Development of a virtual linearizer for correcting transducer static nonlinearity


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Development of a virtual linearizer for correcting transducer static nonlinearity

  1. 1. ISA Transactions® Volume 45, Number 3, July 2006, pages 319–328Development 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 2005͒Abstract This paper reports the development of an artificial neural network based virtual linearizer for correcting nonlinearityassociated with transducers connected to the data-acquisition system of a computer-based measurement system. Inanalog processing techniques, nonlinearity is considered to be a very serious problem that at one time was solvedfrequently by the piecewise linear segment approach modeled by linear electronic circuits. Since the cost ofmicrocomputers has been reduced drastically, they are currently used in most applications of measurement, includingdata-acquisition subsystems. Therefore, the hardware-based analog techniques of linearization are often replaced by thesoftware-based numerical ones. In this context, it has been found that a multilayer feed-forward back-propagationnetwork trained with the Levenberg-Marquardt learning rule provides an optimal solution to implement an efficient softcompensator to correct transducer static-nonlinearity. © 2006 ISA—The Instrumentation, Systems, and AutomationSociety.Keywords: Transducer; Nonlinearity; Inverse model; Artificial neural network; Linearizer1. 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 issystems, transducers are normally highly nonlin- required frequently. Therefore, the issues relatedear 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 inquisition 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 asmodules 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 numericalpractical transducer ͓1͔. Further, inherent manu- methods to estimate scaled output signals fromfacturing tolerances always present an additional transducers ͓5,6͔ correctly. These methods may beproblem in the event of replacement of a faulty divided into three broad groups ͓7͔. The simplesttransducer or signal conditioning module even if way is to store a look-up table in read-onlythe new one is chosen from the same batch of memory and calculate the quantity to be measuredfabrication. 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. 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 ofown 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 ofusing three or more calibration points. In this an artificial neural network trained by least meanmethod, one routine is sufficient to calculate the squares and recursive least squares learning rulesquantity to be measured by any transducer. It is has been used successfully in channel equalizationnot 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, anearity, the technique fails because the reference artificial neural network based inverse model waspoints 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 withrameters 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 waytrical 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 anis sufficient. But each type of transducer requires iterative manner. The schematic of the inverseits own, sometimes rather complicated calculation model of a transducer using an artificial neuralroutine. Besides, in this context, use of artificial network as its adaptive compensating nonlinearneural networks has also been suggested as an ef- model is shown in Fig. 2. Here, the neural networkficient alternative method to linearize the transduc- is suitably adapted to model a nonlinear transducerers 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 ofsponse. The schematic arrangement of an artificial the receiver in communication systems ͓10͔. By anneural network as a nonlinear compensating ele- adaptive learning procedure, the inverse modelment is shown in Fig. 1. A main characteristic of evolves in such a way that the combined transferthis solution is that function ͑F͒ to be approxi- function of the transducer and its inverse modelmated 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 inversecontext, the usage of artificial neural network tech- model of the transducer is used to estimate theniques for modeling the system behavior provides measurand for calibration as well as for providinglower interpolation error when compared with direct digital readout.
  3. 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 informationvolved the development of two integrated software between test-point and MATLAB environmentsmodules ͓9,14͔. The first module was imple- ͓16͔ using the dynamic data exchange feature ofmented in the form of a Data Acquisition and Windows. Selecting “Direction” on the front panelManagement Software supported on the architec- opens another subpanel displaying the stepwiseture 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 hereearizer. for experimental study. The virtual linearizer is implemented to acquire the input-output data from3.1. Synthesis of data acquisition management the data acquisition system-connected pressuresoftware 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 beenmanagement software was developed using fourth made to further validate the implemented inversegeneration, object-oriented, and graphical pro- model of the given transducer for its performancegramming technology in the form of a single in the production phase. In order to do so, theFront-panel and various Subpanels using test-pointsoftware ͓15͔. The different test-point objects werecarefully researched, configured, and interlinkedto develop a highly customized user-interactivefront panel. The synthesized front panel is shownin Fig. 3. The algorithm of control and computa-tions was implemented in the form of an embed-ded code containing different Action Lists writtenfor various test-point objects chosen to developdifferent panels of the data acquisition and man-agement software including the front panel. Thealgorithm of control and computations coordinatesthe 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 virtualson of the actual and estimated values of the in- linearizer.
