**5. Conclusions**

A methodology has been proposed for measuring the vibration frequencies and the amplitude of the oscillations of tall structures by joint use of TLS and GB-RAR. The methodology exploits the possibility of using a TLS in line scan mode, thus extracting a large number of scan lines per second. The use of lines interpolating the individual scanned points makes it possible to obtain results with a precision better than that of the instrument. For a given point on the structure, the stack of TLS lines is used to derive the temporal profile of displacements and from this the spectrum of vibration frequencies. It has been observed the TLS estimate of vibration frequencies is limited by the precision of displacement measurements. For oscillations whose amplitude is much smaller than the TLS precision, the proposed methodology based on TLS data cannot estimate the vibration frequency. This problem

is overcome by the joint use of co-located GB-RAR. The higher precision of GB-RAR measurements of tower displacements provides vibration frequencies corresponding to smaller oscillation amplitudes.

Results provided by the proposed methodology based on the joint use of co-located TLS and GB-RAR systems have been compared to the output of a numerical analysis of tower displacements, modelling the tower as subject to a wind load derived from the anemometric data.

The comparison of results obtained by the numerical analysis and measurements leads to the following conclusions: (a) the proposed processing technique based on the geometrical modelling of the structure can enhance the precision of distance measurements below the 5 mm declared for the TLS instrument; (b) the joint use of co-located TLS and GB-RAR can provide richer information on the dynamical behavior of the structure, with the sub-centimeter spatial resolution of TLS, and on the whole spectral characterization of vibrations, including those having an amplitude much smaller than the TLS precision, thanks to the sub-millimeter precision of GB-RAR measurements.

The proposed methodology can be a useful and cheap support for non-contact inspection and monitoring of tall structures.

**Author Contributions:** Conceptualization, S.A.; methodology, S.A.; software, S.A. and G.N.; investigation, S.A. and G.N.; writing—original draft preparation, S.A. and G.N.; writing—review and editing, S.A. and G.N. All authors have read and agreed to the published version of this manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** Authors acknowledge EON Italia Spa for support during data acquisition. The authors would like to thank the entire DIAN S.R.L. team for the acquisition and processing of GB-RAR data.

**Conflicts of Interest:** The authors declare no conflict of interest.
