Sensors and Actuators A 120 (2005) 518–526

Development of a virtual curve tracer for estimation of transducercharacteristics under the influence of a disturbing variable

A.P. Singha,∗, Tara Singh Kamalb, Shakti Kumarc

a Department of Electrical and Instrumentation Engineering, Sant Longowal Institute of Engineering and Technology (SLIET),Longowal-148106, Sangrur, Punjab, India

b Guru Teg Bahadur Khalsa Institute of Engineering and Technology (GTBKIET), Chhapianwali, Malout-152107, Muktsar, Punjab, Indiac Haryana Engineering College (HEC), Jagadhri-135003, Haryana, India

Received 4 June 2004; received in revised form 27 October 2004; accepted 6 December 2004Available online 15 January 2005

Abstract

This paper presents an artificial neural network (ANN)-based novel virtual curve tracer (VCT) for estimation of transducer response charac-teristics under the influence of a disturbing variable for computer-based measurement systems. The disturbing variable effect on transducer out-p ponse charac-t a multilayerf of trans-d –Marquardtl©

K

1

alTiaamfet[rt

rbingnner

de-risticsctedoweren-cers

ineartoo,rans-

asednderrain-is con-

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ut response is a typical problem that affects the accuracy of such systems. Especially, change in transducer excitation causes its reseristics to be highly nonlinear and complex signal processing is required to obtain its accurate direct model. The proposed VCT usedeed-forward back-propagation artificial neural network (MLFFBP-ANN)-based two-dimensional (2D) model for accurate fittingucer characteristics to measured data under the influence of a disturbing variable. The proposed model is trained with Levenberg

earning algorithm for achieving an extremely fast convergence speed as compared to the existing ANN-based techniques.2004 Elsevier B.V. All rights reserved.

eywords:Virtual curve tracer; Artificial neural network; Direct response; Disturbing variable and transducer model

. Introduction

Transducers are usually nonlinear[1]. However, if linearpproximations were acceptable for a given accuracy level,

inear measurement errors and noise are always present[2].herefore, curve-fitting procedures are required to be used

nvariably to average these effects. In fact, the disturbing vari-ble effect on the transducer output response is a problem thatlways affects the accuracy of a computer-based measure-ent system[3]. Moreover, when small amplitude signals

rom transducers are considered and the disturbing variablexhibit a large range of its variation, the drift error due to dis-urbing variable has a considerable effect on system accuracy2]. Also, with the passage of time, aging further becomesesponsible for introducing variations in sensor characteris-ics [4]. Therefore, the issues related with the estimation of

∗ Corresponding author. Tel.: +91 1672280099; fax: +91 1672280057.E-mail address:amarpartapsingh@yahoo.com (A.P. Singh).

transducer characteristics under the influence of a distuvariable are required to be addressed in a collective mataking into account the transducer static nonlinearity[5] aswell as the drift-error caused by disturbing variables[6]. Inthis work, an ANN-based virtual curve tracer (VCT) isveloped to estimate the transducer response characteunder the effect of a disturbing variable for DAS-connecomputer-based measurement systems. In addition to psupply variations, the effect of change in other environmtal conditions (temperature, humidity, etc.) on the transduand subsequently on the output of the DAS is also nonlin nature. Hence, for other types of disturbing variablethe complex signal processing is required to model the tducer accurately.

The proposed VCT used an artificial neural network-bapproach to implement direct model of the transducer uthe effect of a disturbing variable. As an example, a stgauge transducer-based pressure measurement systemsidered and the influence of power supply circuit on its

924-4247/$ – see front matter © 2004 Elsevier B.V. All rights reserved.

oi:10.1016/j.sna.2004.12.008

A.P. Singh et al. / Sensors and Actuators A 120 (2005) 518–526 519

put response is considered. As the output of the strain-gaugetype of transducers is dependent on the applied measurandas well as on the power supply, the problem becomes two-dimensional (2D) and complex signal-processing technique[7] is required to make necessary corrections to obtain a cor-rect direct model. Here, an artificial neural network is usedfor data optimization and a virtual instrument, using DAS-based instrumentation, is used to collect experimental data. Amajor problem of interpolation is caused by errors and noisethat affect the measured data in a computer-based measure-ment system. With non-exact data like calibration data fromtransducers in computer-based measurement system, ANN-based regression method would actually be more appropriate[8–10].

