARISER

Joyanta kumarRoya and Bansari Deb Majumder

b

aM.C.K.V college of Engineering, WB, India. bNarula Institute of Technology, WB, India.

Emails: [email protected] , [email protected]

______________________________________________________________________________

Submitted: Oct. 16, 2014 Accepted: Nov. 23, 2014 Published: Dec. 1, 2014

Abstract- The cross sensitivity of temperature and ionic concentration are problematic issues in

admittance type level measurement. In this paper cross sensitivity of temperature and ionic

concentration in admittance type level measurement has been thoroughly studied. From the analysis of

results a methodology for elimination of cross sensitivity has developed. This proposes fuzzy based

lineariser to eliminate errors due to temperature and conductivity in admittance type level

measurement. The developed fuzzy based lineariser found an effective tool which is knowledge based

and significantly eliminates high cross sensitivity of temperature and ionic concentration error in

admittance type level sensor. Single electrodes and double electrodes level transmitter cases are also

studied. The result achieved is satisfactory and will help to design suitable smart admittance type level

measurement system for industrial processes.

Keywords: Admittance, level transmitter, fuzzy logic, linearization, cross sensitivity, boiler drum.

INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS VOL. 7, NO. 4, DECEMBER 2014

2035

mailto:[email protected]

mailto:[email protected]

I. INTRODUCTION

Boiler drum level is one of the important parameter to be measured and controlled in process

industry like power plant. The boiler is used to convert water into steam, which is used to turn a

steam turbine eventually generating electricity. Water level control is an important parameter for

operation of boiler effectively. An objective for safe and efficient boiler operation is to maintain

a constant level of water in the boiler drum. If the level is too low, boiler tubes will be damaged

by overheating. Low water conditions have been the most common cause of boiler accidents for

decades. Typically the incidents have occurred as a result of insufficient or inoperable controls.

Many times it is a symptom of improper selection of devices that results in poor performance and

a low availability factor for the safety systems. Instances have occurred where as a result of

continued failures, devices are removed from service due to frustration caused by continued poor

performance even after extensive maintenance effort. This study is intended to direct the design

engineer towards the basic concerns and methods related to specifying Boiler Drum level

measurement [1]. There are different techniques to measure the drum level like conductivity

probe type level transmitter, sight gauges, magnetic type level transmitters etc. [2, 3, and 4].

Unfortunately boiler drum level control is complicated by changes in electrical load requirements

or variation in the fuel and air supply. Hydrastep is a very common water level measuring system

for high pressure or high temperature boiler drum has been used in power plants. There is a need

of continuous level monitoring and easier installation in boiler drum level transmitter for safe

and efficient operation of boiler.

Admittance type level transmitter is one of the low cost level measuring units [5].In case of

admittance level transmitter, the admittance value obtained is proportional to the level of boiler

drum. But the electrical parameter “admittance” has cross sensitivity with other suitable

measurement. Cross sensitivity is the effect of one measurand on the other measurand. Therefore

the admittance level transmitter shows cross sensitivity of temperature and ionic concentration in

boiler drum [6, 7]. The advantage of using admittance type level transmitter is primarily

continuous measurement of level, low cost and can be used in both metallic and non-metallic

tank. Earlier workers tried to develop Admittance type continuous level measurement [8] system

in metallic or non-metallic storage vessel, which is one of the low cost sensing methods for

continuous monitoring the level with some significant cross sensitivity of temperature and ionic

concentration.

The present work has been divided into three parts. Primarily a review on cross sensitivity of

temperature, secondly cross sensitivity of ionic concentration and eventually develop a

computational tool to eliminate these errors which is a fuzzy based linearizer.

Joyanta kumar Roy and Bansari Deb Majumder, ELIMINATION OF CROSS SENSITIVITY IN ADMITTANCE TYPE LEVEL MEASUREMENT USING FUZZY BASED LINEARISER

2036

II. MOTIVATION

In power plants, for measuring the boiler drum level Hydrastep type level transmitter is used

which is costly and very complex level measuring system. This motivates us to use some low

cost level measuring system in boiler drum. Previous researchers already suggested admittance

level transmitter as low cost measuring system. So we have tried to use admittance level

measuring system for measuring the level in boiler drum. But cross sensitivity of temperature

and ionic concentration was a critical issue in case of admittance type level transmitter. Earlier

authors have studied [6, 7]this cross sensitivity effect and found a significant effect of change in

temperature and ionic concentration on admittance type level measurement. We have focused

on admittance type level transmitter and try to eliminate all the cross sensitivity effect to

measure the level accurately and precisely. Meanwhile we have also develop a fuzzy based

linearizer which is multi input system can be incorporated online for elimination of errors from

the measurand.

