1. ISA Transactions® Volume 45, Number 3, July 2006, pages 319–328
Development of a virtual linearizer for correcting transducer static
nonlinearity
Amar Partap Singh,a Tara Singh Kamal,b Shakti Kumarc
a
Department of Electrical and Instrumentation Engineering, SLIET, Longowal-148106 (District: Sangrur) Punjab, India
b
Department of Electronics and Communications Engineering, SLIET, Longowal-148106 (District: Sangrur) Punjab, India
c
Centre for Advanced Technologies, Haryana Engineering College, Jagadhri-135003, Haryana, India
͑Received 21 September 2004; accepted 28 September 2005͒
Abstract
This paper reports the development of an artificial neural network based virtual linearizer for correcting nonlinearity
associated with transducers connected to the data-acquisition system of a computer-based measurement system. In
analog processing techniques, nonlinearity is considered to be a very serious problem that at one time was solved
frequently by the piecewise linear segment approach modeled by linear electronic circuits. Since the cost of
microcomputers has been reduced drastically, they are currently used in most applications of measurement, including
data-acquisition subsystems. Therefore, the hardware-based analog techniques of linearization are often replaced by the
software-based numerical ones. In this context, it has been found that a multilayer feed-forward back-propagation
network trained with the Levenberg-Marquardt learning rule provides an optimal solution to implement an efficient soft
compensator to correct transducer static-nonlinearity. © 2006 ISA—The Instrumentation, Systems, and Automation
Society.
Keywords: Transducer; Nonlinearity; Inverse model; Artificial neural network; Linearizer
1. Introduction aging becomes more responsible for introducing
variations in the transducer characteristics ͓2–4͔.
In almost all the transducer based measurement Under such situations, calibration of transducers is
systems, transducers are normally highly nonlin- required frequently. Therefore, the issues related
ear related to the physical parameter they sense. with the transducer nonlinearity and its self-
Also, if the measurement is done using a data ac- compensation must be addressed collectively in
quisition system-oriented computer-based mea- computer-based measurement, instrumentation,
surement system, a small amount of nonlinearity and control systems taking into account the non-
is added invariably by the signal conditioning linearity associated with the transducer as well as
modules of a data acquisition system in addition to that of signal conditioning modules.
the inherent static nonlinearity associated with the There are several software-based numerical
practical transducer ͓1͔. Further, inherent manu- methods to estimate scaled output signals from
facturing tolerances always present an additional transducers ͓5,6͔ correctly. These methods may be
problem in the event of replacement of a faulty divided into three broad groups ͓7͔. The simplest
transducer or signal conditioning module even if way is to store a look-up table in read-only
the new one is chosen from the same batch of memory and calculate the quantity to be measured
fabrication. Moreover, with the passage of time, by linear interpolation ͓5͔. The calculation for-
0019-0578/2006/$ - see front matter © 2006 ISA—The Instrumentation, Systems, and Automation Society.

2. 320 Singh, Kamal, and Kumar / ISA Transactions 45, (2006) 319–328
classical methods of interpolation stated above ͓9͔.
The main advantages of artificial neural networks
are their ability to generalize results obtained from
known situations to unforeseen situations, fast re-
sponse time in operational phase due to high de-
gree of structural parallelism, reliability, and effi-
Fig. 1. Schematic of inverse modeling of a transducer. ciency. Due to these reasons, the applications of
artificial neural networks have emerged as a prom-
mula is simple and universal, but the difficulty lies ising area of research for linearizing the transduc-
in the fact that each type of transducer requires its ers, since its adaptive behavior has the potential of
own table. Moreover, for good accuracy, this re- conveniently modeling strongly nonlinear charac-
quires a large storage capacity or memory. An- teristics.
