Fault Diagnosis Algorithm for Analog Electronic Circuits based on Node-Frequency Approach

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					                                                   (IJCSIS) International Journal of Computer Science and Information Security,
                                                   Vol. 8, No. 4, July 2010

          Fault Diagnosis Algorithm for Analog Electronic
            Circuits based on Node-Frequency Approach
                                               S.P. Venu Madhava Rao


                                  Dr. N. Sarat Chandra Babu & Dr. K. Lal Kishore

Abstract: In this paper we present a novel approach to            In [5] a new method in the construction of fault
analog electronic circuits fault diagnosis based on               dictionary is proposed where a combination of
selection of both nodes and frequency for the first time          sensitivity based and information channel based
as far as we know. Two fault isolation and localization           approaches are used. Also the construction of integer
algorithms are presented in this paper. The first                 coded fault dictionary using Quasi-Hamming distance
algorithm selects nodes and frequencies which isolate             is proposed in this paper. Heuristic methods using
all or desired number of faults. The second algorithm             evolutionary computation in combination with the
presented converts the fault dictionary contents into             Fuzzy logic is presented in [6], the main purpose of
binary form. Importantly this helps in the automation             such a combination is to generate an optimized
of the fault diagnosis process.                                   frequency test set and also ambiguity sets are provided
                                                                  to avoid take care of tolerance effects. An SBT based
Keywords: Fault Dictionary, Fault Isolation Table,                approach is proposed in [7] where the fault dictionary
Binary dictionary, singletons.                                    is constructed using test node voltages and the method
                                                                  used to approximate is Section wise piecewise linear
                    I. Introduction                               (SPLF) method. A procedure for the selection of test
    Analog Fault Diagnosis has been of immense                    frequencies is presented in [8]. This is based on the
research interest for the past three decades and                  evaluation of algebraic indices and the inverse norm of
continues to sustain the same zeal even today. The                a sensitivity matrix of the circuit under test. In [9], [10]
main challenges today in analog fault diagnosis are to            and [11], fault diagnosis based on different types of
design universally accepted fault models, cost                    neural networks has been proposed. In [12] knowledge
effective, faster and accurate diagnosis of faults.               base and fuzzy logic have been used in fault diagnosis.
Importantly all this is desired even in the presence of           The knowledge base is developed in two ways, one by
inherent characteristics of analog circuits like                  simulations and the second is based on heuristic
tolerances, non linearity, in accessible test nodes etc.          symptoms observed by the operator. In [13] the
                                                                  ambiguity sets are divided based on the lowest error
There are two categories of analog circuit fault                  probability in the construction of fault dictionaries is
diagnosis: Simulation before test (SBT) and                       proposed. This paper used Monte Carlo techniques for
Simulation after test (SAT) [1]. The SBT approach                 sensitivity analysis. In [14] a fault threshold function
involves the generation of fault dictionary by                    and a fault criterion have been proposed for the fault
simulating the circuit and then using pattern                     diagnosis of circuits with tolerance. An algorithm is
recognition to identify the faults. This is the most              proposed in [15], which aims to reduce the size of the
popular method adopted. In SAT approach sufficient                fault dictionary. In [16] and [17] different methods and
measurements are needed to identify faulty parameters.            algorithms are used to reduce the size of the fault
In the SBT approach construction of fault dictionary is           dictionaries. In [18] time slot specification based
an efficient method. Different test measurements like             approach is used in analog fault diagnosis. For this
node voltages, current sources, branch currents,                  built in current sensors and test point insertion is used.
frequency measurements etc are used in the                        A sensitivity based approach using randomized
construction of fault dictionaries [2]. There are some            algorithms is used to diagnose soft faults in [19].In
algorithms developed to find out testable                         [20] the algorithm proposed tries to find the minimum
measurements using numerical approach in [3] and [4].             number of test point for maximum fault isolation. This
                                                                  approach is based on information measure of the test

