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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, 2010 Time Domain Analysis based Fault Diagnosis Methodology for Analog Circuits-A Comparative Study of Fuzzy and Neural Classifier Performance V. Prasannamoorthy1, R. Bharat Ram2, V. Manikandan3, N. Devarajan4 1,2,4 Department of Electrical Engineering, Government College of Technology Coimbatore, India 3 Department of Electrical Engineering, Coimbatore Institute of Technology Coimbatore, India 1 prasanna_gct1995@yahoomail.com Abstract— In this paper, we attempt to diagnose the occurrence intuitional knowledge of the functioning of the CUT. Constant of faults in analog electronic circuits based upon variations in supervision of the circuit is entailed to ensure stable time domain specifications corresponding to the circuit condition performance over an extended period of time. The under consideration relative to the fault free circuit. To achieve identification of faults in systems is often a combination of this, both a fuzzy as well as a neural classifier have been utilized fault detection and isolation, necessarily in the same order, to operate with the fault dictionary data as base. Through this which is commonly known as FDI [10]-[11]. Early detection of process, a general comparison is drawn out between the faults in a circuit can greatly assist in maintenance of the performance of either route in dealing with fault diagnosis of system by avoiding possibly harmful damage borne out of the circuits. An illustrative example is considered, on which both the fault. Occasionally, a circuit may so damaged that it might fuzzy and neural algorithms are tested, and their performance in fault diagnosis is compared. Further, the suitability of the fuzzy assume an unstable state, making it impossible to extract and neural techniques to various kinds of diagnosis problems signatures from it that might help in identifying the fault. In depending upon the nature of data available is also discussed. other cases, a fault might just be too critical or dangerous to be provoked for the sake of obtaining a signature. Keywords—Fault diagnosis, fuzzy logic system, neural Analog fault diagnosis is inherently complicated by poor networks,Sallen-key Bandpass filter. mathematical models, component tolerances, nonlinear behaviour of components, and limited accessibility to internal I. INTRODUCTION nodes of the circuit under test. In this paper, we state the results The identification of faults in any analog circuit is very of a comparative study of the performance of fuzzy and neural useful and, in a few instances, an inevitable measure in routes in the detection and identification of faults in an analog ensuring competent performance of the circuit. In general, the electronic circuit using the Simulation-Before-Test approach. analog diagnosis approaches can be categorized into two [1], This was achieved by taking into consideration the variations in namely-simulation-after-test (SAT) and simulation-before-test time-domain response parameters pertaining to the transient of (SBT). The simulation-after-test [2]-[4] approach involves the the CUT for a step input. A comprehensive fault dictionary was computation of various circuit parameters from the operational prepared from all the possible values of the parameters circuit and fault identification is carried out using these corresponding to each state of the circuit, which was then parameters, assuming that each measurement is independent of effectively utilized to construct a classifier capable of the other. This method is avoided due to the increase in process identifying the various faulty configurations of the CUT. time with increase in the size of the circuit, in addition to issues concerning non-linear circuits. On the other hand, a useful II. GENERALIZED ALGORITHM alternative is found in the simulation-before-test approach The fault diagnosis methodology, involving either a fuzzy which appreciably reduces the time taken for fault diagnosis. or a neural system, may be divided into five distinct steps as In the SBT approach [5]-[9], a predefined set of test