other way is to use an interpolation formula ͓7͔ An adaptive technique based on the concept of
using three or more calibration points. In this an artificial neural network trained by least mean
method, one routine is sufficient to calculate the squares and recursive least squares learning rules
quantity to be measured by any transducer. It is has been used successfully in channel equalization
not necessary to know the transfer function of the ͓10͔, system identification ͓11,12͔ and line en-
transducer explicitly, a limited set of calibration hancement ͓4͔, etc. Based on the concept of adap-
points being sufficient. However, for hard nonlin- tive technique for obtaining the inverse model, an
earity, the technique fails because the reference artificial neural network based inverse model was
points are numerous under such conditions. The implemented in this work using a multilayer feed-
third method is to store a set of characteristic pa- forward back-propagation network trained with
rameters for each transducer and calculate the in- the Levenberg-Marquardt learning algorithm ͓13͔.
verse function of the relationship between its elec- The training process is carried out in such a way
trical output and the physical quantity to be that the combined transfer function of the trans-
measured ͓8͔. Now, only a small set of parameters ducer and its inverse model becomes unity in an
is sufficient. But each type of transducer requires iterative manner. The schematic of the inverse
its own, sometimes rather complicated calculation model of a transducer using an artificial neural
routine. Besides, in this context, use of artificial network as its adaptive compensating nonlinear
neural networks has also been suggested as an ef- model is shown in Fig. 2. Here, the neural network
ficient alternative method to linearize the transduc- is suitably adapted to model a nonlinear transducer
ers and have shown the ability to correct static accurately in inverse mode using a back-
nonlinearity associated with them. propagation learning mechanism based on the in-
formation acquired from the transducer. As a re-
2. Neural linearizer sult, the effect of associated nonlinearity is
neutralized automatically.
For successful implementation of a software This concept of inverse modeling of the trans-
based linearizer, a good inverse model of the ducer, in fact, has been borrowed from the adap-
transducer element is required invariably ͓8͔ in the tive channel equalization process based on the in-
system for linearizing its input-output static re- verse modeling principle performed at the end of
sponse. The schematic arrangement of an artificial the receiver in communication systems ͓10͔. By an
neural network as a nonlinear compensating ele- adaptive learning procedure, the inverse model
ment is shown in Fig. 1. A main characteristic of evolves in such a way that the combined transfer
this solution is that function ͑F͒ to be approxi- function of the transducer and its inverse model
mated is given not explicitly but implicitly becomes unity in an iterative manner. As a result,
through a set of input-output pairs, named as a the measurand is estimated accurately at the out-
training set that can be obtained easily from the put of the inverse model irrespective of the trans-
calibration data of measurement systems. In this ducer static nonlinearity. The synthesized inverse
context, the usage of artificial neural network tech- model of the transducer is used to estimate the
niques for modeling the system behavior provides measurand for calibration as well as for providing
lower interpolation error when compared with direct digital readout.

3. Singh, Kamal, and Kumar / ISA Transactions 45, (2006) 319–328 321
Fig. 2. Schematic of artificial neural network based inverse modeling of a transducer.
3. Development of the virtual linearizer verse response and associated data in the tabular
as well as in graphical form. The algorithm of con-
The development of the virtual linearizer in- trol and computations exchanged the information
volved the development of two integrated software between test-point and MATLAB environments
modules ͓9,14͔. The first module was imple- ͓16͔ using the dynamic data exchange feature of
mented in the form of a Data Acquisition and Windows. Selecting “Direction” on the front panel
Management Software supported on the architec- opens another subpanel displaying the stepwise
ture of an inbuilt Algorithm of Control and Com- operating procedure of the proposed virtual linear-
putations. The second module was implemented in izer.