III. CROSS SENSITIVITY OF TEMPERATURE

The study of cross sensitivity of temperature is carried out initially for single electrode type

admittance measurement system where we have considered a cylindrical metallic electrode A of

radius r is immersed to a depth h in a liquid of permittivity and conductivity σ in a cylindrical

metallic storage vessel of diameter D as shown in figure-1

The impedance between the electrode and the vessel is given by

Where, YParallel is the admittance between the electrode and the vessel. Cparallel is the equivalent of

fringe capacitance and double layer capacitance between the electrodes and the vessel. Rparallelis

Figure.1: Single electrode in a conducting vessel [1]


2037

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

Height of the liquid level (in metre)

Ad

mit

tan

ce (

in m

ho

)

Relation of Admittance and height of the liquid level

the equivalent resistance of fringe, electrode double layer resistance between the electrode and

the vessel.

The equivalent admittance between the electrode and the vessel is given by

Where,Yparallel is the admittance between the electrode and the vessel,

h is the height of the liquid level

d is the separation between the electrodes

r is the radius of the electrode

σ is the conductivity of the liquid

is the permittivity of the liquid

The magnitude of the admittance parallel is given by

The above equation is rewritten as

Where,

For admittance transmitter, the relation between the admittance and height of the liquid level is

very much linear in nature [5] represented by the Fig 1.

Figure.2: Plot between Admittance and height of the liquid level for single electrode

of admittance type level measurement with change at fixed ionic concentration and

temperature [5]


2038

Admittance depends on conductivity and permittivity of the ionic solution [9][10]. The

conductivity of the solution is related to temperature shown in equation (5).

σTref = * σT(5)

where σTref is conductivity at reference temperature, is Temperature coefficient.

The variation of permittivity with temperature is shown in equation (6).

( T)1/2= 8.851*d(T) (6)

Where, [d (T)]2= 1-0.4536.10-2(T-25)+ 0.9319.10-7(T-25)2

Substituting the variation of conductivity from equation (5) and variation of permittivity from

equation (6) in equation (4),

σTref)2 + 2{(8.851)2d(T)2} (7)

Simplifying the above equation and shown in equation (8).

(T) 2

+2

(T) 2

(8)

Computing the above equation in Matlab, considering different temperature ranges from 30

degree Celsius to 60 degree Celsius. The figure 2 shows the error curve obtained with significant

temperature effect on admittance measurement. The error in Admittance measurement due to the

effect of temperature has been calculated by taking difference of equation-8 and equation -4 and

computing the error curve using MATLAB for single electrode measurement system. Figure 3

shows the effect of cross sensitivity of temperature on admittance level measurement.

It is found from the study that the error of the single electrode admittance type level sensor is

with slope 0.5 and the error of the double electrode admittance type level sensor is (-20% to

42%) with slope 0.67. Therefore It can be concluded that the cross sensitivity of the single

electrode admittance type level measurement is less with double electrode type. The study

reveals that the admittance type level measurement has sufficient cross sensitivity of

temperature. This computational analysis is carried in Matlab version R2010.


2039

Figure.4: Plot between Admittance of single electrode type and height of

the liquid level with different values of temperature from 30 degree C to

60 degree C [6]

Figure 3: Error curve for temperature effect on admittance level

measurement [6]


2040

IV. CROSS SENSITIVITY OF IONIC CONCENTRATION

Similar analysis of cross sensitivity is carried out for admittance measurement having cross

sensitivity of ionic concentration. We have considered same metallic storage tank containing

single electrode, where admittance value is shown in equation (4).

Admittance depends on conductivity and permittivity of the liquid. It is noted that if there is no

change in temperature and ionic concentration then admittance within the two electrodes is

proportional to level of the tank. Here the variation of ionic concentration on the conductivity

and permittivity of the liquid is considered at a constant temperature.

Relation between conductivity of the liquid and the variation of ionic concentration [11] in the

solution is given by equation (9).

C=A0+A1 (σref) +A2 (σref)2 (9)

Where C = Ionic concentration

σref= conductivity corrected to Tref temperature

A0, A1and A2 are specific constants depend on the type of solvents present in the

solution.

There are two roots of the quadratic equation and variation is shown in equation [5].

In the equation [9] for the physical measurement, the negative roots are not considered because

they give imaginary solution.

Relation between permittivity of the liquid and the variation of ionic concentration [12][13] in

the solution is given by

Where

is the dielectric constant of the liquid due to presence of all dissolved solute in solvents.

₀ is the dielectric constant results from the presence of all neutral species including

solvents and ions pairs.