stimuli are used to extract certain signatures from the Circuit-Under-Test follows: (CUT) that are unique to each faulty condition. These Step I: Formulation of transfer function of the circuit under signatures can then be suitably systematized to create a “fault test assuming nominal values of all components in the circuit. dictionary”, which is then checked for redundancies that may Step II: Simulation of time-domain response of the circuit result in masking of certain faults. Evidently, the parameters when a unit step signal is given as input, for possible chosen to pose as signatures must be quantities that are combinations of component faults. observable for all conditions of the circuit. Step III: Determination of time-domain response parameters, namely, settling time and peak amplitude for each time Both the above-mentioned approaches are fairly procedural response plot. in nature and do not necessitate the prerequisite of an 306 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, 2010 Step IV: Suitable pre-processing of available data and design that the remaining components maintain their nominal values of classifier. as in the original circuit. Distinct variations in response may be seen for every faulty configuration, as shown in Fig. 2, 3 Step V: Isolation of faults by using the signatures extracted and 4. The two required time-domain response parameters, from a suspicious circuit by feeding its time response settling time and peak amplitude are noted for all the response parameters to the classifier obtained in step IV. curves. These, being characteristic to a particular configuration, are used as the fault signatures. III. TEST CIRCUIT To test the performance of the fuzzy and neural techniques, we chose the Sallen-Key bandpass filter circuit [12] shown in STEP RESPONSE 1.5 F1 Fig. 1. The Sallen-Key bandpass filter is a second order F2 active filter, which is greatly appreciated for its simplicity F3 F4 of design. The filter section shown in Fig. 1 can also be F5 cascaded to form second order filter stages, resulting in larger 1 F6 F7 AMPLITUDE order filters. The op-amp provides buffering between filter F8 F9 stages, so that each stage can be designed independently. This F10 circuit is suitable for filters which have complex conjugate 0.5 F11 F12 poles. When implementing a particular transfer function, a F13 F14 designer will typically find all the poles, and group them into real poles and complex conjugate pairs. Each of the complex 0 conjugate pole pairs are then implemented with a Sallen-Key 0 0.5 1 1.5 2 2.5 3 3.5 4 filter, and the circuits are cascaded together to form the TIME (s) x -5 complete filter. Fig. 2 Step response curves for single faults STEP RESPONSE 1.2 F15 1 F16 F17 0.8 F18 AMPLITUDE F19 F20 0.6 F21 F22 0.4 0.2 Fig. 1 Sallen-Key Bandpass Filter circuit 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 The transfer function of the Sallen-Key bandpass filter circuit - TIME (s) x 10 is Fig. 3 Step response curves for double faults where STEP RESPONSE 1.5 F35 F36 F37 F38 F39 1 F40 AMPLITUDE The circuit shown in Fig. 1 has the component values that correspond to the nominal frequency of operation of 25 kHz. 0.5 IV. SIGNATURE EXTRACTION In order to obtain the fault signatures for each fault condition, the values of components are varied to +50% or - 0 50% of their nominal values shown in Fig. 1 and the circuit is 0 1 2 3 TIME (s) 4 5 6 x 7 -5 excited using a unit step signal as input, thus enabling to construct the fault dictionary. While the values of the Fig. 4 Step response curves for multiple faults supposedly faulty components are manipulated, it is ensured 307 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, 2010 There are a total 2n number of single faults for which the accordingly, fault dictionaries are created. A general rule of step response plot in shown in Fig. 2, whereas there are n(n- thumb is that once the fault signatures have been collected and 1)/2 number of double faults, n(n-1)/3 triple faults and n(n- organized into a fault dictionary, the data must be optimized 1)/4 quadruple faults for which the step response curves by eliminating