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                                                                                              ISSN 1947-5500
                                                    (IJCSIS) International Journal of Computer Science and Information Security,
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points. The diagnosis proposed in this paper [21] is               ambiguity sets. Then the original readings are replaced
based on global sensitivity analysis method. Also                  by integer numbers indicative of the ambiguity set to
fuzzy logic is used to obtain the sensitivity curves. In           which these values belong.
[22] an efficient method is applied in the selection of
test nodes. This is done by searching for the minimum              The test frequency set is represented by f1 to fM, where
entropy index based on the available test points. An               N is the number of frequencies chosen.
efficient graph based method is proposed in [23].This
method can be used to select optimum test point                    The nodes are represented by n1 to nP, where P
selection and also can be sued to build DFT. Efficient             represents the total number of nodes.
Inclusion methods and Exclusion methods are                        The faults are represented by F0(nominal value) to FN,
proposed in [24] to select or de select test nodes, in             where N represents the total number of faults.
other words the faster selection of optimum test points.
A novel multi frequency approach is proposed in [25]               Algorithm 1:
which drastically reduce the number of test frequencies
needed to achieve maximum fault diagnosis. The                     Step 1: Select the test frequency set (f1 to fM).
reduction achieved is better than any known methods.
The method proposed in [26] consists of two parts.                 Step 2: Select the test nodes (n1 to nP) which are
One is the creation of fault dictionary consisting of              accessible for each frequency.
nominal and faulty states of the components and
                                                                   Step 3: Note the actual readings of the circuit for the
second is a novel fault detection and localization
                                                                   test frequency set and nodes chosen in steps 1 and 2.
                                                                   Step 4: Form the integer coded dictionary using the
This paper proposes a novel approach where both test
                                                                   ambiguity sets.
node and multi frequency techniques are used. This
approach is used to diagnose all the faults or the                 Step 5: Identify unique integer codes called singletons
desired number of faults.                                          for each row i.e. for each of the nodes selected.
             II Node-Frequency Approach                            Step 6: Identify the node (nK) which has maximum
                                                                   number of singletons for a frequency fJ., where 1<K≤P
In the analog fault diagnosis the prominent methods
                                                                   and 1<J≤M. Select this node-frequency (nK, fJ) pair. If
used are multi node or multi frequency measurements.
                                                                   more than one node satisfies this condition, then go to
The research so far has been on developing methods to
                                                                   step 9.
find out optimum number of test nodes or test
frequencies that can identify the desired faults. This in          Step 7: If the number of singletons is equal to N+1,
some cases leads to more number of measurements                    then go to step 12. If else go to next step 8.
being made thus drastically increasing the size of the
dictionary.                                                        Step 8: Call Algorithm 2, to form binary dictionary
                                                                   which helps in identifying other nodes from the
In this paper we have taken basically nodal analysis               remaining (P-1) nodes belonging to the frequency fJ,
and then a choice of test frequencies is made based on             which can identify different faults. If all faults are
[27]. The proposed algorithm selects the nodes and                 isolated then go to step 12.
frequencies which isolate all or desired faults.
                                                                   Step 9: Find the total number of singletons for each
In this paper two algorithms are presented. The first              test frequency. Then choose the node belonging to the
algorithm is for fault isolation and localization. The             frequency which has the maximum number of
second algorithm converts the integer coded fault                  singletons. If more than one frequency satisfies this
dictionary into a binary dictionary which helps in                 condition choose any one of the nodes randomly.
faster fault isolation.
                                                                   Step 11: If all the faults or desired number of faults are
The actual measurements of the CUT are noted down                  not isolated, then repeat steps from 6 with the next
and these values are normalized if necessary. From                 highest number of singletons.
these values we form ambiguity sets. Now we
construct another table called integer coded table using           Step 12: Stop

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Algorithm 2:                                                            Table 1: Actual readings of the imaginary CUT

Step 1: Replace all the singletons by the value ‘1’ and                  Node       Nominal Fault-1 Fault-2 Fault-3
others by ‘0’ in the integer coded table, resulting in a
binary table.                                                           Node-1         1.22          0.33         0.78         0.34

