Neural Network Based Fault Diagnosis In Analog Electronic . - IJCA
International Journal of Computer Applications (0975 – 8887)Volume 61– No.16, January 2013Neural Network based Fault Diagnosis in AnalogElectronic Circuit using Polynomial Curve FittingAshwani KumarA.P.SinghElectronics and Communication EngineeringSectionYadavindra College of Engineering, PunjabiUniversity, Guru Kashi Campus, Talwandi SaboDepartment of Electronics and CommunicationEngineeringSant Longowal Institute of Engineering andTechnology, LongowalABSTRACTMany studies have been presented for the fault diagnosis ofelectronic analog circuits with worst case fault models using 50% variation in the parametric values of the components.The study of for parametric fault detection in electronicanalog circuits –faults as small as 10% or less was uncovered.The use of the neural network for parametric fault diagnosis inan analog circuit, based upon the polynomial curve fittingcoefficients of the output response of an analog circuit ispresented in this study. Building upon the theory ofpolynomial coefficients we propose a parametric faultdiagnosis methodology. A polynomial of suitable degree isfitted to the output frequency response of an analog circuit.The coefficients of the polynomial attain different valuesunder faulty and non faulty conditions. Using these features ofpolynomial coefficients, a BPNN is used to detect theparametric faults. Simulation results are presented for abenchmark bi quad filter circuit. Single resistance andcapacitance faults of 1% to 50% deviation from nominalvalues were correctly diagnosed.KeywordsNeural Network, Parametric faults, Analog circuit, Curvefitting, Polynomial coefficients.1. INTRODUCTIONWhenever a system does not behave normally as it should,means system is faulty. Fault diagnosis involves two steps.One the detection of fault in the system is called faultdetection. Second to locate the position of the fault is calledfault isolation. Electronic circuits and systems have becomepart and parcel of our daily life. Major business issues andcustomer expectations for electronic systems are zero systemfailure, high reliability and longevity. Fault diagnosis inanalog electronic circuits is a challenging research area.Tolerance effects of analog components, lack of test nodes,presence of feedback loops, nonlinearity problems etc. makethe diagnosis in analog circuits difficult.Several methods have been presented for parametric faultdiagnosis of analog circuits and systems [1]. A survey of theresearch conducted in this area clearly indicates that analogfault diagnosis is complicated due to the poor fault models,component tolerances, and nonlinearity issues. The artificialneural network is an efficient approach to fault diagnosis dueto its robustness and strong learning ability.Fault diagnosis methods are classified as simulation beforetest (SBT) and simulation after test (SAT). Simulation beforetest approach is more effective as it eliminates on linesimulation process and needs only once off- linecomputational effort before test activity. Fault dictionary is apractical approach belonging to the simulation before testtechniques. An input stimulus is first selected to excite theCUT. The circuit response to the input excitation is thensimulated/measured at different faulty and non faultyconditions.Fault dictionary approach based on SBT is generally used.Different feature extraction techniques to build the faultdictionary for the fault diagnosis of analog electronic circuitsunder SBT method has been given by different researchers.Since limited output nodes are available to have the outputresponse, so for the fault diagnosis needs unique featureswhich represent the faulty and non faulty nature of the analogelectronic circuit. Along with the unique feature extraction itis also desirable that computational overhead should also beminimum. In [2] output response of the circuit is extractedand principal component analysis is performed to reduce thefeature space. The soft and the hard faults of linear analogcircuit using slope fault feature and back propagation neuralnetwork is given. The soft fault diagnosis based on soft faultfeature and back propagation neural network. A linear analogcircuit containing only the resistive components has been usedas an example circuit [3].Fault diagnosis of analog circuit using frequency response andneural network as fault classifier are successfully given forsingle and multiple faults. The peak frequency and peak gainof the frequency response of the analog circuit are used toextract the distinct signatures for faulty