  4. 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 withcess the signal continuously. To increase the flex- the Levenberg-Marquardt learning algorithm. Theibility of its use, the provision has been made in schematic of the proposed multilayer feed-forwardthe virtual linearizer to acquire stored data offline back-propagation network based soft compensatorfrom the excel-sheet in case the transducer is not as an accurate inverse model of transducer isavailable online. The corresponding maximum ab- based on the concept of the well-known systemsolute 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 afor comparison purposes. However, the data ac- transducer is required invariably for linearizing itsquisition and management system was designed to input-output static response in such systems. Aserve the function of measurement, modeling, es- multilayer feed-forward network, trained with thetimation, 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-outputgraphical, 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 fundamentaland estimated inverse response along with their question arises: what is the minimum number ofcorresponding 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 ofnetwork 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 theoremin 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 bypensator is carried out in the form of an inverse the set of inputs x1 , x2 , . . . , xm0 and a target outputmodel of a transducer using a multilayer feed- f͑x1 , x2 , . . . , xm0͒. Based on these observations,
  5. 5. Singh, Kamal, and Kumar / ISA Transactions 45, (2006) 319–328 323Fig. 5. Tabular representation of acquired training data andestimated results displayed by virtual linearizer usingmultilayer feed-forward back-propagation network basedinverse modeling of pressure transducer ͓MTR-Measuredtransducer response ͑in volts͒; Measur͑A͒-Applied measur- Fig. 6. Results of data acquisition constituting the trainingand to the transducer ͑in bars͒; Measur͑E͒-Estimated mea- set displayed by the virtual linearizer.surand ͑in bars͒; Error͑Ab͒-Absolute error between actualand estimated measurands; and Error͑% Full Span͒-Error in back-propagation network based inverse model ofterms 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 itselfelement applied to the multilayer feed-forward as a nested sigmoidal scheme. Therefore, based onFig. 7. Learning characteristics of multilayer feed-forward back-propagation network based inverse model of pressuretransducer.
  6. 6. 324 Singh, Kamal, and Kumar / ISA Transactions 45, (2006) 319–328Fig. 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 athe output function of a multilayer feed-forward standard back-propagation technique that is muchback-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, ͑4͒where N represents the number of neural networklayers, B denotes the bias vectors, W denotes the where W is the weight vector containing currentweight 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 likenetwork approximation of nonlinear activation the quasi-Newton methods and there is no need tofunction, f , is achieved using the Levenberg- compute the Hessian matrix ͑second derivatives͒Marquardt learning algorithm ͓13͔ in which the of the performance index at the current values ofHessian 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 iswhere j is the Jacobian matrix containing first de- calculated as the difference between the desiredrivatives 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 ˆerrors. The algorithm is detailed in Ref. ͓13͔.Fig. 9. Comparison of actual and estimated measurands Fig. 11. Error ͑% full span͒ corresponding to each value ofdisplayed by virtual linearizer. the applied measurand displayed by virtual linearizer.
  7. 7. Singh, Kamal, and Kumar / ISA Transactions 45, (2006) 319–328 325Table 1Results of multilayer feed-forward back-propagation network based inverse modeling of strain-gauge pressure transducerusing 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 theminimize the mean square error ͓19͔ and as a con- proposed virtual linearizer. The acquired trainingsequence 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 traininggramming ͓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. Itthe proposed virtual linearizer. For the example in has been found that a mean square error level ofthis 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 architectureLevenberg-Marquardt learning algorithm with the of a multilayer feed-forward back-propagationfollowing parameters: performance goal ͑MSE͒ network.= 7.89256e-006; learning rate= 0.01; factor to use The estimated measurand displayed as a resultfor memory/speed tradeoff= 1; and maximum of the multilayer feed-forward back-propagationnumber 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 errorizer is examined experimentally for correcting the ͑% full span͒ between the estimated and actualeffect of static nonlinearity associated with the measurands, displayed by the virtual linearizerdata 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 onlyϫ 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 onlytual linearizer for approximating the nonlinear 0.491119. Achievement of such a low level ofstatic 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 truea standard practical strain-gauge type of pressure values. The result of inverse modeling of pressuretransducer ͑SenSym: S ϫ 100DN͒ connected to transducer is also shown Table 1. The use of only