the form of an artificial neural network based Soft A strain-gauge type of pressure transducer con-
Compensator to perform the function of signal nected to the data acquisition system of a com-
processing component of the proposed virtual lin- puter based measurement system is chosen here
earizer. for experimental study. The virtual linearizer is
implemented to acquire the input-output data from
3.1. Synthesis of data acquisition management the data acquisition system-connected pressure
software transducer working in a real-time environment for
the purpose of training the neural network and
In the present work, the data acquisition and subsequent validation thereof. Provision has been
management software was developed using fourth made to further validate the implemented inverse
generation, object-oriented, and graphical pro- model of the given transducer for its performance
gramming technology in the form of a single in the production phase. In order to do so, the
Front-panel and various Subpanels using test-point
software ͓15͔. The different test-point objects were
carefully researched, configured, and interlinked
to develop a highly customized user-interactive
front panel. The synthesized front panel is shown
in Fig. 3. The algorithm of control and computa-
tions was implemented in the form of an embed-
ded code containing different Action Lists written
for various test-point objects chosen to develop
different panels of the data acquisition and man-
agement software including the front panel. The
algorithm of control and computations coordinates
the functioning of various modules ͑front panel,
subpanels, and objects͒ of the proposed virtual lin-
earizer. The virtual linearizer enables a compari- Fig. 3. User-interactive front-panel of the proposed virtual
son of the actual and estimated values of the in- linearizer.

4. 322 Singh, Kamal, and Kumar / ISA Transactions 45, (2006) 319–328
Fig. 4. Schematic of multilayer feed-forward back-propagation network based inverse modeling of a transducer.
implemented virtual linearizer is operated to pro- forward back-propagation network trained with
cess the signal continuously. To increase the flex- the Levenberg-Marquardt learning algorithm. The
ibility of its use, the provision has been made in schematic of the proposed multilayer feed-forward
the virtual linearizer to acquire stored data offline back-propagation network based soft compensator
from the excel-sheet in case the transducer is not as an accurate inverse model of transducer is
available online. The corresponding maximum ab- based on the concept of the well-known system
solute values of absolute error and error ͑% full identification technique ͓17͔ of control engineer-
span͒ are also displayed by the virtual linearizer ing as shown in Fig. 4. The inverse model of a
for comparison purposes. However, the data ac- transducer is required invariably for linearizing its
quisition and management system was designed to input-output static response in such systems. A
serve the function of measurement, modeling, es- multilayer feed-forward network, trained with the
timation, and display of static inverse response of back-propagation algorithm, is viewed as a practi-
transducers. Also, the provision is provided for cal vehicle for performing a nonlinear input-output
graphical, tabular, and digital display of various mapping of a general nature ͓18͔. However, in as-
measured and estimated data related to inverse sessing the capability of the multilayer feed-
modeling. Further, computation of absolute error forward back-propagation network from the view-
as well as error ͑% full span͒ between the actual point of input-output mapping, one fundamental
and estimated inverse response along with their question arises: what is the minimum number of
corresponding maximum absolute values was also
hidden layers in a multilayer feed-forward back-
provided for each calibration point. In addition to
propagation network with an input-output map-
this, the proposed virtual linearizer having a neural
ping that provides an approximate realization of
network as its soft-compensator element may be
any continuous mapping? The answer to this ques-
operated on-line for the display of the measurand
tion lies in the universal approximation theorem
in the form of a digital readout as well as in the
͓17͔ for a nonlinear input-output mapping.
form of a bar indicator.
According to this theorem, a single hidden layer
is sufficient for a multilayer feed-forward back-
3.2. Synthesis of soft compensator propagation network to compute a uniform ap-
In the present work, the synthesis of soft com- proximation for a given training set represented by
pensator is carried out in the form of an inverse the set of inputs x1 , x2 , . . . , xm0 and a target output
model of a transducer using a multilayer feed- f͑x1 , x2 , . . . , xm0͒. Based on these observations,

5. Singh, Kamal, and Kumar / ISA Transactions 45, (2006) 319–328 323
Fig. 5. Tabular representation of acquired training data and
estimated results displayed by virtual linearizer using
multilayer feed-forward back-propagation network based
inverse modeling of pressure transducer ͓MTR-Measured
transducer response ͑in volts͒; Measur͑A͒-Applied measur- Fig. 6. Results of data acquisition constituting the training
and to the transducer ͑in bars͒; Measur͑E͒-Estimated mea- set displayed by the virtual linearizer.