For the estimation of nonlinear static response character-istics of transducers, an ANN-based modeling of transducershas been proposed[2,3,5]with quite satisfactory performancebut without taking into account the effect of a disturbing vari-able. However, here an ANN-based direct model of transduc-ers is reported considering the effect of a disturbing variablealso. This direct model may be used for the purpose of on-linefault detection and quality control of the transducer duringits production. In fact, the direct modeling technique enablesan estimate of the nonlinear response characteristics of thetransducers under calibration. The effectiveness of the pro-posed technique has been verified by extensive experimenta-t prox-io rrorp ntlym tione oly-n ola-t

2i

llelm of di-r ei un-dp thet r andA ed-f eeni d int isticsi ingm sp sedm ailedi itht scent

Fig. 1. Schematic of ANN-based direct modeling of transducer.

with momentum-based learning algorithm suffered from theproblem of slow convergence. In order to increase the speed ofconvergence of the gradient descent with momentum-basedlearning algorithm, the only solution is to increase the num-ber of hidden neurons significantly. Increasing the number ofhidden neurons results in increased ANN complexity signif-icantly and hence increased computational load which is notan optimal solution.

In order to circumvent these problems, the au-thors used the Levenberg–Marquardt learning algorithm[18,19], for training the MLFFBP-ANN in this work.The Levenberg–Marquardt algorithm like the quasi-Newtonmethods, approaches second-order training speed withouthaving to compute the Hessian matrix (second derivatives)of the performance index at the current values of the weightsand biases. In fact, training a neural network is, in most cases,an exercise in numerical optimization of a usually nonlinearerror function. However, there is no single best method fornonlinear optimization. One needs to choose a method basedon the characteristics of the problem to be solved. For ob-jective functions with continuous second derivatives (whichwould include feed-forward nets with the most popular dif-ferentiable activation functions and error functions), threegeneral types of algorithms have been found to be effectivefor most practical purposes[18,20]:

• andgioneffi-

• wton

• ient

op-t th-o heL thant end-i thep hts,L ient

ion studies. The advantages of neural networks as an apmation tool for multivariable functions are[9]: capability toperate based on a multivariate and intrinsically noisy or erone reduced training data set; potentiality of convenieodeling nonlinear characteristics; and lower approximarrors than other conventional numerical methods like pomial interpolation; and good generalization and extrap

ion capabilities.

. Direct modeling of transducers under thenfluence of a disturbing variable

In the direct modeling, the ANN is trained in a paraode to estimate the response of transducer. A scheme

ect modeling of transducer is shown inFig. 1. This schems analogous to that of the system identification problemer dynamic conditions in Control Engineering[11–16]. Theurpose of direct modeling is to obtain an ANN model of

ransducer in such a way that the outputs of the transduceNN match closely. An ANN based on the MLP is a fe

orward network with one or more layers of nodes betwts input and output layers. The only architecture appliehe interpolation of transducer direct response characters the MLFFBP-ANN trained with gradient descent us

omentum-based learning algorithm[12–16]. These studieroved to be the good solutions for MLFFBP-ANN-baodeling of transducers. However, from the results det

n the work[17] and also from our experience of working whe neural networks, it is observed that the gradient de

For a small number of weights, stabilized NewtonGauss–Newton algorithms, including various trust-realgorithms and Levenberg–Marquardt algorithm, arecient.For a moderate number of weights, various quasi-Nealgorithms are efficient.For a large number of weights, various conjugate-gradalgorithms are efficient.

In practice, Levenberg–Marquardt often finds betterima for a variety of problems than do the other meds [19,20]. However, the computational load of tevenberg–Marquardt algorithm is somewhat higher

he gradient descent with momentum algorithm. But depng upon the requirements of a specific application as inresent practical problem, for a smaller number of weigevenberg–Marquardt algorithm, is considered to be effic

520 A.P. Singh et al. / Sensors and Actuators A 120 (2005) 518–526

while having a trade off between the speed of ANN learningand computational load. In fact, the main requirement in thepresent problem is to reduce the calibration time of trans-ducers significantly. Being able to calibrate quickly is neces-sary to reduce down time during system breakdown or shortbreaks in the system during its maintenance or other emer-gent situations. Reducing the number of calibration pointshas lead to the use of smaller number of associated weightsin case of Levenberg–Marquardt algorithm for ANN train-ing which in turn results in decreasing the calibration timesignificantly which is otherwise not possible with gradientdescent with momentum algorithm. Based on these consid-erations, a three layered FFBP-ANN architecture was chosenfor direct modeling of transducer. Different sets of patternsare acquired using VCT for training the ANN. The normal-ized measurand and normalized disturbing variable were usedas input patterns and the DAS channel output was used asthe desired pattern to the MLFFBP-ANN. The algorithm isimplemented using MATLAB Neural Network Toolbox andMATLAB general programming to synthesize the proposedANN model.