Ii is the ionic strength on the mole fraction Basis.

Ai and Bi are temperature dependent parameters

xi is the mole fraction of the component i.

The temperature dependent parameters Ai and Bi are related by given equation-9,


2041

Where T is temperature in Kelvin

ai1, ai2, bi1 and bi2 are the parameters determined from experimental dielectric constant data for

electrolytic solutions. By analyzing experimental data that constant values of the parameters can

be used for any of the ionic species in all of the aqueous solutions.

The Yparallel is represented as

Where, σc is the molar conductivity of solution considering the effect of change in ionic

concentration. c is the permittivity of the solution considering the effect of change in ionic

concentration.

The cross sensitivity of ionic concentration have significant effect too on the admittance level

transmitter. For fixed values of liquid level, % error in admittance can be computed by taking the

difference of the admittance ideal (without the variation of ionic concentration) and actual

admittance (with the effect of variation of ionic concentration). The difference value is the

divided by the ideal admittance value to calculate the error. The figure 5 shows the error curve

obtained by varying the ionic concentration in Nacl solution for admittance level measurement.

Figure 6 shows the effect of cross sensitivity of ionic concentration on admittance level

measurement.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-40

-20

0

20

40

60

80

100

TDS ( Ionic concentration)

%E

rro

r o

f ad

mit

tan

ce

Error curve of admittance due to the variation of ionic concentration in Nacl solution

Figure.5: Error curve of admittance of the liquid at different range of

total dissolved solids in the solution of NaCl [7]


2042

This study reveals that there is significant cross sensitivity after certain ionic concentration

similar cross sensitivity like temperature. For Boiler drum level measurement and control

correction of

Temperature cross sensitivity is required but for other application using normal drinking or non-

drinkable water correction of ionic concentration and temperature are required. The study is

computational based done in MATLAB version R2010.

Our attempt is to eliminate these cross sensitivity effect and suggest some computational tool to

eliminate the errors. For this we have chosen fussy based lineariser which is an effective tool for

error elimination.

V. INTRODUCTION TO FUZZY BASED LINEARIZATION

Linearization is the method of error removal from the measured value of the process

parameter. Fuzzy logic deals with knowledge based computation technique[13] [14] can be

suitable for linearization, error analysis and elimination. Fuzzy lineariser includes input

variables, rule base or inference engine and output variables. There exist knowledge based

systems which related the nature of input and output variables at different condition. The fuzzy

based lineariser designed and computed in MATLAB version 7.10.0 (R2010a).

Here we have considered three inputs variables “A “represents ideal admittance variable ,

“Aerror(T) “ represents measured admittance error of change in temperature and “Aerror(I)”

0 0.5 1 1.5 20

1

2

3

4

5

6

7

8

Height of the liquid level (in metre)

Ad

mit

tan

ce (

in m

ho

)

Liquid level versus admittance at different ionic molar concentration

c=2

c=0.1

Figure.6: Plot between Admittance of single electrode type and height of the

liquid level with different values of molar concentration c=0.1 to 2[7]


2043

represents measured admittance error of change in ionic concentration. The input variables are

feed to the fuzzy rule base(mamdani) named “admittancenew” .there is one output variable

named”Aoutput” represents the fuzzy corrected admittance value. The MATLAB view of the

fuzzy linearizer(.fis file) is shown in figure 6.

Now the membership functions of each of the input and output variables are framed as shown in

figure 7. In this figure we have selected Aerror(I) input variable and considered five membership

functions whose ranges are considered from the error curve of Admittance with varying ionic

concentration i.e., figure 5.

Figure.6: The fuzzy based linearizer by MATLAB

Figure.7: The membership functions of input and output variables of fuzzy based

linearizer


2044

Similarly other input and output variables “Aerror(T)”,”A” and “Aoutput” are represented by the

membership function designed on the basis of the characteristic curve obtained for each of the

parameter. The rule matrix for the input and output variables have been prepared as per

convention that when any of the error is positive in nature Aoutput is subtracted by error value

i.e., Aoutput is decreased. Similarly when any of the error is negative in nature Aoutput is added

by error value and result is obtained or we can say Aoutput is increased. By using these logics

around 56 rules have been prepared and shown in figure 8.

VI. RESULT ANALYSIS

The surface plot of Yerror(I) i.e., Admittance error due to varying TDS of the liquid is varied with

measured admittance (Y) and Youtput i.e., fuzzy corrected data is shown in figure 9 and the

surface plot showing Yerror(T) i.e., Admittance error due to varying temperature the liquid is

varied with measured admittance (Y) and Youtput i.e., fuzzy corrected data is shown in figure 10.