signatures that bring about masking of faults are shown in Fig. 3 and Fig. 4. Other combinations of whose signatures match. However, in the case of a fault component faults get eliminated automatically due to dictionary made up of time-domain response parameters, the repetitions of the same in the fault dictionary, the formulae data is found to be free of redundancies hence making it stated above holding good in determining the final count of feasible to identify each faulty configuration on the basis of fault conditions post elimination. variations in two parameters alone. TABLE I TABLE III TIME DOMAIN SPECIFICATIONS FOR SINGLE FAULTS TIME DOMAIN SPECIFICATIONS FOR TRIPLE FAULTS Faulty Settling time Peak Settling Fault ID Faulty Peak components *10^-5 sec Amplitude Fault ID time components Amplitude F1 R1↑ 4.3834 0.7211 *10^-5 sec F2 R1↓ 4.2557 1.1709 F35 R1↑,R2↑,C1↑ 7.9128 0.8071 F3 R2↑ 5.2859 0.8600 F36 R1↓,R2↓,C1↓ 1.6563 0.9866 F4 R2↓ 3.8230 0.9788 F37 R3↑,R4↑,C2↑ 6.1429 0.7571 F5 R3↑ 5.1273 1.1024 F38 R3↓,R4↓,C2↓ 2.4867 1.2456 F6 R3↓ 3.6507 0.5770 F39 R1↑,R2↑,C2↑ 6.6527 0.586 F7 R4↑ 4.7622 0.7089 F40 R1↓,R2↓,C2↓ 2.9279 1.5191 F8 R4↓ 3.0360 1.5381 F41 R1↑,R3↑,C1↑ 6.5752 1.0816 F9 R5↑ 3.6338 1.1908 F42 R1↓,R3↓,C1↓ 1.7798 0.6463 F10 R5↓ 4.9734 0.6228 F43 R2↑,R3↑,C1↑ 9.2037 1.1879 F11 C1↑ 6.1093 1.0152 F44 R2↓,R3↓,C1↓ 1.6083 0.4277 F12 C1↓ 2.6625 0.6645 F45 R1↑,C1↑,C2↑ 6.5752 0.7211 F13 C2↑ 4.7794 0.7566 F46 R1↓,C1↓,C2↓ 2.1278 1.1709 F14 C2↓ 3.9499 1.1012 F47 R2↑,R5↑,C1↑ 6.7579 1.2896 F48 R2↓,R5↓,C1↓ 1.9938 0.4779 TABLE II TIME DOMAIN SPECIFICATIONS FOR DOUBLE FAULTS TABLE IV Faulty Settling time Peak TIME DOMAIN SPECIFICATIONS FOR QUADRUPLE FAULTS Fault ID components *10^-5 sec Amplitude F15 R1↑,R2↑ 5.7921 0.6968 Settling F16 R1↓,R2↓ 3.0089 1.2654 Faulty Peak Fault ID time components Amplitude F17 R1↑,R3↑ 4.6712 0.9312 *10^-5 sec F18 R1↓,R3↓ 2.9020 0.8483 F49 R1↑,R2↑,R3↑,R5↑ 5.4507 1.1908 F19 R1↑,C1↑ 6.0179 0.8436 F50 R1↓,R2↓,R3↓,R5↓ 2.4867 0.6228 F20 R1↓,C1↓ 2.3671 0.9403 F51 R1↑,R2↑,R3↑,C1↑ 9.1640 1.0152 F21 R2↑,R5↑ 4.8269 1.1242 F52 R1↓,R2↓,R3↓,C1↓ 1.3313 0.6645 F22 R2↓,R5↓ 3.2166 0.6416 F53 R1↑,R4↑,C1↑,C2↑ 7.4992 0.5693 F23 R3↑,R5↑ 4.1115 1.5028 F54 R1↓,R4↓,C1↓,C2↓ 1.7798 1.9389 F24 R3↓,R5↓ 3.9499 0.413 F55 R2↑,R4↑,C1↑,C2↑ 8.362 0.6978 F56 R2↓,R4↓,C1↓,C2↓ 3.3142 2.0385 F25 R3↑,C1↑ 7.4602 1.2456 F57 R4↑,R5↑,C1↑,C2↑ 6.487 0.888 F26 R3↓,C1↓ 2.4867 0.4152 F58 2.1623 0.888 R4↓,R5↓,C1↓,C2↓ F27 R3↑,C2↑ 5.4507 0.9526 F59 R1R2R3R4R5C1C 9.7305 0.888 F28 R3↓,C2↓ 3.0668 0.7383 F60 R1R2R3R4R5C1C 1.0812 0.888 F29 R5↑,C1↑ 5.1273 1.3780 F61 Fault Free 4.3247 0.888 F30 R5↓,C1↓ 3.0089 0.4745 F31 R5↑,C2↑ 4.1115 1.0019 The fault dictionaries for single component fault, F32 R5↓,C2↓ 4.5108 0.7619 double component fault, triple component fault and other F33 R2↑,C2↑ 5.8528 0.7379 multiple component faults are presented in the tables I, II, III F34 R2↓,C2↓ 1.993 1.2744 and IV respectively. An upward arrow indicates a deviation of 50% above the nominal value, whereas a downward arrow From the above shown curves, the values of settling time indicates a 50% decrement. The fault free condition is also and peak value for each fault condition are noted down and tabulated and is given as ID F61. 308 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, 2010 V. NEURAL FAULT DIAGNOSIS SYSTEM with the desired target values, and an error signal (δ) is produced. The network weights are adapted so as to minimize A. Preprocessor the error. The generalized delta rule does the weight A complete fault dictionary containing all feasible adaptation given by Δpωi j =∑δpj xpi, where ∑ is the learning conditions cannot be generated because of the presence of rate, δpj is the error at the jth node due to pattern p; xpi is the ith noise. This problem is solved by giving inputs to the neural element of the output pattern p. The error signal for the output node is δpj = (tpj − opj) fj (netpj), where tpj and opj are the target network in terms of bits—a “0” is assigned if the value and output values respectively. observed for a specific test frequency is out of bounds; a “1” is The number of nodes in a layer and the activation function assigned