surand ͑in bars͒; Error͑Ab͒-Absolute error between actual
and estimated measurands; and Error͑% Full Span͒-Error in back-propagation network based inverse model of
terms of percentage full span͔. a transducer producing an output pattern ͕x͖, n
= ͓1 , 2 , . . . , N͔. In this context, a multilayer feed-
consider N input patterns, ͕y n͖, each with a single forward back-propagation network manifests itself
element applied to the multilayer feed-forward as a nested sigmoidal scheme. Therefore, based on
Fig. 7. Learning characteristics of multilayer feed-forward back-propagation network based inverse model of pressure
transducer.

6. 324 Singh, Kamal, and Kumar / ISA Transactions 45, (2006) 319–328
Fig. 8. Estimated measurand displayed by virtual linearizer Fig. 10. Absolute error displayed by virtual linearizer cor-
as a result of self-compensation provided by inverse trans- responding to each value of the applied measurand.
ducer model.
this analogy, for transducer modeling application, Here, the Jacobian matrix is computed through a
the output function of a multilayer feed-forward standard back-propagation technique that is much
back-propagation network is proposed to be com- less complex than computing the Hessian matrix.
puted based on the following expression ͓17͔: Hence, the Levenberg-Marquardt algorithm based
approximation of a nonlinear activation function
F͑y i͒ = FN͑WN ‫„ ء‬FN−1͑¯F2„W2 ‫ ء‬F1͑W1 ‫ ء‬y 1 used the following Newton-like update:
+ B1͒ + B2… ¯ ͒ + BN−1… + BN͒ , ͑1͒
Wk+1 = Wk − ͓ jT j + ␮I͔−1JTe, ͑4͒
where N represents the number of neural network
layers, B denotes the bias vectors, W denotes the where W is the weight vector containing current
weight vectors, and F is the activation transfer values of weights and biases. In fact, this algo-
function of each layer. However, here, the neural rithm approaches second-order training speed like
network approximation of nonlinear activation the quasi-Newton methods and there is no need to
function, f , is achieved using the Levenberg- compute the Hessian matrix ͑second derivatives͒
Marquardt learning algorithm ͓13͔ in which the of the performance index at the current values of
Hessian matrix is estimated as the weights and biases. In this context, the neural
h = jT j ͑2͒ network is playing the role of f͑ ͒ in X = f͑Y͒,
where Y is the vector of inputs and X is the cor-
and the gradient is approximated as responding vector of outputs. As each input is ap-
␦ = jTe, ͑3͒ plied to the neural model, the network output is
compared to the target. The present linear error is
where j is the Jacobian matrix containing first de- calculated as the difference between the desired
rivatives of the network errors with respect to response, x͑k͒, and neural network linear output,
weights and biases and e is a vector of network x͑k͒, where
ˆ
errors. The algorithm is detailed in Ref. ͓13͔.
Fig. 9. Comparison of actual and estimated measurands Fig. 11. Error ͑% full span͒ corresponding to each value of
displayed by virtual linearizer. the applied measurand displayed by virtual linearizer.

7. Singh, Kamal, and Kumar / ISA Transactions 45, (2006) 319–328 325
Table 1
Results of multilayer feed-forward back-propagation network based inverse modeling of strain-gauge pressure transducer
using training data.
Absolute
Number Absolute value of
of value of maximum
Range of hidden maximum error ͑% full
operation neurons Epochs MSE absolute error span͒
0 – 7 bars 2 69 7.89256e-006 0.0343804 0.491119
xk = WTYk.
