![](bg7.png)
I
L
2
. To differentiate between these two cases (fault
at B
2
or at B
3
), the minimum index should then be
computed. The branch B
2
is directly linked to R
3
,
thus if the fault is in this branch, the minimum
index is I
L
3
. If there was no exclusive minimum
min(I
L
i
) = I
L
1
= I
L
2
, then the fault is in the com-
mon branch of the two receivers as in the case of
fault in B
3
.
4 CONCLUSIONS AND FUTURE
WORK
In this paper, a fault detection and localization
methodology based on the transfer function H( f ) is
proposed to detect a soft fault. This methodology is
based on two indices. At first, the detection index is
computed. Once the fault is detected by one of the
receivers, the localization index is computed at each
endpoint of the network. The localization indices are
checked against one another to verify whether they
are equal or not. The results of these tests are com-
pared to each branch fault’s signature in the proposed
signature matrix. The proposed matrix is constructed
with respect to the network topology. To illustrate our
proposal, two bus networks are considered: a degrad-
ing two nodes network and an Y-shaped (one node)
network.
Further work will be realized to expand the valid-
ity and study the sensitivity of the detection and lo-
calization indices, in more complex networks. Also,
it would be interesting to introduce statistical equal-
ity tests for better and accurate comparison between
localization indices when noise is considered. This
approach will be also validated on a test bench that is
under construction.
ACKNOWLEDGEMENTS
This research work is done in the framework of the
ELSAT2020 project which is co-financed by the Eu-
ropean Union with the European Regional Develop-
ment Fund, the French state and the Hauts-de-France
Region Council.
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