3. Development of virtual curve tracer

r in-v ules.T Ac-q d ont trola singT -p s of

virtual curve tracer. The second module was implemented inthe form of Signal Processing Software comprising a set ofthree neural algorithms. The virtual curve tracer is designedto operate for three different phases of neural modeling,i.e., training, validation and production, in a user-interactivemanner.

3.1. Development of DAMS

The implemented VCT in this section comprises of itsDAMS module in the form of a Front-panel and a sub-panel. The synthesized Front-panel of the proposed VCT isshown inFig. 2. Mouse click at pushbutton, “Instructions”on the VCT Front-panel opens another sub-panel display-ing the step wise operating procedure for its operation ina user-interactive manner. The working of DAMS is con-trolled and coordinated for three separate operating modesof the VCT by a high performance Algorithm of Control andComputations. The signal-processing software is based on theconcept of neural modeling using MLFFBP-ANN trained byLevenberg–Marquardt learning algorithm[17–19]. The pres-sure measurement system chosen for experimental study isbased on a strain-gauge type of transducer operating in realtime environment. The proposed VCT is implemented to ac-quire the input–output data from the transducer on-line fort y ofi e thes duceri

s dis-p iredd ghD -

the pro

The development of the proposed virtual curve traceolved the development of two integrated software modhe first module was implemented in the form of a Datauisition and Management Software (DAMS), supporte

he architecture of a high performance Algorithm of Connd Computations (ACC). The DAMS was developed uest-point software[21]. The Algorithm of Control and Comutations coordinate the functioning of various module

Fig. 2. Front-panel of

he purpose of training the ANN. To increase the flexibilitts use, the provision has been made in the VCT to acquirtored data offline from the Excel sheet in case the transs not available on-line.

To analyze the acquired data, input–output data set ilayed in tabular as well as in graphical form. The acquata is exchanged with the MATLAB environment throuDE technique[22]. MATLAB Programming[23] and Neu

posed virtual curve tracer.

A.P. Singh et al. / Sensors and Actuators A 120 (2005) 518–526 521

ral Network Toolbox[17] are used to synthesize the proposedANN as an SPS module of VCT. However, in order to studythe effective use of VCT for modeling the transducer directresponse characteristics, the VCT is operated for three neuralmodeling phases of the given transducer, namely—trainingphase, validation phase and production phase. Accordingly,three separate SPS modules are implemented. The synthe-sized ANN is trained with suitable learning algorithm to adaptitself to implement the direct model of the transducer. Onlyfew readings of the training data are required to implement thesuitable ANN-based direct model. The synthesized trainedANN predicts the accurate response of the transducer for theuntrained data. In order to validate the implemented ANNas an accurate transducer model, provision has been made tooperate the proposed VCT in the validation and productionphases. The estimated response along with the error data isobtained in the VCT using DDE technique. The actual and es-timated response is presented by the VCT, both graphically aswell as numerically in tabular form. The corresponding val-ues of absolute error and error in terms of %FS are displayedby the VCT for comparison purposes.

3.2. Implementation of signal-processing software

The signal-processing software that performs the model-i iffer-e que.T NN

learning phase, output voltages from the Signal ConditioningCard representing the transducer response are used as inputsof the ANN, and the applied Measurand is the output of theANN. The ANN structure, represented inFig. 3, includes twohidden layers of tansigmoidal neurons with activation func-tion (f1). The first layer receives the normalized transducerresponse from each channel and its output is given as inputof the second hidden layer of tansigmoidal neurons with ac-tivation function (f2). The output from the neurons of secondhidden layer is transmitted to the output layer of single linearneuron with activation function (f3) that computes the net-work output associated with the transducer response, takinginto account drift errors caused by variations in the disturbingvariable.

Using matrix representation, the measured transducer re-sponse is given by

Y = f3([OW](f2([SW](f1([FW] × [X] + [FB])) + [SB]))

+ [OB]), (1)

where

[FW] =

fw11 fw12

fw21 fw22

, (2)

Fo

ng of transducer direct response characteristics for dnt values of disturbing variable used the ANN technio establish the ANN weights and biases, during the A

ig. 3. ANN structure withn tansigmoidal neurons in the first hidden layer,m tanutput layer.

