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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
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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
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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.
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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
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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
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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.
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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
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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 2, 2010
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structure. the application of symbolic techniques to the multiple fault location in
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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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structuring can arise out of human perception of quantities, a [8] K. C. Varghese, J. H.Williams, and D. R. Towill, “Simplified ATPG
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systems”,.Kluwer Academic Publishers. Masssachusetts, 1999.
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frequencies of the processors used to carry out fault diagnosis. Saddle River, NJ, USA, 1994.
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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
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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: 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.
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