ˆ k ͑5͒ the data acquisition system of a computer based
measurement system. Nine pairs of input-output
In fact, the ultimate aim of the neural network data constituting the training set are acquired cov-
based least mean square regression method is to ering the entire range of its operation using the
minimize the mean square error ͓19͔ and as a con- proposed virtual linearizer. The acquired training
sequence the performance index in this case, i.e., pairs displayed by the virtual linearizer numeri-
the mean squared error ͑MSE͒ is given by cally and graphically are shown in Fig. 5 and Fig.
k=N k=N 6, respectively. The results of inverse modeling
1 1
MSE = ͚ e͑k͒2 = N ͚ ͓x͑k͒ − x͑k͔͒2 . ͑6͒
N k=1
ˆ using a multilayer feed-forward back-propagation
k=1
network as a soft compensator element of the pro-
Neural network toolbox ͓20͔ and MATLAB pro- posed virtual linearizer with nine pairs of training
gramming ͓21͔ were used to synthesize the pro- data are also shown in Fig. 5. Learning character-
posed neural model as the soft compensator serv- istics of the proposed inverse model of the pres-
ing the purpose of signal processing component of sure transducer under study are shown in Fig. 7. It
the proposed virtual linearizer. For the example in has been found that a mean square error level of
this part of the work, the multilayer feed-forward 7.89256e-006 is attained at only 69 epochs in re-
back-propagation network is trained with the alizing the inverse model with a 1-2-1 architecture
Levenberg-Marquardt learning algorithm with the of a multilayer feed-forward back-propagation
following parameters: performance goal ͑MSE͒ network.
= 7.89256e-006; learning rate= 0.01; factor to use The estimated measurand displayed as a result
for memory/speed tradeoff= 1; and maximum of the multilayer feed-forward back-propagation
number of epochs= 100. network based inverse modeling of pressure trans-
ducer is shown in Fig. 8. Fig. 9 displays a com-
4. Results and discussion parison between actual and estimated measurands
and shows a close resemblance between them. The
The practical use of the proposed virtual linear- corresponding values of absolute error and error
izer is examined experimentally for correcting the ͑% full span͒ between the estimated and actual
effect of static nonlinearity associated with the measurands, displayed by the virtual linearizer
data acquisition system-connected strain-gauge graphically, are shown in Fig. 10 and Fig. 11, re-
type of pressure transducer ͑SenSym: S spectively. It is found that the assumption of only
ϫ 100DN͒ using the synthesized soft compensator two hidden neurons has led to the maximum ab-
described below. solute error of only 0.0343804 between the actual
and estimated inverse response. The maximum ab-
4.1. Simulation of soft compensator solute value of error ͑% full span͒ between actual
To examine the practical use of a proposed vir- and estimated response is found to be only
tual linearizer for approximating the nonlinear 0.491119. Achievement of such a low level of
static inverse response of transducers, an experi- maximum values of said errors ensures that esti-
mental study is carried out by measuring data from mated values are an accurate measure of the true
a standard practical strain-gauge type of pressure values. The result of inverse modeling of pressure
transducer ͑SenSym: S ϫ 100DN͒ connected to transducer is also shown Table 1. The use of only

8. 326 Singh, Kamal, and Kumar / ISA Transactions 45, (2006) 319–328
Fig. 12. Results of data acquisition constituting the valida- Fig. 13. Estimated measurand displayed by the proposed
tion set displayed by the proposed virtual linearizer. virtual linearizer as a result of self-compensation.
two hidden neurons reduces the architectural com- ment of such a low value for these errors validates
plexity and hence computational load of the neural experimentally our assumption of using 1-2-1 ar-
model drastically. chitecture of the multilayer feed-forward back-
propagation network as an accurate inverse model
of the given transducer.
