Seismic vulnerability analysis of a complex interconnected civil infrastructure - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 460

￿ Area-like (buildings): a special category specifi cally intended to model

large portfolios of residential, offi ce and commercial buildings (making
up the largest proportion of the built environment). For the most
common analysis resolutions, due to computational and information
constraints, they cannot be modelled individually.

While, quite obviously, systems belonging to the second category can be
described as networks or graphs, the remaining systems are also amenable
to such a description. Further, systems exhibit dependencies that can also
be modelled as edges (often called dependency edges or interface links) of
a larger super-graph, connecting nodes belonging to different component
systems. Network or graph theory is therefore a fundamental layer upon
which the model is founded.
Nonetheless, graph theory can only go so far as the connectivity or integ-
rity of the network is analysed, while the aim herein is to analyse functional-
ity/serviceability in addition to connectivity and network integrity. Graph
theory thus needs to be complemented. The second building block of the
model is object-oriented modelling (OOM). Under this modelling para-
digm, the SOS is described as a set of interacting objects, characterised in
terms of attributes and methods. Objects are instances (concrete realisa-
tions) of classes (abstract templates for all objects with the same set of
properties and methods) (Booch et al ., 2007).
One of the major advantages of OOM is the possibility of including
physical laws and hence simulating the functioning of the system beyond
its connectivity. The second advantage is that it allows the behaviour of the
infrastructure to be emulated as it emerges from that of the individual
objects and their interaction. The third is that the atomisation of the system
into parts allows dealing with the complexity of the infrastructure. As far
as the dependencies are concerned, Rinaldi et al. (2001) identifi ed four
general types: physical, cyber, logical and geographic/geo-spatial. Of these
four categories, it has been argued that the functional and geographic ones
are important (Johansson and Hassel, 2011).
The terms inter-dependence and intra-dependence are sometimes used
to indicate the relation between components belonging to distinct systems
or to the same system, respectively. In the following, dependence or inter-
dependence are interchangeably employed to indicate the former, which in
principle requires ad-hoc modelling with dedicated dependency edges , while
the within-system relations, normally of physical/functional type, are already
included within each system model in the form of components. Their pres-
ence is refl ected in the formulation of the fl ow equations and their effect
emerges in the corresponding solution. It should be noted that the depen-
dency edges can be either uni- or bi-directional with respect to the depen-
dence. A super-graph is always a directed one.