## 4 Statistics of the Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Early Category** & \multicolumn{3}{c}{**Frequency Estimator in (6) Using the Rule in (8)**} \\ \hline
**(\# of pulses)** & \(Z=-1.96\) & \(Z=-2.5\) & \(Z=-3\) & \(Z=-4\) & \(Z=-5\) \\ \hline
**Total Early by actual slowing down** & 30 & 16 & 8 & 6 & 1 \\
**and recovery** & 7 & 7 & 1 & 1 & 1 \\
**Early induced by a MHD instability** & 23 & 9 & 7 & 5 & 0 \\ \hline
**Detected** & 147 & 161 & 167 & 166 & 165 \\
**Missed** & 0 & 0 & 2 & 5 & 11 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: “Early” category study regarding the disruptive pulses. The table reports the comparison between the threshold based indicators, currently used in control room at AUG, and the estimator in (6), used for the tracking of the dynamic of the mode. used in (6) allows improving the performance at least of a 25% with respect to the unbiased estimator, it cannot deal with all kind of induced perturbations on the saddle coils. Very large ELMs can occur and they might induce a wrong assessment and consequently, deceive the interpretation about the physical phenomenon involved. For this reason, a sensitivity study has been performed on the optimal Z parameter to set. Concerning the statistics in Table 2, setting a relatively low Z value, e.g., Z = \(-1.96\), the actual number of undetected events (\"missed\") is 0. At the same time, the number of \"early\" is high, 30, even if 7 of them are due to modes that slow down and then start rotating again. Lowering the threshold to Z = \(-2.5\) the number of the \"early\" events decreases because more events are correctly classified as \"detected\" locked modes. This is due to the fact that the number of \"early induced by a MHD Instability\" decreases. By lowering further the Z, e.g., reaching Z = \(-3\), it is also possible to classify correctly the pulses with a slowing down rotating mode that later in the discharge starts rotating again. Consequently, the number of \"detected\" increases again. At the same time, however, the threshold becomes so restrictive that for two pulses no mode has been detected as locked, and consequently, the statistics of \"missed\" increases. To summarize then, a trade-off between sensitivity to the slowing down detection of a \(n\) = 1 mode and specificity has to be considered, but the estimator is physically coherent with the expectation. Figure 8 reports an example of the pulse 30445 showing a 2/1 mode that slows down between 1.15 s and 1.4 s and then accelerates again. In Figure 8, the dynamics of the 2/1 tearing instability can be clearly observed, an interpretation supported by the spectrogram in Figure 8b. The electron cyclotron emission (ECE) allows assessing the presence of a q = 2/1 island with resonant surface between R\(\sim\)1.909m and R\(\sim\)1.968 m. This pulse is particularly exemplificative, since changing the Z threshold from Z = \(-2.5\) to Z = \(-3\), the time instance at which the indicator (6) detects a locked mode moves from t \(\sim\) 1.288s, when it actually had slowed down before starting rotating again, to t = 7.569 s, shortly before the disruption. Table 1 shows also the results obtained for the not-disruptive cases. It can be seen how, increasing the confidence by increasing Z, less pulses are considered to have a locked instability. However, the results regarding the disruptive pulses and the analysis reported in Table 2 have to be considered at the same time to assess a trade-off between detected locked modes and missed ones. In fact, while for the not-disruptive pulses the use of the highest Z = \(-5\) would be suggested, taking also into account the disruptive analysis in the same Table 1 and the study in Table 2, the use of Z = \(-4\) emerges as more appropriate choice because of the fact that moving from Z = \(-4\) to Z = \(-5\) both the number of detected pulses decreases slightly and also the number of missed ones increases slightly.