and non faultyconditions [4]. The parametric variation in the component hasbeen taken as 50% from its nominal values. Ensembles ofthe neural network for fault diagnosis in analog electroniccircuit are described in [5]. Some studies [6, 7, 8, and 9] haveused the transient response of the analog electronic circuit andwavelet transform as a pre processor for fault signatureextraction and finally neural network for fault classification.Some studies used node voltages, DC supply current, and ACresponse of the CUT, simulation of the circuit in frequencydomain and FFT for feature extraction of faulty and non faultyanalog circuit [10-16].In the present fault diagnosis method, fault dictionaryapproach based on SBT technique has been presented. Abenchmark bi quad filter circuit has been used for faultdiagnosis. Only the parametric faults of the components areconsidered in this study. The frequency responses of thecircuit under test (CUT) have been plotted using bode plot ofMULTISIM software. These frequency plots are fitted with apolynomial of suitable order. Polynomial coefficients of thecurve fitted to the frequency response of the CUT are used asfeatures representing the fault and fault free analog circuit.These polynomial coefficients are used to train the neural28
International Journal of Computer Applications (0975 – 8887)Volume 61– No.16, January 2013network used for the classification of the faults. Allparametric faults of the components with 1% to 50%deviation (using 1% deviation resolution) from nominalvalues were correctly diagnosed.The material in this paper is arranged in the following order.In section 2, we briefly discuss proposed methodology forfault diagnosis used in this paper. Section 3, describesexperimental validation of fault diagnosis for a bench markanalog circuit. Section 4 and 5 covers result and discussion,conclusion respectively.2. PROPOSED METHODOLOGYFault diagnosis in analog electronic circuits is a difficult asmost of the analog circuit response is frequency dependentand only output terminal is accessible for most applications inpractice. So it is needed that the features extracted fromcircuit response should be unique under faulty and non faultyconditions. That will result in good fault diagnosis of theanalog circuit. The proposed methodology for fault diagnosisintegrates in the following basic modular steps as shown infigure1.CUTFrequencyResponseExtractionData PreprocessorFaultClassifierFaultDiagnosisFig 1: A block diagram for the proposed fault diagnosismethodology.2.1 Frequency Response ExtractionIn the proposed methodology the unique feature extraction ofthe analog circuit is obtained by extracting its frequencyresponse. Frequency response of an analog circuit is the graphwhich shows the variation in the gain of the analog circuitwith respect to the frequency of operation, when the circuit issimulated by a standard stimulus. This proposed methodologyis for an analog circuit whose output is frequency dependent.When the frequency of the input stimulus is varied the outputvoltage and hence the gain of the circuit varies. By plottingthis variation in the gain with respect to frequency, afrequency response of the circuit is obtained.Mathematically to implement this, the transfer function of theanalog circuit is required to be calculated depending upon itsrequired response and the band width requirement. Thetransfer function of the circuit is the ratio of its output voltageto the input voltage i.e. The component values are alsoselected accordingly. Once the transfer function of the analogcircuit is calculated, one can easily know the value of theoutput voltage of the circuit for a known value of the inputstimulus. These output voltage obtained for different inputfrequencies results the overall frequency response of thecircuit. The transfer function of the bi quad filter circuit is.Where Gp, Q is the Q factor, ω0 is theMATLAB software. This is used to compute the magnitudeand phase of the frequency response of the linear timeinvariant models. In the bode diagram the magnitude isplotted in db and the phase in degrees. Bode plotter is alsoavailable as bode plotter instrument in the MULTISIMsoftware. In this the gain of the circuit under test is plottedwith respect to the frequency. An AC source stimulus isrequired to simulate the circuit. Frequency of the AC sourcedoes not affect the function of the bode plotter. But thepresence of the AC source is must in the circuit.The frequency response of the circuit under test is obtainedusing the bode plotter for faulty and non faulty conditions ofthe components of the