Civil Engineering Reference
In-Depth Information
Sparse regions connecting big clusters
Low redundancy
between
relevant areas
Clusters = macroscopic components
Betweenness
of fictitious links increases
Clusters = nodes
(Betweenness is not so crucial)
17.5
Overall strategy for vulnerability detection.
where
D
(
s
,
t
) is the shortest path between nodes
s
and
t
, whilst
D
(
j
)
(
s
,
t
)
denotes the same index after removing link
j.
The factor
F
strength
(
e
j
) measures the contribution of an actual link to the
failure probability of the fi ctitious link at level
lv
. Because fi ctitious links
are parallel arrangements of actual links,
F
strength
(
e
j
) can be computed as:
∏
∏
()
−
()
Pe
Pe
f
i
f
i
{}
()
=−
i
∈
Φ
\
e
i
∈
Φ
F
e
1
j
[17.4]
strength
j
∏
()
Pe
f
i
{}
i
∈
Φ
\
e
j
\
e
j
denotes the
removal of link
j
and
P
f
(
e
i
) is the failure probability of the
i
th actual link.
The factor
F
strength
(
e
j
) is larger for elements with higher failure probabilities.
In summary,
F
strength
(
e
j
) describes the contribution of the actual edge
e
j
to
the probability of failure of the fi ctitious link to which it belongs.
The proposed vulnerability analysis focuses on identifying critical links
at different levels. An index that evaluates the contribution of an edge to
the system vulnerability can be defi ned as:
where
Φ
is the set of edges that make up the fi ctitious link,
Φ
()
=
[
⋅
[
()
⋅
()
]
()
()
Ve IecF eF
lv
lv
⋅
e
[17.5]
j
j
lv
form
j
strength
j
where
I
(
lv
)
[
e
j
] is an indicator function that denotes whether the actual node
e
j
belongs to a fi ctitious link at level
lv
. Note that only edges that belong to
fi ctitious links will have an impact on the network vulnerability. The weight-
ing factor
c
lv
is a level-dependent coeffi cient based on global descriptors of
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