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of correlation obtained by means of computational intelligence. Then, ele-
ments that are merged into small fi ctitious nodes (lower hierarchy levels)
are more correlated than those merged into larger fi ctitious nodes (higher
hierarchy levels). Correlation does not necessarily imply causality, but in
this context, it allows to estimate overall effects of local events, which is
useful as an input to recovery planning. Figure 17.6 illustrates this idea.
The hierarchy-based correlation requires constructing a matrix
C
such
that its
ij
th component denotes the relationship between elements
i
and
j
according to the hierarchical representation of the network. The matrix
C
can be used to estimate the extent of the impact of a failure scenario on
every node as
I
C
*
e
, where the correlation matrix
C
serves as a mapping
from a direct damage vector (failure scenario)
e
containing nodes affected
by an event, onto a vector
I
that denotes how every other node in the
network is affected. Therefore,
I
can be understood as an impact index on
elements due to a damaging event and its propagation.
There are many ways to construct the matrix
C
. For instance, correlation
functions may include functional relationships of the network; Barzel and
Biham (2009) proposed topological and functional criteria to assess correla-
tion. In general terms, the correlation matrix based on hierarchical descrip-
tion of the system can be obtained as
C
ij
=
=
), where
h
is a function
of the level
lv
in the hierarchy at which the decisions will be made and other
h
(
lv
,
Θ
Nodes merged at
top
level
have
lowest
relative
correlation
Sharing a cluster implies
physical/otherwise
proximity
Nodes exhibit
maximum correlation
with themselves
C
B
A
C
(
A
,
B
) >
C
(
A
,
C
) and
C
(
B
,
A
) >
C
(
B
,
C
)
17.6
Hierarchy-based correlation function.
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