CUT. The parametric fault introducedin each component values are with the variation of 1% andup to 50% i.e. hundred faults are there for each componentkeeping all other components at their nominal values withinthe tolerance limit. It has been observed that for each fault inthe circuit component value a unique frequency responsegraph is obtained. The uniqueness in each of the frequencyresponses graphs leads further to the fault diagnosis process.2.2 Data PreprocessingAfter the circuit simulation, we have different frequencyresponses graphs indicating the different parametric variationfaults in each of the components present in the circuit. Thecollected graphs are applied to the preprocessor to get theproper and distinguishable features. This is done usingpolynomial curve fitting. Polynomials are one of the mostcommonly used types of curves in regression. The PolynomialCurve Fitting uses the method of least squares when fittingdata. The fitting process requires a model that relates theresponse data to the predictor data with one or morecoefficients. The result of the fitting process is an estimate ofthe coefficients of the model. To obtain the coefficientestimates, the least squares method minimizes the summedsquare of residuals.The least-squares jth degree Polynomials method uses jthdegree polynomialstoapproximate the given set of data, (where. The curve of best fit is that for which , E,the sum of squares of the errors is minimum. This is known asthe principle of least squares and was suggested by Legendre.For the best fitting curvehas the least square error. i.e.(i)These unknown coefficients will yield their first derivativezero for Where in equation (i)andare known values.are unknown coefficients least square error.center frequency and s σ jω is the complex frequency.Band width of the filter circuit is approximated by.Apart from the mathematically obtaining the frequencyresponse of the analog circuit, this can also be obtained bysimulating the analog circuit and using the bode plotter. Bodeplotter is very useful for the analysis of filter circuits. Itproduces a graph of circuit’s frequency response. In this thegain of the circuit under test is plotted with respect to thefrequency. Bode plotter is available as bode diagram offrequency response in the control system tool box of29
International Journal of Computer Applications (0975 – 8887)Volume 61– No.16, January 2013mechanism. These neurons are connected to form a networkand are organised in the form of layers. These are connectedby highly synaptic weights.The Artificial Neural Networks(ANN ) have a learning ability as synaptic weights can bestrengthened or weakened during the learning process, and inthis way, information can be stored in the neural network.Each neuron has activation function, as a function of inputs ithas received. A neuron sends its activation as a signal toseveral other neurons. It is important to note that a neuron cansend only one signal at a time, although signals arebroadcasted to several other neurons.(ii)After the expansion of the above equations, in equation (ii) wehaveThe artificial neural network used in proposed methodology isa multilayer backpropagation neural network. This type ofneural network is used in patteren recognition, classification,function approximation etc. The artificial neural networkmodel with multiple inputs and one output for the faultdiagnosis in analog circuit is shown in figure2. HereX [X1,X2,X3, .Xn] is the input vector and n is the numberof neurons in the input layer. Yk is the output of the neuralnetwork. Where k represent the different coponents present inthe analog circuit.InputsX1X2X3MultilayerYkArtificialNeural NetworkOutputXn(iii)The polynomial coefficientscan be obtainedby solving these above given equation (iii), linear equations.Polynomial curve fitting is done using the curve fittingtoolbox of MATLAB software. Which also based on thetheory of least square methods. Since the frequency responsegraphs are different for different fault senarios, polynomialcoefficients are also different and unique for different faults.These polynomial coefficients are used to prepare the faultdictionary, for further classificatin of the faults.2.3 Fault ClassificationFault classification is integrated in two basic steps.Preparation of the fault dictionary for different identifiedfaults in the first step. Fault diagnosis using a proper artificialneural network in the second step. The size of the faultdictionary will be based on number of the identified faults in acomponent and the order of the polynomial used for curvefitting. If the