## 6 Deployment of the Proposed Approach in Support to Model Building  
In the previous section, an explorative case has been described. Data-driven models are derived and tested until the best one is selected. In this section, the same tools are applied to the assessment of the quality of already devised models. For the present example, therefore, guidance, in particular with regard to the signals to be used as inputs to the predictors, is obtained from already proposed empirical models. A first attempt at deriving a reasonable equation separating the safe and disruptive regions of the operational space has been tried, using as inputs the variables of the Hugill and beta limit plots. As described in Section 1, these traditional representations have practically zero predictive power for JET with the ILW, at least for the campaigns considered in this study. On the other hand, one could ask whether the poor success rates are the consequence of the simple mathematical form of the equations, even if the variables have a high information content and could be good inputs to a classifier. To falsify this hypothesis, the developed methodology of SR via GP has been systematically applied to the quantities, which appear in both representations. Unfortunately, the results have been very negative. The success rate has never been sufficient, and the rate of false alarms might even reach 40%. Therefore, it must be concluded that the quantities entering the Hugill and beta limit plots do not constitute an effective set of features to perform prediction on JET with the ILW. The main reason for the poor performance of the Hugill and beta limit representations resides in the fact that they do not include the locked mode and the internal inductance among the inputs. These two signals are really much more informative quantities for disruption prediction than the ones used in the Hugill and beta limit plots. This is also confirmed by a recent model developed for the level of the mode locked leading to disruptions in various Tokamaks [44]. In this study, the amplitude of the locked mode, considered the consequence of magnetic islands locked to the wall, is studied in JET, ASDEX-U and COMPASS. The simple locking of the magnetic configuration to the wall is not deemed a sufficient condition per se to trigger disruptions; the amplitude is proposed to be the real quantity of relevance. Based on theoretical considerations involving the Chirikov criterion, the amplitude of the island size required to trigger a disruption was determined. A scaling for the value of the locked mode threshold for triggering a disruption was derived by fitting its amplitude at the time of the beginning of the current quench. The resulting equation determining the threshold for the occurrence of a disruption is found to be:  
\[LM(r_{c})=c\int_{P}^{a_{1}}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \!\!\!\!\!\!\!\!\!\!\!\!\!\  
where \(LM\) is the amplitude of the locked mode in mT, c is a constant, ai are regression coefficients, \(lp\) is the plasma current, \(q95\) the safety factor at 95% of the radius, a is the minor radius, \(li\) is the internal inductance and \(\rho_{c}\) is the distance between the plasma centre and the location of the magnetic loops measuring the amplitude of the locked mode.  
For the database analysed in this paper, Equation (3) has been calculated using for the parameters the values suggested in [45] and reported in the following:  
\[c=8.5;\ a_{I}=1.07;\ a_{a}=-1.1;\ a_{q}=-1.2;\ a_{li}=1.2;\ a_{p}=-2.8\]  
Unfortunately, Equation (3) does not fit the data of campaigns C29-C30 of JET with the ILW well. A first indication of the discrepancy between the equation and the data can be obtained by an inspection of the plots reported in Figure 7. For the 170 disruptions considered in the present study, the plots of Figure 7 report the critical value of the locked mode, as predicted by Equation (3), versus all the regressors.