......

fwn1 fwn2

sigmoidal neurons in the second hidden layer, and one linear neuron in the

522 A.P. Singh et al. / Sensors and Actuators A 120 (2005) 518–526

[SW] =

sw11 sw12 · · · sw1n

sw21 sw22 · · · sw2n

......

......

swm1 swm2 · · · swmn

, (3)

[OW] = [ ow11 ow12 · · · ow1m ], (4)

[FB] =

fb1

fb2

...

fbn

, (5)

[SB] =

sb1

sb2

...

sbn

, (6)

and

[OB] = [ob] (7)

Here, the Hessian matrix,H, is approximated as

H

a

δ

w va-t bi-ap thatiL of an likeu

W

w htsa thefi ni-m itha ateds fort ped.

4

ex-a elinga

4.1. Results of ANN training

In order to evaluate the performance of the proposed VCTto synthesize the MLFFBP-ANN-based direct model of thetransducers considering the effect of a disturbing variable fora computer-based measurement system, direct modeling ex-periment is performed. However, in this context, when theANN is trained to synthesize the direct model of the giventransducer, the knowledge about the value of the disturbingvariable is also fed to the proposed ANN. The experimen-tal example chosen here is strain-gauge transducer (SenSym:S×100DN)-based pressure measurement system. First, thevalue of disturbing variable, i.e. transducer excitation, is keptfixed at a constant value of 2.0019 V. The input–output datais acquired by the VCT as usual. Then the value of disturbingvariable (transducer excitation) is changed to another con-stant value of 4.0088 V and the data is again acquired usingVCT. Similarly, keeping the transducer excitation at a valueof 6.9678 V, another set of input–output data is acquired. Inthis way, total set of training data contains 27 calibrationpoints. The acquired data is displayed by the VCT graph-ically as shown inFig. 4. These acquired data is used fortraining the proposed 2–4–2–1 ANN structure with learn-ing parameters: performance goal (MSE) = 5e−006, learn-ing rate = 0.01, factor used for memory/speed tradeoff = 1,and maximum number of epochs = 3500. The learning char-a dela

aren low as5 er-f el isa nthe-s ponsef f theg owni alueo llya dt be-

F cer at2 rve)u

= JTJ (8)

nd the gradient,δ, is computed as

= JTe (9)

hereJ is the Jacobian matrix comprising of first deriives of the network errors with respect to weights andses ande a vector of network errors. In fact,J is com-uted through a standard back-propagation technique

s much less complex than computing theH. Hence, theevenberg–Marquardt algorithm-based approximationonlinear activation function used the following Newton-pdate:

k+1 = Wk − [JTJ + µI]−1

JTe (10)

hereW is the vector containing current values of weignd biases. An algorithm was implemented to minimizenal MSE of the ANN training phase. The MSE is miized for a 2–4–2–1 architecture if the ANN is trained wpredefined target and learning rate. Highly sophistic

eparate MATLAB code of the implemented algorithmshe training, validation and production phases are develo

. Practical use of virtual curve tracer

The practical use of proposed virtual curve tracer ismined experimentally for three phases of neural mods explained below.

cteristics of proposed MLFFBP-ANN-based direct more shown inFig. 5.

It has been observed that a total of 2451 epochseeded to reduce the mean square level to a value as.21511e−006. Achievement of such a low value of the p

ormance goal (MSE) indicates that the trained ANN modn accurate direct model of the given transducer. The syized ANN model is used to estimates the transducer resor the training data. The estimated direct response oiven transducer, displayed by the proposed VCT is sh

n Fig. 6. The absolute error and error (%FS) at each vf the calibration point displayed by the VCT graphicare also shown inFigs. 7 and 8, respectively. It is observe

hat the maximum absolute value of the Absolute error

ig. 4. Actual direct response characteristics of pressure transdu.0068 V (lower curve), 4.0088 V (middle curve) and 6.9678 V (upper cusing virtual curve tracer.

A.P. Singh et al. / Sensors and Actuators A 120 (2005) 518–526 523

Fig. 5. Learning characteristics of MLFFBP-ANN-based direct model ofpressure transducer under the effect of a disturbing variable.

Fig. 6. Estimated direct response characteristics of pressure transducer at2.0068 V (lower curve), 4.0088 V (middle curve) and 6.9678 V (upper curve)using virtual curve tracer.

tween the actual and estimated response is found to be only0.03366 and that of error (%FS) is 0.66119 for the trainingdata. Achievement of such a low value for these errors (abso-lute and %FS) further authenticates that the simulated ANNmodel is an accurate representation of the direct model forthe given transducer. The results of data acquisition and trans-ducer modeling are also displayed by the VCT numerically.