if the value observed for a specific test frequency is will affect the learning rate, the computational complexity, and within bounds. That is, if XL ≤ Xm ≤ XH implies ANN input = the usefulness of the network for a specific problem wherein 1, else ANN input = 0. the best results always come from intuition and experience. B. ANN Classifier The number of neurons in the input layer is 10 and the number of neurons in the hidden single layer is 21. So the Artificial neural networks provide an adaptive mechanism ANN structure boils down to 10:21:1. The ANN is adaptively for the task of pattern classification [13]. They are capable of trained to update the weights and the bias by gradient descent reliable classification even in undesirable environments method by the mean-square-error performance. characterized by ill-defined models, noisy inputs and nonlinearity. A comparison of neural network architectures has already been undertaken by S. Hsu, et al [14]. In this paper, the back propagation network (BPN) structure has been chosen for the classification task. A typical BPN has two or three layers of interconnecting weights. Fig. 5 shows a standard two-layer BPN network topology. Each input node is connected to a hidden layer node. Each hidden node is connected to an output node in a Fig. 6 Classifier for test circuit similar fashion. This makes the BPN a fully connected network topology. The classifier structure for the circuit is shown in Fig. 6 In the classifier, the first block indicates the input layer comprising 10 neurons, the center block indicates the hidden layer comprising 21 neurons, and the last block indicating the output layer comprising of 1neuron, respectively. The blocks Fig. 7 Neural network Classifier for single fault Fig. 5 Two layer BPN network topology Here, X1…Xi …Xn indicate the input neurons, Z1 ….Zj …..Zp the hidden layer neurons, and Y1….Yk….Ym the output neurons of the artificial neural network. Vij is the weight from ith input neuron to jth hidden neuron; Wjk is the weight from jth hidden neuron to kth output neuron; Voj is the weight from bias to jth hidden neuron, and W0k is the weight from bias to kth output neuron. The supervised learning in BPN takes place by propagating the node activation function Fig. 8 Performance plot for single fault of input pattern to output nodes. These outputs are compared 309 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, 2010 TABLE V ANN OUPUT FOR RANDOM FAULT CONDITIONS Component Values (R in kΩ and C in nF) Classifier Inputs Settling Peak Fault ID R1 R2 R3 R4 R5 C1 C2 Time Amplitude 1 3 1 4 4 5 5 3.6507 0.5770 F6 1 1.5 2 4 4 5 2.5 1.993 1.2744 F34 1 3 2 4 4 5 2.5 3.9499 1.1012 F14 0.5 1.5 1 4 4 2.5 5 1.3313 0.6645 F52 1 3 2 4 2 5 2.5 4.5108 0.7619 F32 1 3 2 4 6 5 5 3.6338 1.1908 F9 1 3 3 4 6 5 5 4.1115 1.5028 F23 1 3 2 4 4 5 5 4.3247 0.888 F61 in between the input layer and the middle layer indicate the boundaries that can be seen associated with crisp sets, the weight factor (IW {1, 1}) associated with input node, and bias property being termed as vagueness of fuzziness. As a input (b {1}) acts on a neuron like an offset. The blocks in consequence, members of a fuzzy set may possess partial between the middle layer and the output layer indicate the membership to that set as opposed to the concept of crisp sets weight factor (LW {2, 1}) associated with hidden layer, and where an entity is either a member of the set, or it is not. This bias input (b {2}) acts on a neuron like an offset. Fig. 8 shows allows for flexible assignment of degrees of membership to the performance plot for the trained neural network. entities based on their relationship to a set. Also, in fuzzy set theory, variables are described in terms of membership A. Simulation Results functions or “truth value” in relation to a particular fuzzy set, The classifier results for a few randomly generated test the values of the function lying in the range [0,1] [16]. patterns for the filter circuit are shown in Table V. Fuzzy inference systems are a direct application of fuzzy logic and fuzzy sets theory, otherwise known as fuzzy rule- based systems or fuzzy