*3.1. Modal Identification*

The following figures present the obtained results. Selected response spectra are presented in Figure 6. Subsequently, the mode shapes obtained from the PP-CA method for the three kinds of the input signals are plotted in Figure 7. Similar results of the NExT-ERA realization for the SA and SC signals are presented in Figure 8. The accepted modal amplitude coherence (MAC) criterion (95%) allowed us to determine only two mode shape vectors. Selected ERA solutions for different time intervals of ambient responses (SA signals) excited by blasts of wind or river undulations (see Figure 5) are presented in Figure 9, together with the average solution. The MAC criterion at a level of 98% is accepted. In the case of direction 1 (perpendicular to the river), five different parts of visible amplitudes and decay character were selected, while in the case of direction 2 (parallel to the river) three parts of signals could be selected. Signals between 4 s and 8 s in length, depending on the visible amplitude level, were processed by ERA. The considered lighthouse has a cantilever-type structure, so the prediction of the modal forms is intuitive. Thus, the most reasonable results of PP-CA and NExT-ERA were selected and put together with the theoretical forms and the average ERA results. Juxtaposition is presented in Figure 10. The summary of the identified natural frequencies and damping coefficients is presented in Table 1. All the presented results refer to the first pair of natural frequencies, visible in the spectra in Figure 6 (2.26 Hz, 2.78 Hz). However, a reasonable peak is also observed for the frequency 32.46 Hz, which corresponds to the forced vibrations caused by the vibratory hammer action. The related response shape was identified by the ERA and the NExT-ERA techniques. The results are presented in Figure 11, with a similar numerical mode shape.


**Table 1.** Natural frequencies and damping coefficient identified by different methods.

**Figure 6.** Selected spectra of acceleration records of the combined signals (SC).

**Figure 7.** Mode shapes obtained via the PP-CA method for the three kinds of input signals.

**Figure 8.** Mode shapes obtained via the NExT-ERA algorithm for the two kinds of input signals.

**Figure 9.** Mode shapes obtained via the ERA for different free-decay parts of the SA signals and the average result.
