10 Autoregressive Model Applied to the Meazza Stadium for Damage Detection 105 Fig. 10.9 First versus second frequency at daytime 3 3.05 3.1 3.15 3.2 3.25 3.3 5.1 5.2 5.3 5.4 5.5 Frequency [Hz] Frequency [Hz] Fig. 10.10 First versus second frequency at night-time 3 3.05 3.1 3.15 3.2 3.25 3.3 5.1 5.2 5.3 5.4 5.5 Frequency [Hz] Frequency [Hz] 10.4.1 Basic Statistic At first, we divide the record between daytime and night-time to verify if it is possible to distinguish two different trends. We consider few hours for each day and night. The data considered in this section are form January 2011 to July 2011. During daytime the environmental conditions could be quite different from those recorded during night-time, for instance the maintenance staff might work on the stand with producing light forcing; conversely, during the night-time this is unlikely to happen. Moreover, close to the stadium there is the underground building site whose effect is more important during daytime. The same could be affirmed for road traffic. Finally, another possible contribution creating a gap between the two conditions (day and night), is temperature, not just having a seasonal trend but also a daily one. First, we focus on the ratio between the two considered frequencies (2nd and 5th mode), in order to investigate if the different environmental and operational conditions can influence this relationship. In Figs. 10.9 and 10.10, although a not negligible dispersion is present, it is possible observe that, in the two considered situations, a similar trend is exhibited. Besides, it could be recognized a moderate linear trend, due to the linear behaviour of the structure under low load (although points are really concentrated). If a damage occurs, the ratio between the first and second frequency changes, but an uncertainty band has to be fixed, so that if changes are within this band, no damage is supposed to be present. Unfortunately this band is expected to be rather wide. Another aspect which has been considered is the relationship between temperature (provided by a weather station on the stadium roof) and the natural frequencies. For instance, Figs. 10.11 and 10.12 show the result for the frequency around 3 Hz (2nd mode).
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