## 3 Results
### Variation of the Linear Regression for Estimating the Temperature Influence  
For validation of the least squares approach, we also perform Frequency Domain Decomposition (FDD) on the GBR and strain sensor measurements. Since the results are very similar between both sensor types, we will primarily be discussing the GBR results in this section. Figure 6 shows the natural frequencies as a function of temperature estimated by FDD with time windows of 5 and 10 min. In the case of a time window of 5 min, the resulting low-frequency resolution leads to visible quantisation. Additionally, several outliers have to be identified and removed to estimate the linear relationship between temperature and frequency successfully. We detect the outliers by iteratively testing if the residuals of the linear regression fit a normal distribution. The time window of 10 min causes no visible quantisation, and only one outlier is identified. Table 4 shows the results of the linear regression. The slope parameter is approximately \(-0.07\) Hz per 10 \({}^{\circ}\)C for both time windows. After correcting the linear relationship, the frequency estimates of the 5 min time window have a standard deviation of 0.026 Hz and a mean of 3.654 Hz. The results of the 10 min time window are slightly lower, with a standard deviation of 0.023 Hz and a mean of 3.651 Hz. Since practical applications may require shorter measurement times or fewer campaigns, the number of frequency estimations may be reduced, thus influencing the linear regression. In the following, we analyse the reliability of the linear regression by simulating two types of data reductions. At first, the reduction is implemented by drawing uniformly distributed random samples from the least squares and FDD results, respectively. Figure 7 shows the variation of the linear regression's parameters calculated from one thousand samples for each sample size. The standard deviation of the slope parameter in Figure 7a slowly increases as the sample size is reduced. With very small sample sizes, the growth can be characterised as exponential. The standard deviation is continually smaller for the least squares result than it is for the FDD. Although this difference can be observed for both the GBR and the strain sensors, it is much more distinct for the GBR. Figure 7b shows very similar observations for the offset parameter of the linear regression. A second simulation excludes entire measurement days combined with uniformly distributed random samples. Figure 8 exemplarily shows the variation of the linear regression for a sample size of 25%. The measurement days only include the 23 and 24 October 2019, with temperatures in the range of 8 \({}^{\circ}\)C to 15 \({}^{\circ}\)C. The samples are drawn one thousand times from the GBR least squares result to visualise the standard deviation of the linear regression in Figure 8a. Additionally, one sample and its corresponding regression are plotted to illustrate the data reduction. As a direct comparison, Figure 8b shows the FDD result with a time window of 10 min for this simulation. The standard deviation of the linear regression is much higher for the FDD than for the least squares approach, especially in the case of extrapolated values outside the reduced temperature range. A similar result can be seen in Figure 9. The simulation uses two measurement days with a greater differential between lowest and highest temperatures than the first simulation. Temperatures are between 3 and 6 \({}^{\circ}\)C on 27 February 2020 and between 17 and 21 \({}^{\circ}\)C on 29 July 2020. As a result, the linear regression varies much less for the least squares approach and the FDD