  8. 8. 326 Singh, Kamal, and Kumar / ISA Transactions 45, (2006) 319–328Fig. 12. Results of data acquisition constituting the valida- Fig. 13. Estimated measurand displayed by the proposedtion 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 validatesplexity 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 using1-2-1 architecture of a multilayer feed-forward The performance of the proposed multilayerback-propagation network as an accurate inverse feed-forward back-propagation network withmodel of the given pressure transducer, a valida-tion study was carried out with a trained neuralmodel by acquiring all the remaining 34 pairs ofinput-output data as the validation set using theproposed virtual linearizer. In fact, these pairswere not used in the training phase of the neuralmodel and cover the entire range of operation ofthe transducer under study. The acquired input-output pairs constitute the validation set. The re-sults of data acquisition displayed by the virtuallinearizer are shown in Fig. 12. The algorithm ofcontrol and computations was run again in combi-nation with the soft compensator for the validation Fig. 14. Comparison of actual and estimated measurandsphase. 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 theactual and estimated measurands and shows aclose resemblance between them. The correspond-ing values of absolute error and error ͑% full span͒between the estimated and actual measurands dis-played by the virtual linearizer graphically areshown in Figs. 15 and 16, respectively. The maxi-mum absolute values of absolute error and error͑% full span͒ for validation set are also given inTable 2. From the results, it has been observed thatthe absolute value of maximum absolute error isfound 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. 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 ofthe 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 theined with the complete set of input-output data work.used in the training and validation phases coveringthe entire range of operation of the given trans-ducer. The results obtained in the production phase Referencesconfirm the results obtained in the training and ͓1͔ Bolk, W. T., A general digital linearizing method ofvalidation phases. This has further validated the transducers. J. Phys. E 18, 61–64 ͑1985͒.effectiveness of the proposed multilayer feed- ͓2͔ Patra, J. C. and Pal, R. N., Inverse modeling of pres-forward back-propagation network based inverse sure sensors using artificial neural networks. AMSEmodel trained with the Levenber-Marquardt learn- Int. Conf. Signals, Data and Syst., Bangalore, India,ing algorithm as an efficient soft compensator for 1993, pp. 225–236. ͓3͔ Patra, J. C., Panda, G., and Baliarsingh, R., Artificialcorrecting the effect of static-nonlinearity associ- neural network-based nonlinearity estimation of pres-ated with the data acquisition system-connected sure sensors. IEEE Trans. Instrum. Meas. 43͑6͒, 874–transducers. 881 ͑1994͒. ͓4͔ Khan, S. A., Agarwala, A. K., and Shahani, D. T., Artificial neural network ͑ANN͒ based nonlinearity es-5. Conclusion timation of thermistor temperature sensors. Proceed- ings of the 24th National Systems Conference, Ban- The paper proposed a simple practical approach glore, India, ͑2000͒, pp. 296–302.for transducer inverse modeling and correction of ͓5͔ Patranabis, D., Sensors and Transducers. Wheelerits static nonlinearity using an artificial neural net- Publishing Co., Delhi, 1997, pp. 249–254. ͓6͔ Patranabis, D., Ghosh, S., and Bakshi, C., Linearizingwork based virtual linearizer. The main contribu- transducer characteristics. IEEE Trans. Instrum. Meas.tion of this paper is the development of a 37͑1͒, 66–69 ͑1988͒.multilayer feed-forward back-propagation network ͓7͔ Mahana, P. N. and Trofimenkoff, F. N., Transducerbased soft compensator and its performance is ex- output signal processing using an eight-bit microcom- puter. IEEE Trans. Instrum. Meas. IM-35͑2͒, 182–186amined for the solution of linearizing the nonlin- ͑1986͒. ͓8͔ Bentley, J. P., Principles of Measurement Systems, 3rdTable 2 ed., Pearson Education Asia Pte. Ltd., New Delhi,Comparison of the error obtained as a result of inverse 2000.modeling of strain-gauge pressure transducer using valida- ͓9͔ Pereira, J. M. D., Postolache, O., and Girao, P. S., Ation data. temperature compensated system for magnetic field measurement based on artificial neural networks. Absolute value Absolute value IEEE Trans. Instrum. Meas. 47͑2͒, 494–498 ͑1998͒. Range of of maximum of maximum error ͓10͔ Patra, J. C., Pal, R. N., Chatterji, B. N., and Panda, G., operation absolute error ͑% full span͒ Nonlinear channel equalization for QAM signal can- cellation using artificial neural network. IEEE Trans. 0.2– 6.8 bars 0.14834 2.2475 Syst., Man, Cybern., Part B: Cybern. 29͑2͒, 262–271 ͑1999͒.
  10. 10. 328 Singh, Kamal, and Kumar / ISA Transactions 45, (2006) 319–328͓11͔ 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 and͓12͔ 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 Longowal͓16͔ 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 his͓18͔ 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 of͓19͔ 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 thanment of Electrical and Instrumentation Engineering at Sant Lon- 50 research papers in National/International Journals andgowal Institute of Engineering and Technology ͑SLIET͒, Lon- Conferences.gowal ͑District: Sangrur͒, Punjab ͑India͒. He has published morethan 43 papers at various International and National levelSymposia/Conferences and Journals. His areas of interest are Vir-tual Instrumentation, Artificial Neural Networks and MedicalElectronics.