## 4 Experimental Methodology
### Feature Ranking Methods
#### 4.3.2 One-Way ANOVA  
Analysis of variance is used to compare sample means for two or more classes and determine if observed differences may be due to chance or reflect true differences between classes. Like the \(t\)-test, the null hypothesis (that there is no difference between the means of the groups) and the alternative hypothesis (that at least one group is significantly different from the overall mean of the dependent variable) are established. A significant difference in the means indicates that the function has good discriminative capacity and is likely to be useful in discriminating between classes in a classification task. One-way ANOVA was performed in the context of the present paper with the following parameters: \(df=1498\), the significance level \(\alpha\) is \(\alpha=0.05\), and the critical value of \(F_{score}\) is \(F_{score}=3.8477\). Figure 8 shows bar graphs of the \(F_{score}\) for each of the characteristics under investigation. A higher \(F_{score}\) indicates that the group means are more spread out, suggesting that a significant difference may exist between at least one pair of groups. Similar to the \(t\)-test, if the calculated \(F_{score}\) for a given variable is less than a specified critical value, the null hypothesis is confirmed for that trait and the parameter is considered to have low discriminatory power. Table 4 shows for which parameters the null hypothesis was rejected, and the alternative hypothesis was accepted. The results of the one-way ANOVA analysis for sensor 1 (Figure 8) are identical to the \(t\)-test results and again demonstrate that within the X\({}_{1}\) axis and Y\({}_{1}\) axis Mean, Std, and RMS are the features with the highest resolution for the anomalous and normal data. In contrast to X\({}_{1}\) and Y\({}_{1}\), for the Z\({}_{1}\) axis, Impulse Factor has the highest \(F_{score}\), indicating that it is crucial for class distribution in this dataset, but RMS and Std have a very low \(F_{score}\), indicating low relevance of the given features. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **X\({}_{1}\)** & **Y\({}_{1}\)** & **Z\({}_{1}\)** & **X\({}_{2}\)** & **Y\({}_{2}\)** & **Z\({}_{2}\)** & **X\({}_{3}\)** & **Y\({}_{3}\)** & **Z\({}_{3}\)** \\ \hline Mean & H1 & H1 & H0 & H1 & H1 & H1 & H1 & H1 & H1 \\ RMS & H1 & H1 & H0 & H1 & H1 & H1 & H1 & H1 & H0 \\ Std & H1 & H1 & H0 & H1 & H1 & H1 & H1 & H1 & H0 \\ Peak Value & H1 & H1 & H0 & H1 & H1 & H0 & H1 & H1 & H0 \\ Clearance Factor & H0 & H1 & H1 & H1 & H1 & H0 & H1 & H1 & H0 \\ Impulse Factor & H0 & H0 & H1 & H1 & H1 & H1 & H0 & H1 & H1 & H0 \\ Crest Factor & H0 & H0 & H0 & H0 & H1 & H0 & H0 & H1 & H0 \\ Skewness & H0 & H0 & H0 & H0 & H1 & H0 & H0 & H0 & H1 \\ Kurtosis & H0 & H0 & H0 & H0 & H1 & H0 & H0 & H1 & H0 \\ \hline \end{tabular} Parameters for which the alternative hypothesis was accepted are marked in green. Parameters for which the null hypothesis is accepted are marked in red.  
\end{table} 
Table 3: Accepting an alternative or null hypothesis for the specified signal features based on a \(t\)-test. For sensor 2 in all three axes (Figure 8), the Mean parameter has the highest \(F_{score}\), followed by the RMS and Std parameters for the X\({}_{2}\) and Z\({}_{2}\) axes, and the RMS and Peak Value parameters for the Y\({}_{2}\) axis. Sensor 3 differs from the standard displays, especially within the X\({}_{3}\) axis (Figure 8). Peak Value has the highest \(F_{score}\), indicating that it is the most important feature of this data set. This is followed by RMS and Std, while Skewness and Kurtosis have minimal significance. For the Y\({}_{3}\) axis, the dominant feature is again Mean, while for the Z\({}_{3}\) axis dominant features are also Skewness and Kurtosis, as in the case of the \(t\)-test.