models. Fuzzy inference systems offer VI. FUZZY FAULT DIAGNOSIS SYSTEM a great advantage in being compatible with linguistic concepts The first step in analysing the CUT is to study the response and rules that transpire naturally in human beings. In addition of the circuit to a stimulus signal that is exactly the same as to this, they can be used to effortlessly map inputs and outputs that used for simulation of the circuit behaviour during the that bear a non-linear relationship to each other [17]. A typical FIS is a combination of four sections namely: compilation of the fault dictionary. The stimulus signal, in this • Fuzzifier case, being a unit step signal, the output transient of the given circuit is recorded and the settling time and peak amplitude for • Rule-base that transient output signal are determined. These readings are • Inference engine then fed as inputs to the fuzzy inference system (FIS), which • Defuzzier will carry out the task of generation of an output The fuzzifier transforms the crisp inputs given to the corresponding to the inputs given, the relationship being the system into members of fuzzy sets, which are defined inputs and outputs being a non-linear one. linguistically in agreement with human perception of the Earlier approaches to the diagnosis of faults in analog inputs. This step assigns degrees of truth to each input circuits have relied upon the strength of probability theory to parameter. The fuzzy rule-base is usually made up of IF- recognise patterns in the occurrence of faults assuming THEN statements connected with logical operators, the main statistical random characteristics of the fault conditions and purpose being knowledge acquisition with regard to the the surrounding environment. However, it seems a much input values. In the inference engine, the rules in the rule base simpler proposition to consider faulty networks as fuzzy are evaluated and an output fuzzy set is generated systems since there is hardly a necessity to maintain exacting corresponding to each output variable. These output fuzzy sets levels of accuracy while solving problems connected with the are then converted into crisp values in the defuzzifier section. isolation of faults [15]. With the use of a fuzzy inference The method of fault diagnosis under consideration has two system (FIS), the potential for fuzzy logic in the development time-domain specifications (settling time and peak amplitude) of a model that can characterize results through approximate as the inputs to the FIS, from which a numerical value unique reasoning is utilized for the purpose of identification of faults. to each faulty configuration is derived. The numerical value, Fuzzy set theory is a discipline that revels in uncertainties so obtained for each configuration, depends completely upon and approximations rather than the precise and well-defined the membership functions assigned to each variable and the 310 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, 2010 rules that compose the fuzzy rule-base. The Mamdani model has been chosen to construct the fuzzy resulting effect being to reciprocate the designer’s linguistic inference system as it is very well suited to the simplification interpretation of the input values with relation to the range of of problems involving linguistic rules based on human possible values of the parameters. Such a representation of the experience. The FIS proposed to solve the current problem of time-domain specifications transforms them into linguistic fault isolation takes the form shown in Fig. 9. parameters that can be input to the Mamdani FIS. The type of membership function shown in the Fig. 10 and 11 is known as trimf or ‘triangular membership function’, which is particularly efficient as far as computation time is concerned, due to its simple structure. In a similar fashion, the output variable is also assigned a membership function to make it a linguistic fuzzy variable. The membership function shown in Fig. 12 is divided into areas that represent the different fault IDs that may be arrived at after processing of the inputs using the fuzzy rule base. The Fig. 9 Fuzzy inference