AR+ noise versus AR and ARMA models in SHM-oriented identification

The most common approach in Structural Health Monitoring (SHM) consists in performing accelerometric measures of the response of the monitored structures to natural or artificial stimuli (e.g. wind, urban traffic, seismic events etc.) and in modeling the dynamic behavior of the structure on the basis of these measures. The models can be used, in particular, to extract and compare the main modes i.e. the main resonant frequencies and in comparing these frequencies with those concerning the initial state of integrity of the building. This paper compares the results given by traditional AR and ARMA models with those offered by AR+noise models where an additive observation error is considered and shows that these models can offer some advantages in SHM applications in that describe more accurately the stochastic context of the process. The comparisons have been performed on two different sets of data: the first one has been collected on an industrial building in occasion of an heavy seismic event whereas the second one has been collected on a medieval tower excited by urban traffic.