Fig. 7. Absolute error between actual and estimated response of pressuretransducer displayed by virtual curve tracer as a result of direct modeling.

Fig. 8. Error (%FS) between the actual and estimated response of pressuretransducer displayed by virtual curve tracer as a result of direct modeling.

4.2. Results of validation study

The evaluation of the synthesized ANN-based directmodel of the given transducer is further examined by op-erating the proposed VCT for the validation as well as forthe production phases using both the trained and untrainedvalues of the disturbing variable.

4.2.1. Validation with trained disturbing variableIn order to validate our assumption of using proposed

2–4–2–1 ANN structure as an accurate direct model of thegiven transducer, the direct modeling experiment is furthercontinued to estimate the transducer’s direct response usingthe simulated ANN model. In this context, the proposed VCTis operated for the validation phase and the remaining 81 un-trained patterns are acquired for the given values of transducerexcitation as shown inFig. 9. The validation data covers theentire range of operation of the given transducer energizedwith the given values of transducer excitation. The resultsof estimated response, displayed by the VCT, are shown inFig. 10. Maximum absolute value of absolute error betweenthe actual and estimated response, displayed by the VCT asa result of validation study, is found to be only 0.1233 andthat of error (%FS) is only 2.5108. Achievement of such alow value for these errors validates experimentally our as-s re

F cer at2 rve)d

umption of using MLFFBP-ANN with 2–4–2–1 structu

ig. 9. Actual direct response characteristics of pressure transdu.0068 V (lower curve), 4.0088 V (middle curve) and 6.9678 V (upper cuisplayed by virtual curve tracer as validation data.

524 A.P. Singh et al. / Sensors and Actuators A 120 (2005) 518–526

Fig. 10. Estimated direct response characteristics of pressure transducer at2.0068 V (lower curve), 4.0088 V (middle curve) and 6.9678 V (upper curve)displayed by virtual curve tracer as a result of validation study.

Fig. 11. Absolute error between the actual and estimated response of pres-sure transducer displayed by virtual curve tracer as a result of validationstudy.

as an accurate model of the given transducer. The absoluteerror and error (%FS) at each validation pattern displayedby the VCT graphically are also shown inFigs. 11 and 12,respectively. The results of data acquisition and subsequentvalidation study are also displayed by the VCT numerically.

4.2.2. Validation with untrained disturbing variableNext, the validation study is further continued for estimat-

ing the transducer direct response using trained ANN modelfor untrained value of transducer excitation at 5.0098 V. Thisvalue of the disturbing variable was not used during ANN

Fig. 12. Error (%FS) between actual and estimated response of pressuretransducer displayed by virtual curve tracer as a result of validation study.

Fig. 13. Actual direct response characteristics of pressure transducer at5.0098 V displayed by the virtual curve tracer as validation data.

Fig. 14. Estimated direct response characteristics of pressure transducer at5.0098 V displayed by virtual curve tracer as a result of validation study.

training. Using VCT, input–output patterns were acquired asthe validation data using VCT as shown inFig. 13. The re-sponse of the trained ANN model was estimated for eachvalidation pattern and displayed by the VCT as shown inFig. 14. The maximum absolute value of the absolute errordisplayed by VCT is found to be only 0.17848 and that of er-ror (%FS) is only 5.0452. Achievement of such low values ofthese errors validates experimentally our assumption of usingMLFFBP-ANN with 2–4–2–1 ANN structure as an accuratedirect model of the given transducer. The absolute error anderror (%FS) displayed by the VCT graphically are also shownin Figs. 15 and 16, respectively. The results of data acquisi-

Fig. 15. Absolute error between actual and estimated response of pressuret udy.

ransducer displayed by virtual curve tracer as a result of validation st

A.P. Singh et al. / Sensors and Actuators A 120 (2005) 518–526 525

Fig. 16. Error (%FS) between the actual and estimated response of pressuretransducer displayed by virtual curve tracer as a result of validation study.

Table 1Results of maximum error obtained from two-dimensional direct model-ing of a pressure transducer using MLFFBP-ANN with 2–4–2–1 structuretrained with Levenberg–Marquardt learning rule

Data set Maximum absoluteerror (absolute value)

Maximum error(%FS) (absolutevalue)

Training data 0.03366 0.66119Validation with trained

disturbing variable0.1233 2.5108

Validation with untraineddisturbing variable

0.17848 5.0452

tion and subsequent validation study are also displayed bythe VCT numerically.

