## 7 Challenges in Connection with the Running Reference Method  
The running reference method cannot avoid shot noise, in contrast to the procedural noise of the traditional method. Hence, data retrieved by the running reference method still contain outliers (as defined, e.g., by [PERSON] in [PERSON] (1965): \"An outlying observation, or 'outlier', is one that appears to deviate markedly from other members of the sample in which it occurs.\" The sample for which the comparison takes place may be locally defined (cf. Appendix A).). Since the data are added up to get the absolute strain status for each measurement, an outlier in one measurement will be carried through all the subsequent absolute strain values. This can be seen in Figure 3. The two outliers in Measurement Number 21 at a position of ca. 310 mm can also be seen at the same position in Measurement Number 35, but not in Measurement Number 16. In this case, the original outlier was in the data for Measurement Number 18 (not shown). To illustrate this issue better, in Figure 6, the absolute strain data obtained by the running reference method for Measurement Number 250 can be seen. The black dots show the strain values for data retrieved by the running reference method, but not corrected for outliers, while for the red squares each obtained strain; the dataset was corrected for the very few remaining outliers before adding it up. This illustrates the importance of correcting outliers even if the data are retrieved by the running reference approach. Since data have to be summed up to get the strain values for a certain measurement, an outlier cannot just simply be taken out of the dataset. This would be like using the value zero when adding the data up, which would still lead to an outlier, albeit with a different magnitude. These points rather must  
Figure 6: Absolute strain values for Measurement Number 250 (3032 min). Black points/red squares: uncorrected/corrected for outliers in the preceding measurements (cf. text). be substituted by a reasonable value. It is recommended to always report the data with and without outlier correction. This approach allows others to evaluate the validity of the data correction process. However, the following is to be said: approximately 40% of the 450 absolute strain values before the fiber leaves the material in Measurement Number 250 can be seen as outliers. However, one has to consider that the running reference method requires evaluating more then 100,000 data points to acquire Measurement Number 250. This means that the possibility for an outlier is far below one percent. Compared to the traditional method, which returns just noise for the majority of all measurements, this can be seen as an improvement. If these comparatively very few outliers are corrected for in the measurement they occur in, the data can be improved, as the red squares in Figure 6 show. The fiber leaves the material around 400 mm. Since the backscatter amplitude drops at that point to the background noise level, it is a physical impossibility to retrieve any information beyond this point (cf. Section 6). A short summary of such an outlier correction algorithm would be the following. Firstly, search for sections of continuous points that exhibit no strain deviation above a certain, user-defined threshold. This can be regarded as a local minimum/maximum criterion. Secondly, points that exceed the strain threshold are considered outliers. Thirdly, such outliers are replaced by a linear interpolation between the two continuous sections to the left and right of the outlier. Certain measures are taken in order not to dismiss false positives. The interested reader is referred to the Appendix in which a detailed algorithm is presented, which allows the implementation of such outlier detection and correction in simple software. An actual implementation of this algorithm can be found on GitHub [53] under a free software license [54] (see also the location of resources in Section 9).