Inverse analysis for time dependent problems is discussed i
n this chapter. When time
dependent processes are analysed, further uncertainties c
ome from initial conditions
as well as from time dependent boundary conditions and loads
, in addition to model
parameters. Inverse modelling techniques have been specifi
cally developed for this
class of problems, which exploit the availability of a set of
measurement and/or mon-
itoring data at given locations at subsequent time instants
. Sequential Bayesian data
assimilation is introduced, and a brief review of filtering t
echniques is given. In fil-
tering the problem unknown is the time evolution of the proba
bility density function
of the system state, described by means of appropriate time d
ependent variables and
time invariant parameters, conditioned to all previous obs
ervations. Particle filtering
is chosen to conceptually illustrate the methodology, by me
ans of two simple introduc-
tory examples
