## 3 Application to a Case Study
### Analysis of the Factors Affecting the Health of an Offshore Platform Structure
#### 3.5.4 Temperature  
The influence of temperature on the structure has two aspects: first, the elastic modulus of the material is negatively correlated with temperature, as shown in Table 6; second, the statically indeterminate structure produces secondary stress.  
The literature shows that changes in the axial size of slender members caused by temperature make little contribution to changes in their structural frequency [43]. Therefore, in this study, the influence of temperature on the frequency of the structure was considered only from the perspective of changes in elastic modulus.  
The effect of temperature is simulated by reducing the elastic modulus of steel. For the observation platform and wind tower, which are above the sea surface, the temperature at the sea surface is used. The temperature of the jacket part is taken as the average temperature of the layer number in which the rod is located. The temperatures of the layers are listed in Table 7, and the elastic modulus values of steel corresponding to these temperatures are listed in Table 6. Elastic modulus values not directly listed were obtained by linear interpolation.  
As shown in Figure 14, the diagram of overall natural frequency variation of the offshore platform over a whole year. Except for the effect of temperature, the platform frequency generally decreases with the increasing of service time. Scouring and marine organisms had a greater impact on the higher-order modes, and corrosion had a greater impact on the lower-order modes. The climate factor, temperature, had a great influence on the higher-order modes, which showed a strong periodic regularity. The natural vibration frequency of the platform increases in spring and winter (December-March) and decreases in summer and autumn (June-October).  
Based on the above analysis, the main factors causing frequency changes in different months of a year (vertical) and the same month of different years (horizontal) were considered. From this longitudinal analysis, it can be seen from Figure 14 that the frequency in a given year is mainly affected by the temperature in each month, and the influence of external factors is negligible. Therefore, the main influencing factor in the longitudinal analysis was temperature.  
For simplicity, we divided the months seasonally, taking March, July, September, and December as being representative of the four seasons and observed the change rates of the low-order (1 st-3 rd order) natural frequency components corresponding to these months. From this analysis, we can see that the change range of low-order frequency components is 0-5%, and the change range of high-order (4 th-8 th) frequency components is 0-8%.  
From horizontal analysis, we found that the influence of temperature on frequency in a given month is negligible, and the frequency is mainly affected by the external factors. Therefore, the main influence in the horizontal analysis was found to be the external factors. The division of the frequency variation range was consistent with that in the longitudinal analysis; only three external influencing factors were included. The final analysis results are listed in Table 8.  
\begin{table}
\begin{tabular}{c c c c} \hline \(\mathbf{T}\) (\({}^{\circ}\mathbf{C}\)) & \(\mathbf{0}\) & \(\mathbf{5}\) & \(\mathbf{10}\) \\ \hline \(E\) (10\({}^{5}\) MPa) & 2.07 & 2.065 & 2.06 \\ \(T\) (\({}^{\circ}\mathbf{C}\)) & 15 & 20 & 25 \\ \(E\) (10\({}^{5}\) MPa) & 2.055 & 2.05 & 2.045 \\ \hline \end{tabular}
\end{table}
Table 6: Values of metal elastic modulus (\(E\)) at different temperatures [42].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Month** & **3** & **7** & **9** & **12** \\ \hline \multirow{4}{*}{Temperature} & 1 st floor & 4 & 6 & 8 & 12 \\  & 2 st floor & 4 & 10 & 13 & 10 \\ \cline{1-1}  & 3 st floor & 4 & 15 & 16 & 10 \\ \cline{1-1}  & 4 st floor & 4 & 20 & 18 & 10 \\ \cline{1-1}  & 5 st floor & 4 & 20 & 18 & 10 \\ \hline \end{tabular}
\end{table}
Table 7: Temperature of jacket offshore platform (unit: \({}^{\circ}\)C).