number of identified faults in a component are nand the order of the polynomial is m, then there will beentries (n for n numberof faults and one for fault free condition) in the faultdictionary and each entry will have m 1 number ofcoefficient for that component.Artificial Neural Networks, is a parallel distributed processingsystem made up of highly interconnected neural computingelements. These networks have the ability to learn and thereby acquire knowledge. This acquired knowledge makes neuralnetwork to solve problems. Neural Networks architectureshave been classified into various types based on their learningFig 2: Proposed model of artificial neural networkfor the fault diagnosis in analog circuitsX1.Xn represents the coefficients of the polynomial fittedto the output frequency response of the analog circuit. Yk isthe output of the neural network which represent the variationin the component vaule from 1% to 50%. For everycomponent there are 101 samples of input polynomialcoefficients and corresponding 101 outputs. So the totalnumber of input-output samples for ANN will be. These includes 100fault samples for each component and one sample for thenominal value. In this work a neural network with three layerstrctural architecture has been proposed. Input layer, outputlayer and hidden layer. The nodes in the input layer is equal tothe number of coefficients, and the number of nodes in themiddle hidden layers are varied to achieve the best diagnosisclassification. Neural network weights are adapted during thetraining. Evaluation of the fault diagnosis classification isevaluated during the test phase.3. EXPERIMENTAL VALIDATIONThe proposed methodology described in the previous sectionis applied to the benchmark bi quad filter circuit as the circuitunder test. As this circuit has already been used previously inother fault diagnosis studies [17], [18] and has been found tofairly tolerant to component variations, we found it to be asuitable choice.3.1 Circuit SimulationWe have taken up the benchmark bi quad filter circuit shownin figure 3 to illustrate our approach to fault diagnosis.Thecomponent values are C1 C2 10nf, R1 R3 2.7KΩ,R2 1.5KΩ, R4 12KΩ, R5 1KΩ and R6 10KΩ. Theresistors and capacitors are assumed to have the tolerance30
International Journal of Computer Applications (0975 – 8887)Volume 61– No.16, January 2013values 5% and 10% respectively. In order to verify thecorrectness of our proposed methodology, the softwareMULTISIM and MATLAB are adopted to implement thefault diagnosis process. The analog circuit is simulated usingMULTISIM software and the frequency response of thecircuit under test is obtained by its bode plotter instrument.XBP16.This process is repeated for every output frequencyresponse related to each fault senario of eachcomponent of CUT and nine polynomialcoefficients are recorded for each curve fit. Thesecoefficients are further used to build the faultdictionary. The figure 4 shows an example curve fitfor a fault senario in component C1.R3IN2.7kΩR2R43 kΩ2.7kΩV10Fig 3: Bi quad filter circuit (Crcuit Under Test)Hundred soft faults ( for the increase and decrease in theparametric value) are simulated for each components(C1,C2,R1,R2,R3,R4). The component parametric values aretolerated by 1%(increase) and -1% (decrease) faultsrespectively. The maximum variation in the parametric valueis limited to 50%. Total 101 frequency responses, hundredfor the fault classes and one for the nominal value of thecomponent, are recorded for the components of the circuitunder test. It has been observed that each response shows achange with the change in the parametric value of thecomponents. This distinction in frequency response feature ofCUT for the component value serves the basis of faultdiagnosis process. These frequency responses are stored in theform of excel files.3.2 Data PreprocessingThe feature extraction for the purpose of the fault diagnosis isaccomplished with the data preproceesing. The simulationresults are preprocessed using the proposed methodologydescribed in section 2.2.for the preparation of the faultdictionary. For all the faults for the components of the circuitunder test, polynomial curve fitting method is applied to getthe basic polynomial coefficients. The curve fitting isimpemented by using the curve fitting tool box of theMATLAB software. The plonomial curve fitting tool box ofMATLAB uses the least square method. The following stepsare following in the curve fitting process.1.The frequency response graph is first transferredand stored in an microsoft office excel work sheet.2.These values of the graph