# Effect of Environmental Parameters on Structural Health Status Assessment Using OMA Techniques
## 7 Data Analysis with Applied OMA Methods
### Application of the Cov-SSI Method and the Poly-Reference Least Squares Complex Frequency Method  
Two of the most widely used methods of operational modal analysis are presented in this paragraph: Cov-SSI and PolyMAX. Figure 7 compares two stabilization diagrams obtained from the application of the two methods. They are both obtained for a 5-min record extracted at the 36 th hour of sampling for Beam 1 under nominal conditions (72-h dataset). Figure 6: First five peaks extracted from PSD. Correlation with temperature (**a**) Peak 1 (**b**) Peak 2 (**c**) Peak 3 (**d**) Peak 3, cleared of the effects of accelerometer **4 (**e**) Peak 4 (**f**) Peak 5 (**g**) Legend. Red dots indicate unstable poles, i.e., where one of the two conditions expressed in Equations (3) and (4) is not fulfilled. The green points indicate stable poles, where both conditions expressed in Equations (3) and (4) are fulfilled. Where the stable poles (green dots) align vertically, a structural mode is identified. Using PolyMAX, pole stabilization occurs for low-order models, particularly for Mode 2 and Mode 3. On the contrary, using the Cov-SSI algorithm, pole alignment occurs for higher model orders if modes higher than the first mode are considered. In the case of stabilization with a frequency deviation of 1% --Equation (3)--and a damping deviation of 5%--Equation (4)--Cov-SSI algorithm provides more than 50% stable poles (green points) in the alignment. That is, the stable poles that fulfil both conditions expressed in Equations (3) and (4) are more than 50% of the poles in the alignment. The other poles of the alignment fulfil only the condition expressed in Equation (3). Using the PolyMAX, even though the frequencies are aligned, the presence of stable poles (green points) in the alignment is below 20%, in contrast with the Cov-SSI method which ensures that stable poles in the alignment are always above 50%. This indicates that the difference in damping between two consecutive model orders for the same frequency is  
Figure 7: Stabilization diagrams. (**a**) Cov-SSI (**b**) PolyMAX. higher than 5%. To ensure a sufficiently high presence of stable poles for the PolyMAX also, the permissible damping deviation in Equation (4) should be greater than 5%. In addition, it is also possible to notice the presence of an alignment of poles at 25 Hz using both methods, but the presence of stable poles within the alignment is lower than for the poles representing real vibrating modes of the structure (shown in Table 3). Furthermore, for some modal order ranges, no poles are provided at 25 Hz frequency. Thus, the 25 Hz alignment, as already discussed during the application of the peak-picking method, should not be considered as a mode of the structure. The frequency graphs in the function of time for the 72 h interval obtained with the Cov-SSI method and the PolyMAX method for the first three vibration modes are shown in Figure 8.  
Both methods can identify the frequencies for the first three vibration modes. Results are more robust than using peak-picking method for Modes 2 and 3, moreover, the frequen  
Figure 8: Beam 1, discretization of the dataset in 5-min intervals. Comparison between PolyMAX and Cov-SSI identified frequencies for the first three vibration modes. (**a**) Mode 1. (**b**) Mode 2. (**c**) Mode 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Mode** & **Cov-SSI Frequencies [Hz]** & **PolyMAX Frequencies [Hz]** \\ \hline
**1** & 13.94 & 13.94 \\
**2** & 31.25 & 31.10 \\
**3** & 53.24 & 53.10 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: First three modes identified in 5-min interval extracted at the 36 th hour of sampling for Beam 1 under nominal conditions. cies extracted with the Cov-SSI algorithm for Modes 2 and 3 present a lower variance than those extracted with the PolyMAX method. It should be underlined that the structures are very simple and have well separated modes. Such characteristics help the identification remarkably.