system horizontal scale, containing values that will be displayed as the The Mamdani fuzzy inference model has the distinct output fuzzy block, is chosen arbitrarily as per convenience, advantage of greater interpretability of quantities when provided it allows for enough values to distinguish one faulty compared to other fuzzy models such as the Takagi-Sugeno configuration from the other. fuzzy logic system. Interpretability refers to the quality of possessing an inherent connection with the natural way of description of quantities through linguistic expressions. These linguistic variables are described by their respective membership functions, both the inputs and the outputs expected to be fuzzy variables. The membership functions for the inputs to the current FIS, ie. the time-domain response parameters are as follows: Fig. 12 Membership for fault ID The fuzzy rule base is an aggregation of IF-THEN- rules that define the relationship between the input and output fuzzy sets. In effect, the use of linguistic variables and fuzzy IF-THEN- rules exploits the tolerance for imprecision and Fig. 10 Membership function for settling time uncertainty. In this respect, fuzzy logic mimics the crucial ability of the human mind to summarize data and focus on As seen above, the range of occurrence of each input decision-relevant information. Since there are 61 different variable is divided into five regions, namely-‘Very low’, configurations of the CUT in the fault dictionary, there must ‘Low’, ‘Medium’, ‘High’, and ‘Very high’. exist 61 fuzzy rules for the problem under consideration. The The choice of areas over which these classifications format of each of these rules is as follows: IF Settling Time is very low/low/medium/high/very high OR Peak Amplitude very low/low/medium/high/very high THEN Fault is 0-5/5-10/10-15...........50-55/55-60 OR denotes the fuzzy ‘max’ operator, which selects the maximum of two values. It is also used to symbolize the union of two fuzzy sets. After the OR operation between the two Fig. 11 Membership function for peak amplitude inputs, a fuzzy set is generated as the output. Finally, a extend depend solely upon the knowledge accumulated defuzzification algorithm is implemented on the resultant through simulation of the circuit for all the conditions, the output fuzzy set to calculate the output of the fuzzy system as a precise numerical value. 311 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, 2010 TABLE VII FIS OUPUT FOR RANDOM FAULT CONDITIONS Component Values (R in kΩ and C in nF) FIS Inputs FIS Fault Settling Peak Output ID R1 R2 R3 R4 R5 C1 C2 Time Amplitude 1 4.5 2 4 4 5 5 5.2859 0.8600 3113 F3 1 3 2 4 4 5 2.5 3.9499 1.1012 2977 F14 1 4.5 2 4 6 5 5 4.8269 1.1242 2872 F21 1 3 2 4 2 5 2.5 4.5108 0.7619 2912 F32 0.5 3 2 4 2 2.5 5 2.5534 0.6810 2874 F44 1.5 4.5 3 4 6 5 5 5.4507 1.1908 2792 F49 1 3 3 4 6 7.5 7.5 6.1672 1.5028 3223 F55 1 3 2 4 4 5 5 4.3247 0.888 2847 F61 The centroid method of defuzzification was employed on the VII. DISCUSSION fuzzy set ‘Fault’ to obtain a crisp value which can be Although both fuzzy and neural systems are equally identified easily to isolate faults. The centroid method, accurate in identifying the faulty configurations, an analysis of acclaimed to be the most reliable of all defuzzification the paths taken to reach that final step yields sufficient methods, gives the value corresponding to the centre of the parameters to compare the two systems. Firstly, the time taken area of the fuzzy set as the crisp output, favouring the rule to complete the process is longer with neural systems as with the greatest output area. The crisp value so obtained as compared with the time taken by fuzzy systems. An increase the output of the FIS is unique to each faulty configuration, a in the size of the circuit noticeably increases the time taken by property that can be exploited for the identification of faults in neural networks, this factor not playing a major role in the components that constitute the circuit under test. case of fuzzy systems. The formulation of the rules for the current problem of fault diagnosis can be clearly portrayed through