Design of an adaptive calibration technique based on LSSVM for

ICETACS 2013

Design of an Adaptive Calibration technique based on LSSVM for Liquid Level Measurement Santhosh K V

B K Roy

Department of Electrical Engineering National Institute of Technology Silchar Silchar, India [email protected]

Department of Electrical Engineering National Institute of Technology Silchar Silchar, India [email protected]

Abstract— Design of an adaptive calibration technique using Least S quare Support Vector Method (LS -S VM) for liquid level measurement using Capacitance Level Sensor (CLS ) is reported in this paper. The objectives of the present work are (i) to extend the linearity range of measurement to 100% of the full scale, (ii) to make the measurement technique adapti ve for variations in permittivity of liquid, liquid temperature, and diameter of the storage tank. The output of CLS is capacitance. A data conversion unit is used to convert it to voltage. A suitable LS -S VM model is designed to replace the conventional calibration circuit, in cascade to the existing data conversion unit. The proposed technique provides linear relationship of the overall system over the full input range and makes it adaptive of variation in liquid permittivity, and/or temperature, and/or tank diameter. LS -S VM is trained with simulated data considering variations in liquid level, liquid permittivity, liquid temperatures, and tank diameters. Results show that the proposed scheme has fulfilled the objectives. Keywords-Least square support vector machine, capacitance level sensor, adaptation, calibration, optimization.

I.

INT RODUCT ION

Level measurement is one of the “Big 4” measurements in industrial plants. As important as flow, pressure and temperature, the worldwide level market in 2004 was estimated at US$1.32 Billion. Approximately 12% of all measurements in the industrial marketplace are used for level measurement. The market estimate included continuous level devices which measure the continuous level of liquid or solids in a tank, as well as point level devices which measure liquids or solids at one or more points in a tank. Many devices used for liquid level measurement [1]. Continuous level devices are used when it is important to control or monitor the material at all points in a tank. Point level devices are usually used when it is important to know the lowest point or highest point. Of these, continuous level devices are commonly used. Level is measured by a variety of method by contact and non contact techniques. The contact-type-level-sensing probes are the most commonly used, because of their higher sensitivity, less power dissipation, and ruggedness in design. Capacitance level sensor is a most common contact type level sensing for continuous measurement. Ho wever in a capacitance level sensor, the problem of offset and high nonlinear response characteristics as well as dependence of output on tank diameter, permittivity, and temperature of liquid have imposed restriction and difficulties in using such sensors.

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To overcome the above difficult ies, an intelligent level measurement technique is proposed in this paper using the technique of least square support vector machine. This network is trained to obtain linearity and make the output independent of tank diameter, permittiv ity, and temperature of liquid. Literature survey carried on the following reported work similar to one proposed. In [2], a look up table approach is used to calibrate the capacitance sensor for a certain range. Linearization of sensor is achieved with the help of circuits is reported in [3-5, 10]. In [6], Fourier transform techniques are used to calibrate the capacitance level sensor. A program is written on microcontroller to calibrate capacitance level sensor is reported in [7]. In [8], dig ital signal processing techniques are used for linearizat ion of capacitance level sensors. Artificial neural network model is used to linearize the capacitance level sensor. Further the output is made independent of variations in temperature by using a redundant sensor to cancel the effect of temperature is reported in [9]. In [11], signal processing technique using Fast Fourier Transform (FFT) algorith m is used to linearizat ion of level sensor by fiber-bragg grating principle . Measurement of level using image processing technique is reported in [12]. In [13], artificial neural network algorithm is used for calibration of capacitance level sensor. Support vector machine is used to linearize the ultrasonic level sensor over a certain range of full scale is reported in [14]. Fro m the studies carried it is found that many techniques are adopted for linearization of level sensors, but most of these are used for linearization in a certain range. Few reported works also discuss adaptation to variations in temperature but it‟s achieved using a redundant sensor. To overcome the above short falls of the reported work like extension of linearity range to full scale, adaptive to variations of tank diameter, and/or liquid permittiv ity, and/or liquid temperature a method has been proposed in this paper using the concept of LSSVM. The LSSVM model is added in cascade to the data conversion unit to achieve the set objectives. The paper is organized as follo ws: after introduction in Section-I, a brief description on CLS is given in Section-II. The output of CLS is capacitance; a brief d iscussion on data conversion unit i.e. a t imer and frequency to voltage converter are discussed in Section-III. Section-IV deals with the

