## 5 Results and Discussion
### Results for the IM Operating at 20 Hz
Finally, by looking at Figure 6c, it is clear that when the GA-MCSA technique is used, the measured amplitudes behave as expected and, in addition, the amplitudes are smaller than those measured in the original signal. Moreover, the boxplots do not overlap in the y-axis, and the amplitude of the fault harmonic can be better measured. Again, it is necessary to mention that these results are achieved due to the suppression of the FFC performed using the GA. This suppression considerably reduces the spectral leakage around the FFC, allowing the correct measurement of the amplitude from the failure harmonics. In this sense, it can be said that another of the important contributions of this work consists of the development of a technique that reduces the detrimental effects of the spectral leakage in the vicinity of the FFC. In order to demonstrate that the proposed methodology also allows to obtain a better grouping in the amplitudes of the LSH, the intra-cluster distance \(D^{(intra)}\), and the inter-cluster distance \(D^{(inter)}\) as defined in [39] are used as features to measure the quality of the groping. The intra-cluster distance measures the scatter within every group, and the inter-cluster distance measures the separation between groups. Thus, the best grouping strategy consists of minimizing the intra-cluster distance and maximizing the inter-cluster distance. These indexes are computed for the three slip levels and for the two operation frequencies. Table 1 presents the results for the intra-cluster distance applied to groups resulting from the three different methodologies. It is easy to observe that in all the cases, the lowest value for the groups correspond to those reported by the proposed methodology. This is a strength of the GA-MCSA methodology because it implies that the values reported from one measurement to another are similar. It is also appreciated, that the highest scatter in the data occurs when the conventional MCSA is applied. This is indicative that, by itself, the MCSA may lead to wrong results. The NF-MCSA proves to be an intermediate point between the conventional MCSA and the proposed methodology; it improves the results but it is still affected by the spectral leakage around the FFC. The inter-cluster distances are also calculated for the results delivered by the three methodologies and the obtained data are summarized in Table 2. The term \(D^{(inter)}_{24}\) represents the inter-cluster distance between the case for a 2% slip and the case for a 4% slip. On the other hand, the term \(D^{(inter)}_{46}\) represents the inter-cluster distance between the case for a 4% slip and the case for a 6% slip. The conventional MCSA and the NF-MCSA present good separation between the 2% slip and the 4% slip and this situation is appreciated in the results from Table 2. However, they present a high scatter and, therefore, the  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Frequency**} & \multicolumn{2}{c}{\(D^{(intra)}\) (**MCCSA**)} & \multicolumn{2}{c}{\(D^{(inter)}\) (**NX-MCSA**)} & \multicolumn{2}{c}{\(D^{(intra)}\) (**GA-MCSA**)} \\  & \(s=2\%\) & \(s=4\%\) & \(s=6\%\) & \(s=2\%\) & \(s=4\%\) & \(s=6\%\) & \(s=2\%\) & \(s=4\%\) & \(s=6\%\) \\ \hline
31 Hz & \(3.8\times 10^{-3}\) & \(  
results for the distance between the 4% slip and the 6% slip are not as good as expected. The GA-MCSA methodology presents good values for the inter-cluster distance and combined with the low scatter in the data, it results in the best option for the proper detection of the fault severity. As an additional analysis, Table 3 presents the computational cost and acquisition time related with every methodology. All the methodologies are implemented in a personal computer with 8 GB RAM memory and a microprocessor Intel (R) Core (TM) i7-5500U. It is observed that the fastest technique is the MCSA. This is a remarkable situation because this technique is also the one that uses the highest acquisition time.