Figure 8: The Rule viewer page of Matlab.


2045

Now, data’s are recorded for the values of the Admittance value from the lineariser output i.e., Y

corrected from fuzzy lineariser from the rule viewer window, Y ideal from the values evaluated

from the equation shows the relation between admittance and height of the liquid level in meter

and measured admittance(Y) with varying ionic concentration from the equation of admittance

Figure 9: The surface plot of Aerror(I) and A with relation with Aoutput

Figure 10: The surface plot of Aerror(T) and A with relation with Aoutput


2046

and height of the liquid level in meter considering only the change of ionic concentration at

constant temperature. The recorded data’s are plotted in figure 11 and figure 12 at varying ionic

concentration and temperature respectively.

The figure 11 shows the comparison study between ideal admittance data with actual admittance

data and also with fuzzy corrected data keeping the temperature constant at 21.9deg.C. Here the

value of ionic concentration (TDS) is varied though out the recorded data. Statistical analysis of

the recorded data have been done and found a Standard deviation of 0.00769 which is under

tolerance range. Now the same analysis have been carried out with fuzzy linearized data at

constant ionic concentration (TDS) and shown graphically in figure 12.

0.0000

0.786(TDS)

0.806(TDS)

0.821(TDS)

1.26

1.36 (TDS)

1.42(TDS)

1.82

2.1(TDS)

)

0.0000

0.5000

1.0000

1.5000

2.0000

2.5000

3.0000

0.00 0.20 0.40 0.60 0.80 1.00

Leve

l se

nso

r A

dn

itta

nce

(Y

)

Liquid level (m)

Comparison study of ideal-vs- actual-vs- fuzzy corrected data

Yparallel without error(Ideal)

Measured (Y) withvarrying ionicconcentration

**All the datas are collected keeping the temperature constant=21.9 deg.C Min error=-0.075 Max error=0.0459 Std Deviation=0.0769

Figure 11: Comparison study of ideal-vs.-actual-vs. fuzzy corrected data at varying

ionic concentration (TDS)


2047

In the figure 12, the statistical analysis have been carried out and found a standard deviation of

0.0904.

VII. CONCLUSION

The target of the study is to find out nature of errors in admittance type measurement of level due

to cross sensitivity of temperature and ionic concentration, theoretical analysis of the study

reveals the nature of such variation due to cross sensitivity demands practical validation though

experiments. It is observed that fuzzy based linearization technique developed has high

linearizing ability and eliminated the error of temperature and ionic concentration from the

measured value more accurately. The standard deviations noted are within the tolerance range.

The next target of the study will be implementation of theatrical knowledge in developing

experimental setup in suitable laboratory scale for measurement of process liquid level with

variation of temperature and conductivity. The admittance and other parameters will be

converted to digital data, electronic data acquisition system and fuzzy linearization will be taken

in action using suitable data acquisition and graphical analysis software platform. Elimination of

the error of temperature and ionic concentration is one of the requirements for proper

measurement of level in boiler drum. These effects of temperature and ionic concentration also

20.7˚C

25.1˚C

34.8˚C 39˚C

50˚C

53.7˚C

55.2˚C

57.3˚C

y = 3.2888x - 0.0971 R² = 0.9845

0

0.5

1

1.5

2

2.5

3

0 0.2 0.4 0.6 0.8 1

Ideal admittance(inmho)MeasuredAdmittance(in mho)CorrectedAdmittance(in mho)Linear (CorrectedAdmittance(in mho))Linear (CorrectedAdmittance(in mho))

Comparitive study of Ideal Admittance-vs-Measured Admittance -vs-Corrected Admittance (fuzzy linearised data)

Liquid Level (in metre)

Ad

mit

tan

ce (

in m

ho

)

**All the datas are collected keeping the ionic concentration at 0.184TDS Min error=-0.2337 Max error=0.0673 Std Deviation=0.090419869

Figure 12: Comparison study of ideal-vs.-actual-vs.- fuzzy corrected data at varying

temperature


2048

give an advantage to measure level, temperature and quality of the boiler water simultaneously.

This method of sensing three or more parameter called as multifunction sensor [16] which is one

of the significant areas to work. There are many applications of multifunction sensors in today’s

world and hence is the future scope of the work.

Finally the target is to develop low cost but continuous level transmitter suitable for high steam

temperature and pressure.

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2049

[10] Matthias Weiß and Reinhard Knöchel, A Novel Method of Determining the Permittivity of

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[16] M.Iwahara, S.C.Mukhopadhyay, S.Yamada and F.P.Dawson, "Development of Passive

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International conference on multisensory fusion and integration for intelligent systems,

2003,pp 209-212.


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