from excel worksheet aretranferred to the matlab workspace.3.The data stored in the matlab workspace is importedin the curve fitting tool box.4.The imported graph in the curve fiiting tool box iscurve fitted using polynomial curve fitting.5.A ninth order polynomial is used to fit outputfrequency response of CUT yielding ninepolynomial coefficients.Fig 4: Curve fit example of fault senario in component C13.3 Fault ClassificationThe first step in fault classification procedure is theidentification of the faults and preparing the fault dictionary.The output response of the circuit is curve fitted with 9th orderpolynomial.For fault classification purpose we use tenpolynomial coefficients . The fault classification results arefairly good by using these coeffiecients. Hence for everycomponent in the circuit a 10 101 fault dictionary matrix isprepared. For simplicity in the fault dictionary plots of thecoefficients naming P1 and P2 are shown in figure 5. Theseplots show the polynomial coefficient values with respect tothe change in the % variation in the component value.The second step is the design of proper design of neuralnetwork for the diagnosis of the faults. The NN toolbox ofMATLAB software is used to design the neural networkarchitecture for fault classification. In the experimental workthe neural network degined contains three layered structure,input layer, output layer and one hidden layer as shown infigure 6.There are h numbers of hidden layer neurons andB1 [b1, b2, b3, ., bh] is the bias vector of the hidden layerneurons. Output layer contains one output neuron with theirbias vector bo. The outputof the hth neuron in the hiddenlayer is given by(iv)The outputof the output neuron in the output layer is(v)31
0.50.40.2Values of Polynomial CoefficientsPlot of Values of Polynomial Coefficients vs.% Variation in Parametric Value of alues of Polynomial -50-40-30-20-1001020304050Plot of Values of Polynomial Coefficients vs.% Variation in Parametric Value of R1Plot of Values of Polynomial Coefficients vs.% Variation in Parametric Value of 1.1-1.3-40-30-20-10010203040Percentage Variation in Parametric Value of R350-40-30-20-1001020304050Percentage Variation in Parametric Value of R2Values of Polynomial Coefficients0.1P2-0.9Plot of Values of Polynomial Coefficients vs.% Variation in Parametric Value of R30.3P1-0.5Percentage Variation in Parametric Value of R1Values of Polynomial CoefficientsP2-0.8Percentage Variation in Parametric Value of C12-1.5-50P1-0.6Percentage Variation in Parametric Value of C230.5Plot of Values of Polynomial Coefficients vs.% Variation in Parametric Value of C20.2504-5-500.50.4Values of Polynomial CoefficientsValues of Polynomial CoefficientsInternational Journal of Computer Applications (0975 – 8887)Volume 61– No.16, January 20134Plot of Values of Polynomial Coefficients vs.% Variation in Parametric Value of 50Percentage Variation in Parametric Value of R4Fig 5: Plots of the fault dictionaries for the components fault models of circuit under test32
International Journal of Computer Applications (0975 – 8887)Volume 61– No.16, January putsP21P2inFig 6: Proposed ANN model for the fault diagnosis of analog circuit.Table 1: Fault diagnosis results for Bi Quad Filter 058.9e-005Test0.0247Validation355Absolute Error5TrainingC1MaximumHidden Layer neurons1No. of EpochS. No.Mean Square ErrorComponentThe network is trained with Levenberg Marquardt trainingalgorithm and the performance metric is taken as mean square(1)error (MSE)and maximum absolute error. The mean square(n) difference between the target outputerror is calculated as theand the network output. The goal is to minimize the averageof the sum of these errors.(vi)Whereoutput.is the target output andis the neural networkThe neural network with 10 (X 10) nodes In the input layerand one node in the output layer is realized. Six neuralnetwork architecture each for one comonent under thediagnosis process is realized.The number of nodes in thehidden layer are varied to achieve the best fault classificationperformance. The total data collected in the dictionary ispartitioned into three sets for training,validation and testing.Using the random selection for each of the component fault,70 percent patterns are selected for training the neuralnetwork, 15 percent patterns are used for validation processand the remaining 15 persent patterns are used for testingpurpose. Number of nodes in the hidden layer are varied tillbest classification evaluation is obtained. The best results ofclassification evaluation are obtained when the number ofnodes in the hidden layer are as shown