## 4 Result and Discussion
### Fault Related Feature Evaluation
The evaluation of the statistical significance of differences (\(p\)-value \(\leq\) 0.05) was verified with a two-way ANOVA based on the motor condition, starting load condition, and their interaction. [PERSON]'s honest significant differences method was also applied for multiple comparisons after ANOVA. Table 3 presents the results of the ANOVA models for the Shannon entropy feature in three different sub-band frequencies based on the condition as mention above. As can be seen in this table, the \(p\)-value for the features that were extracted from (A6) is more than 0.05 for the interaction condition states and also for (D7) in both the motor condition and their interaction, which can be checked with a post-hoc test. The performed ANOVA for Shannon entropy at (A7) reveals it can significantly distinguish different conditions. Table 4 presents the results of the ANOVA models for the log-energy entropy feature in three different sub-band frequencies based on similar conditions, as mentioned earlier. The performed ANOVA for log-energy entropy features at different sub-band frequencies reveals its capability to differentiate various states tested, as the \(p\)-value for all decomposition levels is significant. To carry out a statistical evaluation between the means for the features in various situations, [PERSON]'s honest significant differences technique was used as a post-hoc test. Table 5 shows the outcomes of the post-hoc test for two different features in three different sub-band frequencies. The mean values were compared using [PERSON]'s honest significant differences test at \(p\leq\) 0.05. As is  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Source**} & **Sum of Squares** & **df** & **Mean Square** & **F** & \(p\)**-Value** \\ \cline{3-8} \multirow{6}{*}{**A6**} & \multirow{2}{*}{Motor Condition} & 2.43 \(\times\) 10\({}^{8}\) & 1 & 2.43 \(\times\) 10\({}^{8}\) & 304.907 & 4.17 \(\times\) 10\({}^{-48}\) \\  & & Load & 1.56 \(\times\) 10\({}^{9}\) & 3  
clear in Table 5, only the log-energy entropy feature is significant in (A6 and D7), and this feature is not significant in a load of 1 Nm for sub-band frequencies belonging to the (A7). The Shannon entropy feature is also not significant in (A6 and D7) and also in (A7) at the loads (0 and 1 Nm). Table 6 presents the conclusion of the feature validation of the simulation and the experimental results for two different features, using Coiflet mother wavelets. As is clear in this table, Shannon entropy is not capable to detect the BRB in all frequency band ranges used. The log-energy entropy is very significant in detecting BRB in the two frequency band ranges of 39.06-19.53 Hz, which belongs to the decomposition of the original signal in the detail of level seven, and 39.06-0 Hz, which belongs to decomposition of the original signal in the approximation of level six. However, log-energy entropy is not significant for BRB detection in the frequency band range of 19.53-0 Hz, which belongs to the decomposition of the original signal in the approximation of level seven. The results of the simulation are also in accordance with the experimental results. Correspondingly, the most effective sub-band frequency is the detail of level seven which includes the frequency band ranges of 39.06-19.53 Hz, because this sub-band frequency is located in both (A6 and D7).