Risk assessment and management of civil infrastructure networks: a systems approach - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 440

all actual vertices v p in V i ( lv ) and v q in V ( lv ) . Therefore, the probability of
failure of a fi ctitious edge u at level lv is given by the product of individual
failure probabilities of links e pq since they comprise parallel arrangements.
Once the fi ctitious node probabilities are estimated, global reliability cal-
culations on the corresponding fi ctitious network can be made. At interme-
diate levels of description, the computational cost is still much lower than
the cost of evaluating the entire network, even if network reliability com-
putations are required at every fi ctitious node. The cost of such effi ciencies
is the loss in accuracy that results from assuming that elements within dif-
ferent clusters fail independently, which is not necessarily true.

17.4.2 Vulnerability analysis
A global measure of network vulnerability evaluates the change in perfor-
mance when the network is exposed to a set of damaging scenarios d i

D
( D is the set of all possible failure scenarios) (Latora and Marchiori, 2005;
Bell et al. , 2008; Schuchmann, 2010). Then, if F ( S ) defi nes a performance
measure of the system S , the relative drop in the system's performance for
a given scenario d i V ( S

∈

| d i ), can be computed as follows:

() − ( ) FS FSd

FS

( ) =

i

VSd [17.2]

i

()

where F ( S | d i ) describes the system's performance measure given the occur-
rence of damaging scenario d i . Because a comprehensive vulnerability
analysis requires the assessment of all d i in D , the overall vulnerability can
be calculated as V ( S )

d i ) (Latora and Marchiori, 2005), which is
computationally unfeasible for complex networks. Connectivity loss (or
increase in shortest-paths) can be used in a similar way (Albert and Bara-
basi, 2002; Gong et al. , 2008; Barzel and Biham, 2009). Further discussion
on available approaches to assess vulnerability can be found in Gómez et
al. (2011b).
A network vulnerability analysis includes the following tasks: (1) system
identifi cation and characterization; (2) defi nition of evaluation criteria (e.g.,
form and strength); (3) identifi cation of possible failure scenarios; (4)
assessment of potential losses per scenario; and (5) evaluation of vulnerabil-
ity indices.
The proposed analysis focuses on identifying critical links for connec-
tivity (i.e., importance) while taking into consideration failure probability
throughout the hierarchy. Fictitious nodes at high hierarchical levels consist
of macroscopic network components which represent areas of major impor-
tance in a system, e.g., ports that should maintain connectivity with indus-
trial areas. The clustering process maximizes density within clusters and

= max i V ( S |