PSI - Issue 64

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Luigi Petti et al. / Procedia Structural Integrity 64 (2024) 637–644 Petti L., Lupo C., D’Angelo T., Dallocchio P. & Guizzetti D. / Structural Integrity Procedia 00 (2019) 000 – 000

( ) = 0 2 +∑ ( ∞ =1 cos( 2 )+ sin( 2 )) where: • represents the summation order; • and are the Fourier coefficients; • is the length of the function;

(1)

With this well recognized approach is possible to assess the signal’s frequency content and the relevance, in terms of amplitude, of each component. In this way, for example, it is possible to remove the daily evolution from the structural response, thus enabling a more detailed analysis of potential evolution not related to daily climate variations. By varying the frequency range of the filter, it is therefore possible to deeply assess the daily, weekly or monthly behaviour. To the scope, a low-pass band filter is considered to cutoff the higher frequency content, see Brunton S. L. and Kutz N. J. (2019) Figure 8 shows the comparison between raw and filtered displacement (a) and temperature (b) signals using cutoff frequencies of 0.0417 h -1 (1/24h) and 0.5 h -1 (Nyquist Frequency). The correlation analysis can be now carried out by considering the filtered signals to exclude the effects of daily climate variation, as shown in figure 9.

(a)

(b)

Fig. 8. Comparison between raw and filtered signals: (a) Displacement, (b) Temperature.

(a)

(b)

Fig. 9. Correlation analysis between displacement and temperature after filtering procedure: (a) maximum correlation coefficients (blue points), taking into account the delay in the response and rainy days (red rectangle), (b) correlation coefficients trends considering delays in the response to the thermal variation from 0 to 8 hours. The last figure shows a more stable trend over the time, with scattered points mainly occurring during rainy days. However, the results show few changes in the correlation coefficients, which could be attributed to false measurements