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problem of real-time or near-real-time decision-making (analyst positioned
within the time-frame of interest, as in Section 18.2). This is due to its capa-
bility of updating random variables and probabilities associated with system
states real-time under a continuous stream of incoming information on the
states of an enlarging set of components in the aftermath of an earthquake.
Two problems, however, may severely hinder its application to problems of
realistic dimensions.
The fi rst one is the computational effort, which can be enormous since
the system state must be known in advance for all possible combinations
of the components' states. As it is frankly put in Der Kiureghian (2009):
m
1
m
2
.
. .
m
n
distinct confi gurations, where
n
denotes the number of components
[and
m
i
is the number of possible states of component
i
]. For example
a [system] with two-state components, has
N
After an earthquake, the [system] assumes one of
N
=
2
n
distinct confi gurations.
[. . .] For each of these distinct confi gurations one can perform
disciplinary analysis (e.g., water, power, traffi c connectivity or fl ow
analysis) to determine the state of the infrastructure and whether or
not it performs the intended function. . . . It should be obvious that a
[system] with a large number of components can have an extremely
large number of distinct confi gurations. Therefore, disciplinary analysis
will have to be performed for a very large number of cases. One of the
challenges in infrastructure risk assessment is to devise methods to
handle the large amount of computations.
=
The second problem is that the BN model itself is a directed acyclic graph,
where nodes represent uncertainties (random variables) and edges describe
their statistical dependence. The size and topology of this graph are related
to those of the corresponding physical system. Therefore, its very construc-
tion, before even thinking of carrying out inference upon it, can be a daunt-
ing task for a problem of realistic dimensions. Hence, a way to automatically
set up a BN given the infrastructure and hazards is needed for practical
application.
18.7.3 Implemented simulation framework
The
Simulation
class currently has two sub-classes only:
MonteCarlo
and
ImportanceSamplingKmeans
. The former is a straightforward implementa-
tion of plain Monte Carlo (MC) simulation, while the latter is an imple-
mentation of the importance sampling method (ISKm) described in Jayaram
and Baker (2010). This importance sampling method is quite effective for
'developing a small but stochastically representative catalogue of
earthquake ground-motion intensity maps that can be used for risk
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