Results of maximum error obtained from two-dimensional direct modeling of a pressure transducerusing MLFFBP-ANN with 2–4–2–1 structure trained withLevenberg–Marquardt learning rule are summarized inTable 1. The performance of the proposed VCT is alsovalidated by operating it in the production phase. TheMLFFBP-ANN model, trained with Levenberg–Marquardtlearning algorithm, is validated experimentally with thecomplete set of input–output data used in the training andvalidation phases. The results obtained in the productionphase confirm to the results obtained in the training andvalidation phases.

5. Conclusion

The present paper proposed an artificial neural network-based simple approach for fitting transducer characteristicsaccurately to the measured data under the effect of a dis-turbing variable. The main contribution of this work is thedevelopment of a new ANN-based intelligent virtual curvetracer for approximating the direct response characteristicsof the transducers considering the combined effect of trans-d ari-a opol-o rdtl rect

modeling of the transducers. The overall experimental re-sults from the presented MLFFBP-ANN-based approach in-dicate that this approach is a useful alternative to the ex-isting conventional numerical and ANN-based techniques.The proposed technique reveals that the implemented ANN-based VCT is very convenient to model a transducer di-rect response characteristics under the effect of a disturbingvariable.

Acknowledgement

The authors are greatly indebted to the Instrument Calibra-tion Center of EIE Department, Sant Longowal Institute ofEngineering and Technology (SLIET), Longowal (District:Sangrur) Punjab, India, for providing the facilities that madethis work possible.

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Biographies

A.P. Singh was born in 1967 at Sangrur (Punjab) India. He received hisBTech (Electronics Engineering) Degree in 1990 from Guru Nanak DevUniversity, Amritsar and MTech (Instrumentation) in 1994 from NationalInstitute of Technology (earlier known as REC), Kurukshetra. At present,he is doing his PhD Degree from Punjab Technical University, Jalandhar.He is working as an Assistant Professor in the Department of Electricaland Instrumentation Engineering at Sant Longowal Institute of Engineer-i dia.H d Na-t st areV

Tara Singh Kamal was born at Dhanaula (District Sangrur), Punjab (In-dia) in 1941. He graduated in Electronics and Communications Engineer-ing and obtained his Masters Degree in Communication Systems, bothfrom University of Roorkee, Roorkee and got Gold Medal by standingfirst in ME He got his PhD Degree from Punjab University, Chandi-garh. He started teaching in the Department of Electrical and ElectronicsCommunications Engineering in Punjab Engineering College, Chandigarhin January 1966 and retired as a Professor in Electrical and Electron-ics Communications in June 1999 from the same college. At present,he is the Principal of Guru Teg Bahadar Khalsa Institute of Engineer-ing and Technology, Chhapianwali (Malout), District Muktsar, Punjab(India). He held various prestigious positions such as Dean (Researchand Technology Transfer) and has guided seven PhD students. Threemore research scholars under his guidance are in the completion stageof their PhD Theses. He is a widely traveled teacher and has publishedmore than 105 papers in the Internationals and National Journals andConferences. He is life fellow of IE (I), IETE, member ISTE and Se-nior Member of IEEE (USA). He was the Chairman of Punjab andChandigarh State Center of the Institution of Engineers (India) for theyear 1999–2001 and also remained as the Vice President of the Institu-tion of Engineers (India) for the term 2001–2002. His areas of interestare Artificial Neural networks, Digital Communications and intelligentinstrumentation.

Shakti Kumar did his MS from BITS Pilani in 1990, and PhD in 1996.He has taught at BITS, Pilani Dubai Centre of Al Ghurair UniversityDubai, UAE, Atlim University, Ankara, Turkey and National Institute ofTechnology. Kurukshetra (Formerly REC Kurukshetra). At present he isworking as Professor and Additional Director, Haryana Engineering Col-l ystemD Ku-m ationalJ

ng and Technology (SLIET), Longowal (District: Sangrur), Punjab, Ine has published more than 39 papers at various International an

ional level Symposia/Conferences and Journals. His areas of intereirtual Instrumentation, Soft-computing and Medical Electronics.

ege Jagadhri. His areas of interest include Fuzzy Logic-Based Sesign, Artificial Neural Networks and Digital System Design. Prof.ar has published more than 50 research papers in National/Intern

ournals and Conferences.