the use of a Fuzzy TABLE VI Associative Memory (FAM) table. Fuzzy associative memory FUZZY ASSOCIATIVE MEMORY TABLE (FAM) is a rule-based system based on fuzzy sets and logic. Peak Fuzzy associative memories embody a bank of fuzzy rules that Amplitude Very reflect expert knowledge in linguistic form. A compound Very \ Low Medium High High FAM rule is a compound linguistic condition: “If X1 is A1 Low Settling and X2 is A2. …and Xn is An then Y is B”. A fuzzy Time associative memory can be used to combine associative F25-F30 F40-F45 F15-F20 F45-F50 memory and fuzzy logic, thus encoding the fuzzy output set Very Low F45-F50 F45-F50 F35-F40 F50-F55 -------- F55-F60 F50-F55 F55-F60 with the fuzzy input set. The framework of FAM allows us to F10-F15 adaptively add and modify fuzzy rules, directly from experts F5-F10 F20-F25 F0-F5 F5-F10 F5-F10 Low F20-F25 or from statistical techniques. A fuzzy associative matrix is F25-F30 F25-F30 F15-F20 F15-F20 F35-F40 constructed to map the input to the associated output by a F40-F45 F0-F5 F0-F5 max–min composition operation. If an input is fuzzy (a degree F0-F5 F15-F20 F10-F15 of membership is provided to indicate the closeness), the F5-F10 F20-F25 Medium -------- F10-F15 F25-F30 F20-F25 F25-F30 output will also be a fuzzy set. FAM is transparent in the F30-F35 F30-F35 F40-F45 sense that knowledge is explicitly revealed in the rules. F55-F60 F45-F50 F10-F15 F20-F25 Here, the two fuzzy variables, settling time and peak High F35-F40 F40-F45 F15-F20 F40-F45 F50-F55 amplitude can be laid out in a 2D matrix such that one F50-F55 F30-F35 F45-F50 variable represents each axis. Each entry in the matrix is the F35-F40 output corresponding to a logical proposition defined by the Very High -------- F30-F35 F55-F60 F50-F55 -------- values of the variables in that particular row and column, as shown in Table VI. This difference in times taken for processing can be The outputs of the suggested FIS for a few randomly attributed to the computational burden that is laid on the manipulated faults are listed in Table VII. It can be inferred processor(s) by either system. Neural networks, with multiple from the table that each faulty configuration gives a unique hidden layers, tend to require greater processing in comparison FIS output thus reducing the process of fault identification to to fuzzy systems. Even with fuzzy systems, experimentation that of mere numerical matching with the previously created was done with two membership functions - the triangular fault dictionary for the same circuit. membership function (trimf) and the Bell membership function (bellmf). The results obtained using both these 312 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 2, 2010 functions were equally good, there being no major difference [2] J. A. Starzy and J. W. Bandler, “Multiport approach to multiple fault location in analog circuits,” IEEE Trans. Circuits Syst., vol. 30, 1983, in their ability to distinguish between the various fault pp. 762–765. conditions. However, it is more favourable to use the [3] M. Tadeusiewic and M. Korzybski, “A method for fault diagnosis in triangular membership function as it is computationally lighter linear electronic circuits,” Int. J. Circuits Theory Applications, vol. 28, than the Bell membership function by virtue of its simple 2000, pp.254–262. [4] G. Fedi, R. Giomi, A. Luchetta, S. Manetti, and M. C. Piccirilli, “On structure. the application of symbolic techniques to the multiple fault location in Apart from this, fuzzy systems can be expected to be more low testability analog circuits,” IEEE Trans. Circuits Syst. II, vol. 45, robust than neural systems because of the ‘fuzziness factor’ Oct. 1998, pp.1383–1388. that allows deviations from the originally programmed pattern. [5] R. Spina and S. Upadhyaya, “Linear circuit fault diagnosis using neuromorphic analyzers,” IEEE Trans. Circuits Syst. II, vol. 44, Mar. Finally, choice of system must be made keeping in mind the 1997, pp. 188–196. kind of data that is available for use. Data that is readily [6] M. Catelani and M. Gori, “On the application of neural network to fault available in structured