Step 2: If nK is the node chosen, then calculate (nM-                   Node-2         1.33            0          0.09          2.1
nK), where 1<M≤P, thus forming another table called
Node-Wise Fault Isolation table. This results in three                  Node-3         1.45            0          0.99          2.5
values 0,-1 or 1. The value ‘0’ indicates that the fault
has been identified by both nM and nK or both the
nodes did not isolate the fault, whereas ‘-1’ indicates            As seen from the Table 1 above, we see that for
that the fault has been isolated by only nK and ‘1’ is an          node -1 measurement, fault-1 and fault -3 have almost
indication that the fault has been identified by the node          the same value and thus belong to the same ambiguity
of interest i.e. nM. Therefore choose the node nM which            group. Also these two values are the least among all
has maximum number of 1’s.                                         and are assigned values ‘1’. The other values do not
Step 3: Check the total number of faults isolated by the           belong to any ambiguity group and are assigned values
                                                                   2 for fault-2 and 3 for nominal, based on the ascending
nodes nk and nM. If this sum is equal to P, then Stop,
otherwise choose the node which has the next highest               range of the values. Using the same procedure for all
                                                                   the remaining nodes, integer coded fault dictionary is
number of 1’s.
                                                                   formed and is shown in Table 2.
Step 4: Repeat step 3 till the desired fault isolation is
                                                                             Table 2: Integer Coded Fault Dictionary
achieved or no further isolation is possible.

Step 5: Return to Algorithm 1                                            Node       Nominal Fault-1 Fault-2 Fault-3

 III. Integer coded dictionary based on ambiguity sets                  Node-1           3             1            2            1

The formation of the Integer coded dictionary based on                  Node-2           2             1            1            3
ambiguity sets is illustrated by an example in this
                                                                        Node-3           3             1            2            4
section. Assume that the actual readings of an
imaginary circuit under test are given in Table 1
                                                                   In the Table 2, we see that node-1 has 2 singletons,
                                                                   node-2 has 2 singletons and node 3 has 4 singletons.

                                                                                              IV Illustration

                                                                   The circuit used here is a 2nd order Butterworth High
                                                                   Pass Filter as shown in Fig. 1. The circuit has been
                                                                   simulated using Tina Spice software.

                                                                   The faults chosen are taken as 50% increase or
                                                                   decrease in the component values. Thus CUT has been
                                                                   simulated for these faults by changing the component
                                                                   values by ±50%.

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                               Figure 1: Second Order Butterworth-High Pass Filter

                                                  R2                                              R3

                                                                                                             V1 15
                                     1                                                                   6                            4
                      C1                     C2                     2           3       +         OP1


                                                                                                 V2 15

                                                                                                                                             R5 10k


Using the Step1 from the Algorithm 1, we have                           that all these nodes are accessible. Using Step3
chosen the test frequency fT= {500Hz, 800 Hz,                           and 4, the CUT has been simulated and the
1000Hz, 1200Hz, and 1500Hz}. From Step 2,                               integer coded dictionary as shown in Table 3 is
we have chosen four nodes with the assumption                           formed based on the actual readings.

                                Table 3: Integer coded Dictionary for the HP Filter


Nodes/Faults     F0    F1            F2      F3         F4      F5          F6              F7                 F8        F9       F10       F11       F12

    N1           5         7             2   4           7          6       4               8                        3    8         1            6      4

    N2           2         3             1   2           3          2       2               5                        6    4         1            4      1

    N3           2         3             1   2           3          2       2               5                        6    4         1            4      1

    N4           5         6             2   4           9          7       3               10                       1    7         1            8      1

                                                       Frequency =800 Hz

    N1           7         6             3   5          11      10          4               12                       2    9         1            8      4

    N2           6         5             4   5           9          7       5               10                       1    7         3            8      2

    N3           6         5             4   5           9          7       5               10                       1    7         3            8      2

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    N4          7      6      5         5        12   10        4       11       1        8        3         9         2


