PSI - Issue 44

Gianluca Standoli et al. / Procedia Structural Integrity 44 (2023) 2066–2073 G. Standoli et al. / Structural Integrity Procedia 00 (2022) 000 – 000

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shapes that are in anti-phasis for corresponding modes. Acceleration files stored through MEMS sensors are initially pre-processed, repeating the operations described for the short-time data. The parameters extraction process is instead operated recurring to two clustering levels. The first step extrapolates modal parameters for every model order, based on two sets of criteria. The first one eliminates poles associated to negative or zero valued damping ratios (Reynders et al. (2012)); the second one is based on the minimization of a two terms objective function (Eq. 1), accounting for modal frequencies variation and MAC values (Pastor et al. (2012)) between poles corresponding to two consecutive model orders (Standoli et al. (2021)):

(1)

Moreover, the code evaluates the relation between the identified parameters and the environmental data regarding external temperatures, relative humidity, and wind speed (Fig. 4). A linear increment of frequencies values with the increment of temperature was observed, while an opposite relation stands between frequencies and relative humidity. Wind speed increment tend to produce a decrement in the modal frequencies associated to the first two modes, while this relation is reversed for the last two modes.

Fig. 4. Example of correlation between the first frequencies and the environmental parameters (Temperature, Relative Humidity and Average Wind Speed: (a) left tower; (b) right tower

Once the dependencies are established, the influence of environmental agents is removed from the tracked frequencies through the application of linear regressive methods. In Table 2 the results of this operation are reported, showing the mean values for frequencies. The mean values are calculated both for the parameters tracked till June 2021, both considering the two years of monitoring, to evaluate possible variation in the dynamic behaviour of the towers in time. As it possible to see, no significant variations are registered, meaning no valuable changes occurred.

Table 2. Variation of tracked frequencies between June 2021 and June 2022.

Left Tower ̅̅̅ 2021 [Hz] ̅̅̅ 2022 [Hz] 1.902 1.904

Right Tower ̅̅̅ 2021 [Hz] ̅̅̅ 2022 [Hz] 1.807 1.815

Mode

Δ f [%]

Δ f [%] 0.430 0.239 0.003 0.045

1 2 3 4

0.084 0.377 0.012 0.024

2.318 4.286 5.916

2.309 4.287 5.914

2.337 4.104 5.871

2.332 4.104 5.873