Resilience-based design (RBD) modelling of civil infrastructure to assess seismic hazards - Seismic Risk Analysis and Management of Civil Infrastructure Systems - page 279

parameters that depend on the type of a community considered. Therefore
at time t after the crisis, functionality is given by
Qt

() = ( )

f t x , ,.., x n

[11.8]

1

where x 1 , . . . , x n are the parameters involved in describing the recovery
model. Several models have been presented in Cimellaro et al. (2010a) to
describe the recovery function which can be either empirical or analytical ,
depending on the source of data and the type of analysis.
Empirical recovery functions are based on test or fi eld data interpretation
and engineering judgment. They can be built using the maximum likelihood
method based on data reported from past extreme events as well as Monte
Carlo simulations of specifi ed community models. Since the complexity of
the problem changes case by case, no specifi c model is presented in this
part.
Analytical recovery functions are developed from community response
data obtained through analysis of the system using numerical simulations.
For example, for the case of earthquake events, they can be obtained from
nonlinear time history analysis, response spectral analysis, etc.
Since the recovery process is characterized by uncertainties, the param-
eters considered in the model are modelled as random variables in order
to quantify the uncertainties in the system. These uncertainties can be
divided in aleatoric and epistemic uncertainties (Ang and Tang, 2007).
Several models can be fi tted to the observed data and, subsequently,
model selection can be carried out using as goodness of fi t measure, such
as the r 2 value. The essential requirement of the analytical recovery models
is simplicity, therefore the model should be selected so that it is easy to fi t
to real or numerical observation data and the number of parameters
involved should be as low as possible. Five different recovery models are
reported below, grouped according to the two control periods ( short term
vs long term ). Long-term recovery models are used when the reconstruction
phase needs to be modelled, while short-term recovery models are used
when the emergency phase after the extreme event needs to be focused
upon.
Several long-term recovery models are proposed in Cimellaro et al.
(2010a). They can be grouped according to the number of parameters (one,
two or three parameters). Complex recovery models with more parameters
can be proposed, but simpler mathematical models have benefi ts over more
complex ones. They have fewer unknown parameters, and thus it is easier
to fi t to data (fewer experiments are needed). There is also less chance of
'overfi tting'. With more free parameters, a model can be made to fi t any
data; however, at best the exercise is little more than curve fi tting (with little
meaningful understanding gained), while at worst the model may give an
overconfi dence in its predictive ability.