    N1          4      3      5         3        8     6        3       7        1        5        2         5         3

    N2          6      5      7         5        9     8        4       10       1        7        3         8         2

    N3          6      5      7         5        9     8        4       10       1        7        3         8         2

    N4          6      5      7         4        12   10        3       11       1        8        3         9         2

                                            Frequency= 1200 Hz

    N1          5      3      9         4        10    7        3       8        1        6        2         6         4

    N2          6      4      9         5        11    8        4       10       1        6        3         7         2

    N3          6      4      9         5        11    8        4       10       1        6        3         7         2

    N4          6      5      9         4        11    9        3       10       1        7        4         8         2


    N1          5      2      8         3        7     6        2       6        1        5        3         5         4

    N2          4      3      9         3        8     6        3       7        1        4        3         5         2

    N3          4      3      9         3        8     6        3       7        1        4        3         5         2

    N4          7      5     11         4        11   10        3       9        1        7        6         8         2

The number of singletons for each node for the              As seen from the Table 4, node1 and node 4 of
whole frequency set is calculated (Step 5) and              frequency set f2, and node 4 of frequency set f3
tabulated in Table 4. Here the frequencies are              have maximum number of singletons equal to
f1=500Hz, f2=800Hz, f3=1000Hz, f4=1200Hz                    11, i.e. these nodes can isolate 11 of the total
and f5=1500Hz.                                              thirteen faults. We have chosen node 1(or even
                                                            node 4 can be chosen) of the frequency set f2 i.e.
      Table 4: Total number of singletons                   800Hz as it has maximum number of total
                                                            singletons (step 9). As the condition mentioned
  Node/Freq     f1    f2     f3    f4       f5              in step 7 is not satisfied, binary table is formed
                                                            as per step 8.
      N1        4     11     6     7        4
                                                            The binary table is formed replacing Table 3
      N2        2     8      7     9        7
                                                            contents by either ‘0’ or ‘1’. All the singletons
      N3        2     8      7     9        7               are replaced by ‘1’and ambiguity sets by ‘0’
                                                            (step 1 of Algorithm 2). The binary fault
      N4        8     11    11     9        9               dictionary is shown in Table 5.

     Total      16    38    31    34        27              After the execution of the step 2(Algorithm 2),
                                                            the results are shown in the Node-wise Fault
                                                            isolation Table 6.

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                                               Table 5: Binary Dictionary

                                                     Frequency: 800Hz

                     Nodes F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12

                       N1      1     1    1      1     1     1      0      1   1    1     1      1     0

                       N2      1     0    1      0     1     0      0      1   1    0     1      1     1

                       N3      1     0    1      0     1     0      0      1   1    0     1      1     1

                       N4      1     1    0      0     1     1      1      1   1    1     1      1     1

                                    Table 6: Node-Wise Fault Isolation Table

                                                     Frequency: 800Hz

                     Nodes     F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12

                       N1      1     1    1      1     1     1      0      1   1    1     1      1      0

                     N2-N1     0    -1    0     -1     0     -1     0      0   0   -1     0      0      1

                    N3- N1     0    -1    0     -1     0     -1     0      0   0   -1     0      0      1

                    N4- N1     0     0    -1    -1     0     0      1      0   0    0     0      0      1

From the Binary dictionary of Table 5, we can                           is achieved by a single test frequency of 800Hz
see that the faults isolated are F0, F1, F2, F3, F4, F5,                and nodes 1 and 4.
F7, F8, F9, F10, and F11, where as faults F6 and F12
are not isolated. The faults not isolated is                                             V. Conclusions
deduced from the ‘0’ entry in the corresponding
columns. As seen from the Table 6, the total                            In this paper we have presented a novel method
number of 1’s is two for (N4-N1), one for (N3-                          using node-frequency approach in analog fault
N1) and (N2-N1). So we choose the (N4-N1)                               diagnosis. We have presented two algorithms,
column, i.e. node 4 is chosen. The faults isolated                      the first one for choosing the frequencies and
by this node 4 are F6 and F12. As seen these are                        nodes for the desired fault isolation and the
the faults which are not isolated by node 1.                            second is for the generation of binary
                                                                        dictionaries. The effectiveness of these two
In the example discussed in this paper we have                          algorithms was demonstrated using a HP filter
been able to achieve 100% fault diagnosis. This                         circuit.

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