Analysing time dependent problems

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.