# An Examination of Thermal Features' Relevance in the Task of Battery-Fault Detection
## 4 Discussion and Conclusions  
The experiment presented in our article observes and measures a feature set describing the lead-acid batteries during their charging and discharging phases. Thermal and voltage based features were measured and examined for their relevance towards the battery-fault prediction. Several statistical tests revealed the facts about similarity of the features behavior, clarity and information content of the data representation and also the relevance towards the predicted battery state. The results of the correlation analysis between the maximum temperature values and obtained voltage levels are listed Table 2. These obtained coefficients mean that the most of the time, there is no correlation between these variables. This fact only confirms an absence of informational redundancy among the thermal and voltage data. The analysis of variance (ANOVA) rejected the null hypothesis about the equality of the examined variables means. The results confirm that the examined input variables are significantly different among the tested battery sets and some of these sets are separable by the means of these variables. The results of the cluster analysis visible in Figures 10 and 11 demonstrate that 3 and 4 are the most suitable numbers of clusters according to the gap statistic. The clarity of the clusters is also the highest at these points as it is confirmed by silhouette score. Most of the time, this score value is over the value of 0.7, which implies a higher clarity of clusters, relevant data representation, and a lower amount of noise. The final non-linear relevancy comparison was performed by [PERSON]'s MI estimation. As we can see in Table 3, the relevancy of thermal features is very high and, in most cases, it is almost similar to the voltage data, which slightly confirms our hypothesis about thermal data applicability in the fault detection task. This small difference indicates the lower relevancy when compared to the very relevant voltage vectors. In our last test, we examined how much this difference affected the results of the classification algorithm, which was the simplest kNN in our case. The kNN algorithm was used for multi-class classification and binary classification. In both cases, the input data from the thermal features were comparable to the voltage levels. The success rates above 80% in detection of most of the classes in case of thermal features confirm their validity of use. In all the multi-class detections, the voltage features perform better as it was expected. In cases of binary-classification, the ability to predict whether the battery set contains a battery with malfunction, the voltage data were more relevant again. On the other hand, the thermal features \begin{table}
\begin{tabular}{c c c} \hline \hline
**Charging** & **Temp Data** & **Voltage Data** \\ \hline Accuracy (\%) & 97.72 & 99.75 \\ Precision (\%) & 99.16 & 100 \\ Recall (\%) & 97.13 & 99.59 \\ F-score (\%) & 98.14 & 99.79 \\ \hline
**Discharging** & **Temp Data** & **Voltage Data** \\ \hline Accuracy (\%) & 90.95 & 97.74 \\ Precision (\%) & 96.21 & 100 \\ Recall (\%) & 89.44 & 96.48 \\ F-score (\%) & 92.70 & 98.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluations of binary classification performance (fault and failure-free battery battery set) processed on dimensionally reduced data obtained from charging and discharging process. relevance was very high and during the charing process, the difference was mostly lower than 2% only (see Table 4). This confirms the high relevancy of thermal data. In conclusion, while the battery voltage features are certainly related to the predicted issue, their measurement requires an additional effort and cost. The execution of thermal measurements is less demanding, while its outcome preserves comparable relevance to the predicted issue according to the statistical tests performed in this study.