in table I. The networkis adaptively trained to update the weights with LevenbergMarquardt backpropagation algorithm (trainlm) by the meansquare error performance.4. RESULTS AND DISCUSSIONSThe diagnosis results for the components (C1, C2, R1, R2, R3and R4) of CUT are tabulated in table 1. The first metric usedfor fault classification is maximum absolute errror and thesecond is the mean square error for all three phases of theneural network classifier i.e. training, validation and testingphase.Maximum absolute error ranges from 0.0247 to 0.1552. Meansqure error ranges from 1.3e-007 to 6.2e-006, 1.2e-005 to7.9e-005 , 1.5e-005 to 8.9e-005 for training, validation andtest phases of neural network respectively. The neuralnetwork taraining, validation and test pattern performance plotfor C1 is shown in figure7. The performance graph indicatesthat the best validation performance is obtained at 345 epochs.In this section an analysis of the proposed methodology andits implementation for a practical example is also done. As itis clear from the results that one percent variation in theparametric value of the component is detectable with amaximum absolute error ranges from 0.0247 to 0.1552. Wehave classified sucessfully all the faults of table I, except twoR5 and R6, which are placed in ambugity group. This isbecause the output of the circuit overlap for these faults.33
International Journal of Computer Applications (0975 – 8887)Volume 61– No.16, January 2013[5][6][7][8]Fig 7: Performance plot of NN for capacitor C1The results of the proposed methodology clearly indicate thatthrough appropriate processing of analog circuit, one can traina neural network to correctly diagnose the single parametricfaults with a fine variation in the parametric value of thecomponent. This study indicates that the proposedpreprocessing techniques have a significant imact on analogfault diagnosis, one due is ability to diagnose the singleparametric faults of the components and secondly diagnosiswith high sensitivity. The main contribution of this work isformulation and solving the fault diagnois problem infrequency domain. Hence in general, the method workscorrectly and gives results with minimum erorr as illustratedvia example.5. CONCLUSIONThe use of the neural network, based upon the polynomialcoefficients of the output frequency response of an analogcircuit under test is presented in this paper. By performing thefrequency response and curve fitting, polynomial coefficientsare obtained for faulty and non faulty conditions of CUT.These polynomial coefficients are used as signature for thetraining, validation and test sets for artificial neural network. .The result of the proposed method applied to the Bi QuadFilter circuit is quite encouraging.6. ACKNOWLEDGEMENTSAuthors are greatly indebted to the Department of Electronicsand Communication Engineering, SLIET, Longowal-148106(District: Sangrur), Punjab, India for providing excellent labfacilities that make this work feasible.[9][10][11][12][13][14][15]7. REFERENCES[1] William G. Fenton, T. M. McGinnity, and LiamP.Maguire, Fault Diagnosis of Electronic Systems UsingIntelligent Techniques: A Review, IEEE Transactions onSystems, Man, and Cybernetics—part c: Applicationsand Reviews 31, No.3 (2001) 269-281.[2] Yuan Haiying, Chen Guangju and Xie Yongle, FeatureEvaluation and Extraction Based on Neural Network inAnalog Circuit Fault Diagnosis, Journal of SystemsEngineering and Electronics 18, No. 2 (2007) 434-436.[3] HU Mei, WANG Hong, Hu Geng and YANG Shiyuan,Soft Fault Diagnosis for Analog Circuits Based on SlopeFault Feature and BP Neural Networks, TSINGHUASCIENCE AND TECHNOLOGY ISSN 1007-021405/49, 12, No. SI, (2007) 26-31.[4] V. Manikandan and N. Devarajan, SBT Approachtowards Analog Electronic Circuit Fault Diagnosis,[16][17][18]Hindawi Publishing Corporation, Active and PassiveElectronic Components, ID 59856, (2007).M. A. El-Gamal and M. D. A. Mohamed, Ensembles ofNeural Networks for Fault Diagnosis in Analog Circuits,Journal of Electronic Testing: Theory and Application 23(2007) 323-339.Yin Shirong, Chen Guangju and Xie Yongle, WaveletNeural Network Based Fault Diagnosis in NonlinearAnalog Circuits, Journal of System Engineering andElectronics 17 No. 3 (2006) 521-526.P. Kalpana , K. Gunavathi, Wavelet based fault detectionin analog VLSI circuits using neural networks,ELSEVIER, Applied Soft Computing 8 (2008) 1592–1598.Mehran Aminian and Farzan Aminian, Neural-NetworkBased Analog-Circuit Fault Diagnosis Using WaveletTransform as Preprocessor, IEEE Transactions onCircuits and Systems—II: Analog and Digital