Risk assessment and management of civil infrastructure networks: a systems approach - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 439

(i) block sampling techniques, such as the dagger sampling method (Kuma-
moto et al. , 1980); (ii) variance reduction methods like importance sampling,
which can be further improved with random processes including Markov
chains (Au, 2004), and (iii) statistical learning methods, such as neural net-
works or support vector machines (Hurtado, 2007). Finally, recent develop-
ments on subset simulation have become popular in reliability analysis,
which facilitates the computation of reliability in high dimensions (Au and
Beck, 2001) and assessment of seismic risk (Au and Beck, 2003).
The connectivity failure probability problem in a network can be done
by estimating the probability that two nodes remain connected for all pos-
sible failure scenarios. The computational burden of this combinatorial
problem (exponential on the number of elements) might be reduced by
using fi ctitious networks as discussed in Gómez et al. (2011a). The idea is
to solve the failure probability problem for each individual fi ctitious node
and link at a level of abstraction. Then, the reliability problem for the fi cti-
tious network is solved. Figure 17.3 illustrates the general process for esti-
mating reliability at fi ctitious networks. The selection of the level is an
optimization problem that must take computational cost and relevance for
decision-making (i.e., complexity/relevance ratio) into account. At higher
levels, complexity results from solving big fi ctitious nodes, whereas at lower
levels complexity results from solving the fi ctitious network.
Consider a fi ctitious network at level lv obtained after a hierarchical
decomposition of a network. Then, the fi ctitious link E ( lv ) connecting fi cti-
tious vertices V i ( lv ) and V ( lv ) is constituted by N ( lv ) actual links e pq that connect
3. Find global estimation
in terms of clusters
2. Solve small nets within clusters
(e.g., parallel computing)
1. Known individual
probabilities
17.3 Methodology for hierarchical reliability assessment.