# Effect of Environmental Parameters on Structural Health Status Assessment Using OMA Techniques
## 8 Correlation of Natural Frequencies with Temperature and Axial Force
### Evaluation of the Effect of Simulated Damage  
The following tables quantify the frequency variations between the 12-h datasets and the 72-h dataset that was chosen as benchmark. The variation is the difference between the  
Figure 11: Comparison of the corrected frequencies of the 5 analyzed datasets. (**a**) Beam 1, dataset discretized in 5-min intervals. (**b**) Beam 1, dataset discretized in 10-min intervals. (**c**) Beam 2, dataset discretized in 5-min intervals. (**d**) Beam 2, dataset discretized in 10-min intervals. Figure 10: Temperature corrected frequencies vs. axial force corrected frequencies. (**a**) Beam 1, data set discretized in 5-min intervals. (**b**) Beam 1, data set discretized in 10-min intervals. (**c**) Beam 2, data set discretized in 5-min intervals. (**d**) Beam 2, data set discretized in 10-min intervals. averages of the corrected frequencies done on the 12-h dataset and on the first 12 h of the 72-h dataset. The results obtained by applying peak-picking, Cov-SSI and PolyMAX methods are comparable, but peak picking gives clear results only for Mode 1. The differences between datasets discretized in 5-min records and datasets discretized in 10-min records are negligible. The most important difference is between frequency corrections with temperature and with axial force. Beam 2 is sound in each dataset; therefore, no frequency variation should be appreciated between the 72 h benchmark and the 12 h datasets. When the correction is carried out by using axial force (Tables 4 and 5), the absolute maximum frequency variation between the different datasets is smaller than 0.5%; this result is in line with what expected, since Beam 2 remains in nominal conditions in each dataset. When the correction is carried out using ambient temperature (Tables 6 and 7), wider spreads can be observed, up to 2.5%. In the _set 3a_ dataset, no results were obtained for Mode 2 due to the interference caused by a neighboring laboratory test. The neighboring fatigue test produced a forcing \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **PP** & \multicolumn{3}{c}{**Cov-SSI**} & \multicolumn{3}{c}{**PolyMAX**} \\ \cline{2-9}  & **Mode 1** & **Mode 1** & **Mode 2** & **Mode 3** & **Mode 1** & **Mode 2** & **Mode 3** \\ \hline
**Set 1** & \(-\)0.1\% & 0.0\% & \(-\)0.1\% & 0.0\% & \(-\)0.1\% & 0.0\% & +0.1\% \\
**Set 3a** & \(-\)0.3\% & \(-\)0.3\% & [-] & \(-\)0.2\% & \(-\)0.2\% & [-] & \(-\)0.3\% \\
**Set 3b** & \(-\)0.2\% & \(-\)0.1\% & \(-\)0.2\% & \(-\)0.1\% & \(-\)0.2\% & \(-\)0.2\% & \(-\)0.1\% \\
**Set 5** & \(-\)0.5\% & \(-\)0.4\% & 0.0\% & 0.0\% & \(-\)0.4\% & \(-\)0.3\% & \(-\)0.2\% \\ \hline \end{tabular}
\end{table} 
Table 4: Beam 2: frequency variation, 5-min intervals discretization, correction with axial force. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **PP** & \multicolumn{3}{c}{**Cov-SSI**} & \multicolumn{3}{c}{**PolyMAX**} \\ \cline{2-9}  & **Mode 1** & **Mode 1** & **Mode 2** & **Mode 3** & **Mode 1** & **Mode 2** & **Mode 3** \\ \hline
**Set 1** & \(-\)1.9\% & \(-\)2.0\% & \(-\)1.7\% & \(-\)1.2\% & \(-\)2.1\% & \(-\)1.6\% & \(-\)1.3\% \\
**Set 3a** & \(+\)0.4\% & \(+\)0.3\% & [-] & \(+\)0.2\% & \(+\)0.4\% & [-] & \(+\)0.1\% \\
**Set 3b** & \(-\)0.4\% & \(-\)0.5\% & \(-\)0.5\% & \(-\)0.3\% & \(-\)0.6\% & \(-\)0.4\% & \(-\)0.4\% \\
**Set 5** & \(-\)2.4\% & \(-\)2.5\% & \(-\)1.9\% & \(-\)1.3\% & \(-\)2.4\% & \(-\)2.0\% & \(-\)1.6\% \\ \hline \end{tabular}
\end{table} 
Table 7: Beam 2: frequency variation, 10-min intervals discretization, correction with temperature.