format is ideally suited for use with diagnosis of electronic analog circuits,” Measurement, vol. 17, 1996, fuzzy systems. On the other hand, in circumstances where pp.73–80. [7] W. Hochwald and J. D. Bastian, “A dc approach for analog fault numerical data is available but there is no apparent way to dictionary determination,” IEEE Trans. Circuits Syst. I, vol. 26, May structure the data, neural systems are more convenient. The 1979 pp. 523–529. structuring can arise out of human perception of quantities, a [8] K. C. Varghese, J. H.Williams, and D. R. Towill, “Simplified ATPG defining quality of fuzzy logic systems. However, prior and analog fault location via a clustering and separability technique,” IEEE Trans. Circuits Syst., vol. 26, May 1979, pp. 496–505. knowledge concerning the data is a necessary requirement in [9] A. Mckeon and A. Wakeling, “Fault diagnosis in analogue circuit using the design of fuzzy systems. Neural networks do not require AI technique,” in IEEE Int. Test Conf., 1989, pp. 118–123. prior knowledge as they are capable of learning and evolving [10] Gertler,J.,J.,.fault Detection and Diagnosis in Engineering Systems”,. through a number of learning algorithms. Marcel Dekker.New York, 1998. [11] Chen,J.,Patton,R.J. “Robust Model-Based Fault Diagnosis for Dynamic systems”,.Kluwer Academic Publishers. Masssachusetts, 1999. [12] V. Manikandan and N. Devarajan “SBT Approach towards Analog VIII. CONCLUDING REMARKS Electronic Circuit Fault Diagnosis” Hindawi Publishing Corporation, The above discussion carries weight mainly when there are Active and Passive Electronic Components, Volume 2007, Article ID 59856, 11 pages. constraints on the memory capacities and operating [13] L.Fausrtt, “Fundamentals of Neural Networks,” Prentice-Hall, Upper frequencies of the processors used to carry out fault diagnosis. Saddle River, NJ, USA, 1994. In the presence of high performance processors, the [14] S.HSU, et al., “Comparative analysis of five neural network models,” disadvantages of prolonged processing duration in neural Remote Sensing Review, Vol.6, 1992, pp.319-329. [15] Jonghee Lee and Samuel D. Bedrosian, “Fault isolation algorithm for networks are effectively cancelled out, thus equating the analog electronic systems using the fuzzy concept”, IEEE Transactions efficiencies of both fuzzy and neural systems. Hence, on Circuits and Systems, Vol. CAS-26, No. 7, July 1979. depending upon the availability of hardware, one must decide [16] Dubois, Prade, “Fuzzy sets and systems,” Academic Press, New York, upon the priority to be given to reduction in processing time in 1980. [17] Serge G, “Designing Fuzzy Inference Systems from Data: order to be better able to choose between neural and fuzzy Interpretability oriented Review”, IEEE Transactions on Fuzzy logic systems. Further, for certain applications where Systems, 2001. robustness of the system is awarded more importance, a fuzzy system will be more beneficial. The experience of the AUTHORS PROFILE programmer in dealing with datasets similar to the one in consideration also influences a choice in favour of fuzzy logic. V.Prasannamoorthy is currently Senior Grade Lecturer in the Department of On the other hand, a lack of such familiarity automatically tilts Electrical Engineering, Government College of Technology, Coimbatore. the balance in favour of neural networks. Hence, based on (phone: +919443750031, e-mail: prasanna_gct1995@yahoo.com) these parameters, a judicious choice of system should be R. Bharat Ram is pursuing B.E. degree in Electrical and Electronics arrived upon. Engineering at Government College of Technology, Coimbatore. REFERENCES V. Manikandan is currently Assistant Professor in the Department of Electrical Engineering, Coimbatore Institute of Technology, Coimbatore. [1] J. W. Bandler and A. E. Salama, “Fault diagnosis of analog circuits,” N.Devarajan is currently Assistant Professor in the Department of Electrical Proc. IEEE, vol. 73, 1985, pp. 1279–1325. Engineering, Government College of Technology, Coimbatore. 313 http://sites.google.com/site/ijcsis/ ISSN 1947-5500

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