ICETACS 2013

problem statement followed by proposed solution in Section V. Finally, result and conclusion is given in Section-VI. II.

CAPACIT ANCE LEVEL SENSOR

Level measurement system using CLS is shown in Fig.1. A capacitor is formed when a level sensing electrode is installed in a vessel. The metal rod of the electrode acts as one plate of the capacitor and the tank wall (or reference electrode in a non-metallic vessel) acts as the other plate. As the liquid level rises, the air or gas normally surrounding the electrode is displaced by liquid having different dielectric constant. A change in the value of the capacitor takes place because of such change in dielectric between the plates. Capacitance instruments detect this change and convert it into a relay actuation or a proportional output signal. The capacitance relationship in general is given by the following equation [15], [16]. F

(1)

Where C : output capacitance B : diameter of the probe A : diameter of the vessel H : height of the probe

Figure 2. Equivalent Capacitance

F

(2)

where: C1 = capacitance due to lid. F F Substituting C2 , C3 in (2) results, F

(3)

Capacitance is also a function of temperature, wh ich can be shown [17] by the following equation.

Now, considering a level measuring system using CLS as shown in Fig.1.

F

(4)

: Capacitance at temperature t o C : Capacitance at temperature t 0 0 C : Temperature constants.

where: Ct C0 α, β

III.

DAT A CONVERSION UNIT

The block diagram representation of the proposed technique is given in Fig 3. Temperature Sensor Level

CLS

Data conversion unit

LS-SVM

Display

Figure 1. Level measurement system using CLS Known values of

where

H : Height of the capacitance probe h : Level of liquid under measure ϵ o : Permittivity of air (8.854 x 10-12 F/m) ϵ r : Permittivity of liquid Ce : Capacitance measured

The effective capacitance of level measurement technique using CLS is shown in Fig. 2 and its value is given by (2).

,D

Figure 3: Block diagram of the proposed measuring technique

A : Timer Circuit An astable mult ivibrator is shown in Fig 4 which produces a 's quare wave'. This is a digital waveform with sharp transitions between low (0V) and high (+Vs ) voltages. With the output high (+Vs) the capacitor Ct is charged by current flowing through R1 and R2. The threshold and trigger inputs monitor the capacitor voltage and when it reaches 2/3Vs (threshold voltage), the output becomes low and the discharge pin is connected to 0V [18].

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ICETACS 2013

The capacitor now discharges with current flowing through R2 into the discharge pin. When the voltage falls to 1/3Vs (t rigger voltage), the output becomes high again and the discharge pin is disconnected, allowing the capacitor to start charging again. This cycle is repeated continuously unless the reset input is connected to 0V which fo rces the output low wh ile reset is 0V. The frequency of output wave is given in (5)

PROBLEM ST AT EMENT

The characteristics of the capacitance level sensor for the variations in level, tank d iameter, liquid permittiv ities and temperatures of the liquid under measurement are simu lated using the MATLAB environ ment and the following characteristics are found. 5

(5) Voltage in volts

Hz

IV.

t = 50 C t = 100 C t = 150 C

4 3 2 1 0

0

0.1

0.2

0.3 0.4 Level in meter

0.5

0.6

Figure 6. Frequency to voltage converter outputs for variation of level and temperature, tank diameter = 0.1m, and permittivity of liquid is 30 5

Figure 4. 555 as an astable multivibrator

Er = 30 Er = 60 Er = 90

4

TC 9400 frequency to voltage converter circuit is shown in Fig 5. When used as a F/ V converter, the TC9400 generates an output voltage linearly proportional to the input frequency waveform. Each zero crossing at the threshold detector's input causes a precise amount of charge (q = CREF * VREF) to be dispensed into the operational amp lifier‟s summing junction. Th is charge in turn flows through the feedback resistor, generating voltage pulses at the output of the operational amplifier. A capacitor (CINT) across RINT averages these pulses into a DC voltage which is linearly proportional to the input frequency [19].

