## 3 Test and Results
### Case Study  
For the case study, a wind farm was chosen located in Tarsia, Southern Italy. Figure 7 displays the geographical location (a), an aerial Google(r) image (b) and a photo of the wind farm (c). The wind farm is made up of 22 2.0 MW wind turbines, mounted on 65 m tall towers. The turbines are Games(r) G90, characterized by a three-blade rotor and a diameter of \(\phi\) = 90 m. The swept area is A = 6362 m\({}^{2}\) and the cut-in wind speed is v = 3.0 m/s. The tower has a truncated cone shape, the diameter is \(\phi_{\rm b}\) = 4.034 m at the base and \(\phi_{\rm t}\) = 2.314 m at the top; the height is H = 65 m.  
Figure 6: Sketch of proposed methodology to estimate vibration frequencies by the joint use of TLS and GB-RAR techniques. Figure 7: Google(r) images of the study area: (**a**) geographic position; (**b**) wind farm area (the investigated tower is circled in red); (**c**) panoramic view. The monitored wind tower is located at the most eastern side, where on the acquisition day the wind speed was greater than the threshold of v = 3 m/sec necessary to activate the wind turbines. The wind direction was almost constant during data acquisition, with a prevalent direction from the north-east, with an azimuth angle of 69\({}^{\circ}\). The rotations of the nacelle during the data acquisition reached a maximum value of 5\({}^{\circ}\), so they had no appreciable effect on the results. A topographic survey was carried out in order to obtain a local reference system for all acquisitions. The survey made it possible to have a single reference also for the heights; zero was fixed at the base of the tower, not visible from the TLS and the GB-RAR up to the height of 1.80 m. For the alignment of the acquisitions, a TS Leica TP 1201+\({}^{\circledR}\), Leica Geosystem AG, Heerbrugg, Switzerland (angular accuracy 1\({}^{\prime\prime}\), distance accuracy \(\pm\) 1 mm \(\pm\) 1 mm/km) was used. The acquisitions from TLS and GB RAR were carried out simultaneously, from 12.30 to 14.10 Central European Time (CET) on 17 July 2019. The TLS, in line scanner configuration, was placed with the main axis vertical, so that the zenith angles of the laser beam varied between 30\({}^{\circ}\) and 130 \({}^{\circ}\). The maximum scan speed of 120 lines/sec. was selected. The time taken per scan is \(3.326\times 10^{-3}\) sec, while the time between two consecutive lines is \(8.324\times 10^{-3}\) sec, with a time gap of \(4.998\times 10^{-3}\) sec due to the geometry of the multi-facet mirror. The time taken to scan the only tower is \(1.126\times 10^{-3}\) sec. Each line scanned describes a section comprising the wind tower and the ground between the TLS and the tower. Each TLS scan line provides a set of 140 point-like distance measurements, covering the whole tower. Given the scan speed of 120 lines per second, several thousand lines were acquired for each acquisition session. For the processing of the lines, measurement points near the connection of the nacelle were excluded to avoid outliers due to the pitch motion. The best-interpolating polynomial was obtained using the procedure described in Section 2.3.2. At this point, for a given height, it was possible to compute the value of the horizontal distance from the TLS for each line, approximately every 8 msec. The positions of the points on the same line, given the line scan time of about 1 msec, can be considered contemporary. GB-RAR data were acquired using an elevation angle of 10\({}^{\circ}\) and antennas with a main irradiation lobe having an aperture of 39\({}^{\circ}\) in elevation and 11\({}^{\circ}\) in azimuth. As for time synchronization, the TLS is equipped with a GPS receiver, which makes it possible to convert timestamps to Central European Time (CET). For GB-RAR, the recorded acquisition time was converted using the CET provided by the operating system of the computer used as a data logger.