# Effect of Environmental Parameters on Structural Health Status Assessment Using OMA Techniques
## 7 Data Analysis with Applied OMA Methods
### Application of the Peak-Picking Method  
The PSDs are estimated using [PERSON]'s method with a Hanning-type window with three different extensions: 1 min, 30 s and 15 s.  
Two PSDs coming from two different sampling intervals for Beam 1 under nominal conditions (72-h dataset) are shown in Figure 5. Windows with a larger amplitude (i.e., 1 min) provide higher PSD frequency resolution. On the other hand, a smaller window width guarantees a higher number of averages, with a reduction in the signal-to-noise ratio. In this paper, fairly large windows were used in order to guarantee good frequency resolution to be able to investigate frequency variations arising from small damages. Figure 5: Comparison of PSD peaks. (**a**) PSD obtained for a 5-min discretization interval at the start of sampling. (**b**) PSD obtained for a 5-min discretization interval at the 36 th hour of sampling. By comparing the two diagrams shown in Figure 5, it is possible to notice a considerable variability in the amplitude of the peaks between the intervals due to different levels of environmental excitation during sampling. Furthermore, in some intervals, the peaks are confused with the PSD noise, as happens for the first peak; present in Figure 5a around 14 Hz and not present in Figure 5b. In this paper, the amplitude of the peaks is not taken into consideration because the uncontrolled environmental conditions cause the peaks' amplitudes to vary considerably. Only the position of the peaks is assessed. The signal-to-noise ratio is relatively low, as the two beams are only subjected to ambient excitation. Therefore, when there is very little environmental excitation, noise dominates, especially during the night when no human activity is present in the laboratory. In addition, the first frequency of the rods is about 14 Hz (because they are tensed) which is difficult to excite with ambient excitations. The second and third mode are therefore even more difficult to excite. The peak-picking operation is performed by using the 'findpeaks' function of the MatLab package [26]. The results obtained for Beam 1 under nominal conditions (72-h data set) are shown in Figure 6.  
Peak 1--Figure 6a--has a frequency between 14.5 and 13 Hz with an inverse correlation between the frequency and the environmental temperature. This range of frequencies (with an average of 13.8 Hz) lies between the natural frequencies calculated for the simply supported beam and the fully restrained beam in Section 6 (11.67 < 13.8 < 14.65). Peak 2--Figure 6b--is around the frequency of 25 Hz. The lack of correlation with ambient temperature suggests that this peak represents a narrow band not controlled excitation, rather than a dynamic system behavior; this is an important warning about the verification of the presence of broad-band noise excitation to properly work with OMA. In addition, 25 Hz lies outside the range of natural frequencies calculated for Mode 2 in Section 6. Peak 3--Figure 6c,d--has a frequency between 32.3 and 29.7 Hz, with inverse correlation between identified frequencies and ambient temperature. Moreover, Accelerometer 4, positioned in the middle of the beam, is ineffective as it is blinded by noise; therefore, Peak 3 can represent an even-order vibration mode of the beam. The natural frequencies calculated for Mode 2 for the simply supported beam and the fully restrained beam in Section 5 are well coupled with the results for this peak (22.4 < 31.0 < 40.7). The frequencies of Peak 4 and Peak 5--Figures 6e and 6f--can be found around 50 Hz, inversely correlated with temperature; however, the outputs are considerably disturbed. This is due to the fact that high-order modes are difficult to excite; in PSD they are confused with the noise of the transform. It should be noted that the vertical lines in Figure 6 represent outliers, i.e., frequencies that cannot be identified. The presence of these outliers increases with increase in the mode order being considered.