Voltage in volts

B: Frequency to Voltage Converter

3 2 1 0

0

0.1

0.2

0.3 Level in meter

0.4

0.5

0.6

Figure 7. Frequency to voltage converter outputs for variation of level and permittivity, tank diameter = 0.3m, and liquid temperature in 25 o C

5 A = 0.1m A = 0.2m A = 0.3m

Voltage in volts

4 3 2 1 0

Figure 5. T C9400 Frequency to voltage converter

The output voltage is related to the input frequency (f) by the transfer equation as shown in (6). V

(6)

0

0.1

0.2

0.3 0.4 Level in meter

0.5

0.6

Figure 8. Frequency to voltage converter outputs for variation of level and tank diameter, at permittivity = 30, and liquid temperature in 25 o C

Fig.6, Fig.7, and Fig.8 show the nonlinear variation o f voltage with the change in level, tank diameter, liquid temperature, and permittivity of the liquid. It has been observed from the above graphs that the output from frequency to voltage converter circuit has a nonlinear relat ion to liquid level. The datasheet suggests that

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ICETACS 2013

10% to 60% of full scale is used as input range for considering linearity. It may be observed that output voltage also varies with the change in tank diameter, liquid temperature, and permittivity of the liquid. These are the reasons which have made the user to go for calibration techniques using some circuits. Such measurement technique is not desirable in industries. So, improvement in the measurement technique by making it adaptive of variat ion in tank diameter, and/or liquid permittivity and/or temperature of liquid is essential. This paper makes an attempt to design a technique incorporating intelligence to produce linear output and to make the system adaptive of variat ion in tank d iameter, liquid permitt ivity, and temperature using the concept of LSSVM.

(3) (4)

TABLE I.

SUMMARY OF SVM MODEL P ROP OSED

PARAMETERS O F THE SVM MO DEL

PROBLEM SOLUT ION

When we establish a calibration model of CLS sensor based on SVM, we should solve a regression problem in deed. Support Vector Machines provide a framework for the regression problem and it can be applied to regression analysis. There is only one kind of samp le in SVM regression analysis and the optimal hyper plane is not to separate the two kinds of samp les, but to min imize the margin between all samples and optimal hyper planes [20, 21]. The calibration principle based on SVM makes use of the input parameters mapped to high-dimensional space by nonlinear transformation function, thus regression analysis can be performed in the high-d imensional space, and finally the Input/ Output function can be obtained [22-25] . Considering a set of t rain ing data about the capacitance level sensor input and output: {xik ,y ik }, i = 1,…….., n, where xik ϵ RN is input parameter of the capacitance level sensor data conversion output for variat ions in level, at different tank diameter, liquid permittivity, and liquid temperature. y ik ϵ R is output parameter of the measurement technique for variation of level and independent of tank d iameter, permittiv ity of liquid, and liquid temperature. The regression function based on LSSVM is denoted as (1): (1) Where ω.Φ(x) is the inner product of ω and Φ(x), ω is the vector in hign-dimensional space. b ϵ R is the bias. By using the relaxation variable ζ, ζ* ≥ 0, the value of ω and b in (1) can be solving an optimization problem: (2) First, the calibration model should be trained to get the corresponding parameters of the calibration model, such as kernel function, chastisement parameter and error bias ε and so on. Second, the calibration model should make use of the training sampling data to obtain the values of αi and b. If the

20% training for CV 20% training for test Projection algorithm o/p dimension Input optimization Level

18 18 K-mean clustering 50% Back elimination

Database

Input

V.

output error is satisfied, the training ends. Otherwise the calibrat ion model parameters should be adjusted according to the error. Finally, the verifying sampling data should be used to verify the calibrat ion model to determine the parameters of the calibration model. According to the Karush-Kuhn-Tucker Conditions, b can be calculated as follow equations:

Te mp

min

0m

30

0 oC

max

0.6 m

90

150 o C

VI.