SignalProcessing 47, No. 2 (2000) 151-156.Wenji Zhu, Yigang He, A Neural-Network-Based FaultDiagnosis Approach for Analog Circuits by UsingWavelet Transformation and Fractal Dimension as aPreprocessor, World Academy of Science, Engineeringand Technology 68 (2010) 571-579A.Rathinam, R.Srinivasa Raghavan and R.Venkatraman,Fault Diagnosis in Analog Integrated Circuits UsingArtificial Neural Networks, International Journal ofComputer Applications (0975 - 8887) 1 No. 27 (2010)63-69.M. F. Abu El-Yazeed and Adel A. K.Mohsen, APreprocessor for Analog Circuit Fault Diagnosis BasedonProny’s Method, AEU International Journal ofElectronics and Communications (2003) 16-22.Marcantonio Catelani, Ada Fort, Cesare Alippi, A fuzzyapproach for soft fault detection in analog circuits,ELESEVIER, Measurement 32 (2002) 73–83.K. Mohammadi, S.J. Seyyed Mahdavi , On improvingtraining time of neural networks in mixed signal ectronics Reliability 48 (2008) 781–793.Vanco Litovski, Miona Andrejevic, and Mark Zwolinski,Analogue Electronic Circuit Diagnosis Based on ANNs,Microelectronics Reliability 46 (2006) 1382-1391.Marcantonio Catelani and Ada Fort, Soft Fault Detectionand Isolation in Analog Circuits: Some Results and aComparison between a Fuzzy Approach and Radial ation and Measurement 51, No. 2 (2002) 196202.Doried Mismar,and Ayman AbuBaker, Neural NetworkBased Algorithm of Soft Fault Diagnosis in AnalogElectronic Circuits, IJCSNS International Journal ofComputer Science and Network Security,10 No.1 (2010)107-111.Kaminska, B.; Arabi, K.; Goteti, P.; Huertas, J.; Kim, B.;Rueda, A.; and Soma, M., Analog and mixed signalbenchmark circuits. First release, IEEE ProceedingsInternational
polynomial curve fitting. Polynomials are one of the most The Polynomial Curve Fitting uses the method of least squares when fitting data. The fitting process requires a model that relates the response data to the predictor data with one or more coefficients. The result of the fitting process is an estimate of
in the research and application of fault diagnosis. In this paper, some notions and the basic principles for the unanticipated fault detection and diagnosis are given. A general process model applied to the diagnosis for the unanticipated fault is designed, by adopting a three-layer progressive structure,
Step 5: Fault dictionary construction: The fault dictionary is a collection of potential faulty and fault-free responses. The signatures obtained will be stored in the dictionary. This dictionary involves for each fault a correspondence between the faulty circuit responses and the defect sites.
CDS G3 Fault List (Numerical Order) Fault codes may be classified as sticky or not sticky: Type of fault Method to clear Not sticky Clears immediately after the fault is resolved Sticky Requires a key cycle (off and on) after the fault is resolved to clear. CDS G3 Fault Tables 90-8M0086113 SEPTEMBER 2013 Page 2G-3
Capacitors 5 – 6 Fault Finding & Testing Diodes,Varistors, EMC capacitors & Recifiers 7 – 10 Fault Finding & Testing Rotors 11 – 12 Fault Finding & Testing Stators 13 – 14 Fault Finding & Testing DC Welders 15 – 20 Fault Finding & Testing 3 Phase Alternators 21 – 26 Fault Finding & Testing
illustrated in Figure 3. This is a fault occurring with phase A to ground fault at 8 km measured from the sending bus as depicted in Figure 1. The fault signals generated using ATP/EMTP are interfaced to the MATLAB for the fault detection algorithm. (a) Sending end (b) Receiving end Figure 3. Example of ATP/EMTP simulated fault signals for AG fault
In this paper, the calculation of double line to ground fault on 66/33 kV transmission line is emphasized. Figure 3. Double-Line-to-Ground Fault 2.4 Three-Phase Fault In this case, falling tower, failure of equipment or . ground fault, fault current on phase a is I a 0. Fault voltages at phase b and c are: V b .
application of neural networks is to test the trained neural network. Testing the artificial neural network is very important in order to make sure the trained network can generalize well and produce desired outputs when new data is presented to it. There are several techniques used to test the performance of a trained network, a few of which are
neural networks and substantial trials of experiments to design e ective neural network structures. Thus we believe that the design of neural network structure needs a uni ed guidance. This paper serves as a preliminary trial towards this goal. 1.1. Related Work There has been extensive work on the neural network structure design. Generic algorithm (Scha er et al.,1992;Lam et al.,2003) based .
