Time Domain Analysis Based Fault Diagnosis Methodology for Analog Circuits - A Comparative Study of - PDF

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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
                                 Department of Electrical Engineering, Government College of Technology
                                                           Coimbatore, India
                                Department of Electrical Engineering, Coimbatore Institute of Technology
                                                           Coimbatore, India

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

                                                                                                           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
Fig. 1. The Sallen-Key bandpass filter is a second order                                                                                                                 F2

active filter, which is greatly appreciated for its simplicity                                                                                                           F3
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
order filters. The op-amp provides buffering between filter                                                                                                              F8
stages, so that each stage can be designed independently. This                                                                                                           F10

circuit is suitable for filters which have complex conjugate                        0.5                                                                                  F11
poles. When implementing a particular transfer function, a                                                                                                               F13
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

complete filter.
                                                                                                       Fig. 2 Step response curves for single faults

                                                                                                                                         STEP RESPONSE


                                                                                               0.8                                                                               F18
                                                                                               0.6                                                                               F21


               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

                                                                                                   Fig. 3 Step response curves for double faults

where                                                                                                                                STEP RESPONSE
                                                                                             1.5                                                                                 F35
                                                                                              1                                                                                  F40
The circuit shown in Fig. 1 has the component values that
correspond to the nominal frequency of operation of 25 kHz.

   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

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

                                                                                                                               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
                 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
                                                                                                   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
      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.

                                                                                                 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

                                                                                                          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

                                                                                                      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:

                                                                           Settling Time is very low/low/medium/high/very high
                                                                           Peak Amplitude very low/low/medium/high/very high
                                                                                   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.

                                                                                                     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
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
memory and fuzzy logic, thus encoding the fuzzy output set                 Very Low     F45-F50      F45-F50    F35-F40
                                                                                        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       --------
                                                                                                                F25-F30     F20-F25
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
                                                                                                     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
                                                                                                                            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

                                                                                                         ISSN 1947-5500
                                                                       (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                                 Vol. 8, No. 2, 2010
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that allows deviations from the originally programmed pattern.                      [5]    R. Spina and S. Upadhyaya, “Linear circuit fault diagnosis using
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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
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prior knowledge as they are capable of learning and evolving                        [10]   Gertler,J.,J.,.fault Detection and Diagnosis in Engineering Systems”,.
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                                                                                    [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,”
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                                                                                    [15]   Jonghee Lee and Samuel D. Bedrosian, “Fault isolation algorithm for
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depending upon the availability of hardware, one must decide                        [16]   Dubois, Prade, “Fuzzy sets and systems,” Academic Press, New York,
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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:
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.

                                                                                                                       ISSN 1947-5500