## 5 Comparison of Strain Data Yielded by the Regular and the New Running Reference Method
### Strain Determined by the Running Reference Method  
In Figure 3, the strain values can be seen that were retrieved by the running reference method.  
The most notable difference between Figures 2 and 3 is the clear measurement curves and that scatter and noise have largely disappeared. To visualize that the proposed new method does indeed lead to the same results as the traditional method, the data shown in Figure 2 are reproduced in Figure 3 as thick grey points in the background.  
Even with the rather coarse scale in Figure 3, it can already be seen that both methods yield the same strain values. Of course, a comparison can just take place for the data points in which the absolute reference method yields meaningful results.  
Usually, some kind of Root-Mean-Square Error (RMSE) is given to compare the accuracy of two different methods. However, this is just of very limited applicability for the data presented here, since the traditional method yields mainly noise for later measurements. Only meaningful values could be used, but this would already include a comparison with the strain values determined by the running reference technique. At which threshold of difference a data point is considered to be \"correct\" is a very subjective, probably hard to justify, interpretation of the data and may amount to \"cherry picking\" or p-hacking in the worst cases. Hence, to further investigate the accuracy of the running reference method, not the RMSE, but the absolute difference between the strain values obtained by both methods is shown in Figure 4.  
The left image in Figure 4 shows that the strain values obtained by both methods are equal within an error range of below 100 \(\times\) 10\({}^{-6}\) strain. When the data points obtained by the traditional method are more reliable (e.g., in the area before the fiber enters the material or for measurements before the epoxy \"grips\" the fiber), this error can be considered ten-times smaller, as can be seen in the right image in Figure 4. The \"bands\" in Measurement 16 are due to the maximum resolution of the OBR.  
When the traditional method yields noise, the differences in the values obtained by the running reference method exceed by far the herein shown y-scale. This however need not be considered.  
It may be noted that for Measurement 16, an RMSE of 5.5 \(\times\) 10\({}^{-6}\) strain is calculated. This is almost the resolution limit for strain values of the instrument used. Ten obvious outliers had to be removed from the data retrieved by the traditional method to calculate the RMSE. These outliers  
Figure 4: Differentiated by the running and the absolute reference method (cf. the text). The right image contains the same data as the left image, albeit with a magnified strain scale that allows a more detailed presentation of the information. Measurement times: \(\#16\to 200\,\mathrm{min}\), \(\#21\to 226\,\mathrm{min}\), \(\#34\to 267\,\mathrm{min}\).  
Figure 3: In color: added up strain differences between two subsequent measurements, obtained by the running reference method, yield the absolute strain (cf. the text). Grey points: same data as shown in Figure 2 with the exception of the noise. Data points having the same shape belong to the same measurement (cf. the text). Measurement times: \(\#16\to 200\,\mathrm{min}\), \(\#21\to 226\,\mathrm{min}\), \(\#34\to 267\,\mathrm{min}\).  
were detected by the algorithm described in the Appendix A. For the other measurements, the above comments are valid. Hence, no such values will be presented here.  
These results show that both methods yield the same absolute strain values within an error almost solely defined by the instrument resolution. However, the much lower occurrence of outliers in the data obtained by the running reference method, and thus far more reliable results, shows the superiority of the proposed analysis method compared to the traditional approach.