4.2. Validation of the soft compensator
4.3. Practical use of virtual linearizer
In order to validate our assumption of using
1-2-1 architecture of a multilayer feed-forward The performance of the proposed multilayer
back-propagation network as an accurate inverse feed-forward back-propagation network with
model of the given pressure transducer, a valida-
tion study was carried out with a trained neural
model by acquiring all the remaining 34 pairs of
input-output data as the validation set using the
proposed virtual linearizer. In fact, these pairs
were not used in the training phase of the neural
model and cover the entire range of operation of
the transducer under study. The acquired input-
output pairs constitute the validation set. The re-
sults of data acquisition displayed by the virtual
linearizer are shown in Fig. 12. The algorithm of
control and computations was run again in combi-
nation with the soft compensator for the validation Fig. 14. Comparison of actual and estimated measurands
phase. The estimated measurand is shown in Fig. displayed by virtual linearizer.
13 for each value of the measured transducer re-
sponse. Fig. 14 displays a comparison between the
actual and estimated measurands and shows a
close resemblance between them. The correspond-
ing values of absolute error and error ͑% full span͒
between the estimated and actual measurands dis-
played by the virtual linearizer graphically are
shown in Figs. 15 and 16, respectively. The maxi-
mum absolute values of absolute error and error
͑% full span͒ for validation set are also given in
Table 2. From the results, it has been observed that
the absolute value of maximum absolute error is
found to be only 0.14834 and that of error ͑% full Fig. 15. Absolute error displayed by virtual linearizer cor-
span͒ is 2.2475 for the validation data. Achieve- responding to each value of the applied measurand.

9. Singh, Kamal, and Kumar / ISA Transactions 45, (2006) 319–328 327
ear transducer. Use of the Levenberg-Marquardt
learning algorithm provided an extremely fast
learning for the synthesis of inverse models of
transducers while ensuring an optimal solution
with regard to network architectural complexity
and hence computational load. The method de-
scribed in this paper has a large area of applica-
tions in all transducer based measurement systems
where transducer static nonlinearity is the main
factor to be considered.
Fig. 16. Error ͑% full span͒ corresponding to each value of
the applied measurand displayed by virtual linearizer. Acknowledgment
The authors wish to thank Prof. ͑Dr.͒ N. P.
1-2-1 structure as an efficient signal processing
Singh, Director, Sant Longowal Institute of Engi-
component is further evaluated by operating the
neering and Technology, Longowal-148106 ͑Dis-
virtual linearizer in the production phase. The per-
trict: Sangrur͒ Punjab, India for his stimulating in-
formance of the proposed neural model is exam-
terest and constant encouragement throughout the
ined with the complete set of input-output data
work.
used in the training and validation phases covering
the entire range of operation of the given trans-
ducer. The results obtained in the production phase References
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͓11͔ Teeter, J. and Chow, M., Application of functional link Prof. (Dr.) Tara Singh Kamal
neural network in HVAC thermal dynamic system was born at Dhanaula ͑District:
identification. IEEE Trans. Ind. Electron. 45, 170–176 Sangrur͒, Punjab ͑India͒ in 1941.
͑1998͒. He graduated in Electronics and
Communications Engineering and
͓12͔ Patra, J. C., Pal, R. N., Chatterji, B. N., and Panda, G., obtained his Masters Degree in
Identification of nonlinear dynamic systems using Communication Systems, both
functional link artificial neural networks. IEEE Trans. from the University of Roorkee,
Syst., Man, Cybern., Part B: Cybern. 29͑2͒, 254–262 Roorkee, and he received a Gold
͑1999͒. Medal by standing first in M.E.
͓13͔ Hagan, M. T. and Menhaj, M., Training feed-forward He got his Ph.D. degree from
networks with the Marquardt algorithm, IEEE Trans. Punjab University, Chandigarh.
