## 4 Application to Data
### Testing the Methodology on a Reference Pulse: The 92238 Case
The probability that a natural ELM has a peak in this time window is 2.0% \(\pm\) 3.4% (95% CI), which means 1.4 \(\pm\) 2.4 (95% CI) false positives for the present shot. The analysis on shot 92238 returned that 70 of 114 ELMs are natural, while 44 were triggered. Thus, the triggered ELM percentage is 38.6%, while the triggering pellet percentage is 74.58% (44/59). The accordance between the beryllium line and diamond UV analyses is 100% (all the ELMs have been classified in the same way). The \(K_{score}\) is 1.83 for beryllium line analysis and 1.97 for diamond UV, suggesting that the cluster quality is quite high. A specificity analysis has been performed to test the capability of the algorithm to avoid false triggered ELMs. Basically, the triggering assessment analysis has been done between the ELM signals of pulse 92237 and the pellet signal of pulse 92238 (Figure 8). In this case, of course, we should have that none of the pellets has triggered an ELM. Figure 7: Top row (**a**): SPCC profiles (left using beryllium line, right using diamond UV) of the 114 detected ELMs. Middle row (**b**): average SPCC profile; bottom row (**c**): clustered SPCC profiles using the k-means algorithm. By performing the SPCC, the profiles in Figure 9 can be obtained. Contrary to the pulse 92238, there are no statistical peak locations, and they are homogeneously distributed on the time window. The SPCC peaks are due to fortuitous correlations. The number of ELM is 84 (all to be considered untriggered by the pellets), the number of ELMs with SPCC peaks is 13, while the expected number due to fortuitous correlation is 16.8 \(\pm\) 7.3 (95% CI). The k-means returns a \(K_{score}\) below one for both ELM signals (0.90 for beryllium and 0.98 for diamond UV), involving that a separation in two clusters is not statistically significant and would worsen the analysis. Therefore, the presence of ELMs triggered by pellets must be excluded and a unique cluster of untriggered or natural ELMs emerges. Considering the test pulse 92238, then, once the SPCC profiles have been clustered, it is possible to obtain further pieces of information by the analysis of the clusters, i.e., to evaluate the mean value and the standard deviation for both classes. Figure 8: The ELM signals of shot 92237 (**top** plot, beryllium in blue and diamond UV in red) and the pellet signal of shot 92238 (**bottom** plot) used for the specificity analysis. Figure 9: SPCC profiles (**left** using beryllium line, **right** using diamond UV) of the detected ELMs of shot 92237 correlated with the pellet of shot 92238. The differences between natural (blue for beryllium, light blue for diamond UV) and triggered (red for beryllium and purple for diamond UV) ELMs are highlighted in Figure 10. Triggered ELMs have high S PCC values for time delay smaller than 2 ms, with a maximum value located at 200 \(\upmu\)s for the beryllium line and 250 \(\upmu\)s for the diamond UV diagnostics, while for time delays higher than 2 ms, the triggered SPCs converge to the natural ones, indicating that those time delays do not provide any piece of information for the triggering assessment. It must be noted that the beryllium line S PCC is affected by two local maxima smaller than the diamond UV one. This difference, even if small, suggests that the diamond UV may return more accurate values, especially for difficult pulses. This improved information can be due to two main reasons: (a) the time resolutions of the two diagnostics are different (beryllium line is 100 \(\upmu\)s, while diamond UV is 5 \(\upmu\)s); (b) the shape of a typical ELM on the Be II signal is wider than the diamond UV. The statistical analysis of triggering times can be performed by calculating the time delays at which a maximum S PCC is observed for each triggered ELM (\(\Delta t_{trig,i}\)).