# 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
\begin{table}
\begin{tabular}{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** & \(0.0\%\) & \(0.0\%\) & \(0.0\%\) & \(0.0\%\) & \(-\)0.1\% & 0.0\% & +0.1\% \\
**Set 3a** & \(-\)0.3\% & \(-\)0.3\% & [-] & \(-\)0.2\% & \(-\)0.1\% & [-] & \(-\)0.1\% \\
**Set 3b** & \(-\)0.2\% & \(-\)0.1\% & \(-\)0.2\% & \(-\)0.1\% & \(-\)0.2\% & \(-\)0.2\% & 0.0\% \\
**Set 5** & \(-\)0.4\% & \(-\)0.4\% & \(-\)0.2\% & \(-\)0.0\% & \(-\)0.4\% & \(-\)0.4\% & 0.0\% \\ \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} \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 5: Beam 2: frequency variation, 10-min intervals discretization, correction with axial force. with a frequency close to the second mode of vibration of the beam. Therefore, for the entire duration of the sampling, for Mode 2, values at a constant frequency of 33.75 Hz were obtained. Consequently, it was not possible to correlate the frequencies with either temperature or axial force. In case of \"Mass 1%\" tests, Beam 1 has a fixed mass of 1% in midspan. A frequency variation on Mode 1 of 0.0% \(\div-\)0.1% on the sound beam (Tables 4 and 5) and of \(-\)1.3% \(\div-\)1.4% on the damaged beam (Tables 8 and 9) is appreciated by all methods using the correction with axial force. It can be therefore be estimated that the additional 1% mass causes a variation of the first mode frequency of \(-\)1.2% \(\div-\)1.4%. When the correction is performed using ambient temperature, the difference can rise to \(-\)1.9% \(\div-\)2.1% on the sound beam (Tables 6 and 7) and to \(-\)3.3% \(\div-\)3.5% on the damaged beam (Tables 10 and 11). The compensation with ambient temperature provides an initial error on the frequency of about \(-\)2%; this is greater than the effect of 1% mass in midspan (1.3% to 1.5% of variation on frequency). Therefore, the introduction of this mass cannot be clearly appreciated if frequency correction is done using ambient temperature. A limit in detecting a structural change due to the imperfect environmental effects correction is therefore recognized. In case \"Mass 3%\", Beam 1 has a fixed mass of 3% in midspan. When correction with axial force is done, a frequency variation on Mode 1 of \(-\)0.1% \(\div\)0.3% on the sound beam (Tables 4 and 5) and of \(-\)3.9% \(\div-\)4.2% on the damaged beam (Tables 8 and 9), can be appreciated by all methods. Therefore, it can be estimated that the additional mass causes a variation of the frequency of the first mode of \(-\)3.6% \(\div-\)4.1%; this is about 3 times that measured for 1% additional mass. When the correction is performed using ambient temperature, the frequency variation is \(-\)0.6% \(\div+\)0.5% on the sound beam (Tables 6 and 7) and \(-\)3.3% \(\div-\)4.4% on the damaged beam (Tables 10 and 11). Therefore, it can be estimated that the frequency variation of the first mode, visible after temperature compensation, is \(-\)2.7% \(\div-\)4.9% (less accurate than \(-\)3.6% \(\div-\)4.1% estimated with axial force compensation). In case \"Mass 5%\", Beam 1 has a fixed mass of 5% at L/10. The most accurate predictions can be done observing Mode 3.