Neural Netw. 5͑6͒, 989–993 ͑1994͒. He started teaching at the Depart-
͓14͔ Bilski, P. and Winiecki, W., Virtual spectrum analyzer ment of Electrical and Electronics
Communications Engineering in Punjab Engineering College,
based on data acquisition card. IEEE Trans. Instrum. Chandigarh in January 1966 and retired as a Professor in Electrical
Meas. 51͑1͒, 82–87 ͑2002͒. and Electronics Communications in June 1999 from the same col-
͓15͔ Test-Point Software-User’s Manual ͑Version 3.1͒. lege. At present, he is working as a Professor in the Department of
Capital Equipment Corp., 1997. Electronics and Communications Engineering at Sant Longowal
͓16͔ MATLAB Application Program Interface Guide Us- Institute of Engineering and Technology ͑SLIET͒, Longowal ͑Dis-
er’s Manual ͑Version 5͒. 7.32–7.42, 1998. trict: Sangrur͒, Punjab ͑India͒. He held various prestigious posi-
͓17͔ Haykin, S., Neural networks: A Comprehensive Foun- tions, such as Dean ͑Research and Technology Transfer͒, and has
dation. Pearson Education Asia, 2001, pp. 118–120. guided nine Ph.D. students. Two more research scholars under his
͓18͔ Widrow, B. and Steams, S. D., Adaptive Signal Pro- guidance are in the completion stage of their Ph.D. theses. He is a
widely traveled teacher and has published more than 110 papers in
cessing, Prentice Hall, Englewood Cliffs, NJ, 1995, the International and National Journals and Conferences. He is a
pp. 118–120. life fellow of IE ͑I͒, IETE, member ISTE, and Senior Member of
͓19͔ Hornik, K. M., Stinchcombe, M., and White, H., IEEE ͑USA͒. He was the Chairman of Punjab and Chandigarh
Multilayer feed-forward networks are universal ap- State Center of the Institution of Engineers ͑India͒ for the years
proximators. Neural Networks 2͑5͒, 359–366 ͑1989͒. 1999–2001 and also remained as the Vice President of the Institu-
͓20͔ Demuth, H. and Beale, M., Neural Network Toolbox tion of Engineers ͑India͒ for the term 2001–2002. His areas of
for use with MATLAB-User’s Guide. Natick, M. A., interest are Artificial Neural Networks, Digital Communications,
The Maths Works Inc., 1993. and Intelligent Instrumentation.
͓21͔ Pratap, R., Getting Started with MATLAB 5. Oxford
University Press, 2001, pp. 14–122.
Prof. (Dr.) Shakti Kumar re-
ceived his MS from BITS Pilani
Dr. Amar Partap Singh was
in 1990, and his Ph.D. in 1996.
born in 1967 at Sangrur ͑Punjab͒
He has taught at BITS, Pilani
India. He received his B. Tech.
Dubai Centre of Al Ghurair Uni-
͑Electronics Engineering͒ Degree
versity Dubai, UAE, Atlim Uni-
in 1990 from Guru Nanak Dev
versity, Ankara, Turkey, and Na-
University, Amritsar and M. Tech.
tional Institute of Technology,
͑Instrumentation͒ in 1994 from
Kurukshetra ͑formerly REC, Ku-
Regional Engineering College,
rukshetra͒. At present he is work-
Kurukshetra. Also, he got his
ing as Professor and Additional
Ph.D. ͑Electronics and Communi-
Director, Haryana Engineering
cations Engineering͒ in 2005
College Jagadhri ͑Haryana͒, In-
from Punjab Technical University,
dia. His areas of interest include
Jalandhar. He is working as an
Fuzzy Logic Based System Design, Artificial Neural Networks,
Assistant Professor in the Depart-
and Digital System Design. Prof. Kumar has published more than
ment of Electrical and Instrumentation Engineering at Sant Lon-
50 research papers in National/International Journals and
gowal Institute of Engineering and Technology ͑SLIET͒, Lon-
Conferences.
gowal ͑District: Sangrur͒, Punjab ͑India͒. He has published more
than 43 papers at various International and National level
Symposia/Conferences and Journals. His areas of interest are Vir-
tual Instrumentation, Artificial Neural Networks and Medical
Electronics.