RESULT S AND CONCLUSION

The proposed LSSVM after being trained with simu lated data is subjected to various test inputs corresponding to different tank diameters, liquid permittiv ities, and temperatures of liquid, all within the specified ranges. For testing purposes, the range of level is considered fro m 0.0 to 0.6 m, range of tank diameters is 0.1 to 0.3 m, range of is 30 to 90, and range of temperature is 0 to 150 o C. The outputs corresponding to sampled test inputs are listed in table-2. It is evident from table-1 that the proposed measuring technique has gained intelligence in addit ion to increase in the linearity range. The output is made adaptive of variation in tank diameter, liquid permittivities, and temperatures. Thus, if the tank is replaced by other with that of different diameter and/or liquid is changed by another liquid of different permittivity and/or the temperature of the liquid is changed, the system does not require any further calibration to give the accurate reading. All these have been achieved by using system trained by LSSVM . LSSVM is used for training, validation, and testing using Karush-Kuhn-Tucker Conditions for calibrat ion of capacitance level sensor, and adaptive of variations in tank diameter, liquid permittiv ity, and liquid temperature. Table-2 suggests that measured levels are same as actual levels. Mean square of % error for 24 d ifferent simu lated test conditions is 0.0373. It may be noted that the test conditions in Table I are d ifferent fro m the train ing data set. Table I show that the proposed system is made adaptive of variations in tank diameter, liquid permitt ivity, and liquid temperature, and thus repeated calibration can be avoided.

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ICETACS 2013 TABLE II. Actual Le ve l in m 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.6

[6]

RESULT OF P ROP OSED MEASUREMENT TECHNIQUE

35 40 50 55 30 65 80 90 85 80 75 70 65 60 55 50 45 40 35 30 32 47 62 77

Temp in o C 25 50 65 75 32 90 100 38 72 68 50 48 32 41 50 59 67 76 85 88 79 70 61 52

Tank dia D 0.1 0.15 0.20 0.25 0.30 0.25 0.20 0.15 0.10 0.20 0.30 0.20 0.10 0.12 0.17 0.22 0.27 0.24 0.19 0.14 0.11 0.16 0.21 0.26

Measured level in m 0.09993 0.09989 0.09996 0.10002 0.20006 0.20011 0.19996 0.19991 0.29982 0.29995 0.29992 0.30005 0.40006 0.40009 0.40013 0.39997 0.49999 0.49996 0.49995 0.50002 0.60006 0.60013 0.59991 0.59989

% Error 0.070 0.110 0.040 -0.020 -0.030 -0.055 0.020 0.045 0.060 0.017 0.027 -0.017 -0.015 -0.022 -0.032 0.008 0.002 0.008 0.010 -0.004 -0.010 -0.022 0.015 0.018

[7]

[8]

[9]

[10]

[11]

[12]

[13]

Available reported works have discussed different techniques for calibration of level measurement, but these are not adaptive of variations in permittiv ity‟s and temperatures of liquid. Hence, repeated calibration is required for any change of tank diameter, and/or liquid and/or liquid temperature. Further, some reported works have not utilized the full scale of measurement. In comparison to these, the proposed measurement technique achieves linear input output characteristics for full input range and makes the output adaptive of variations in tank diameter, liquid permittivities, and temperatures. So, proposed technique avoids repeated calibration every time liquid is replaced and/or the temperature of liquid is changed.

[14]

[15] [16] [17]

[18] [19] [20]

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