# Detection of Broken Bars in Induction Motors Using Histogram Analysis of Current Signals
## 3 Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Iteration** & **Best** & **Best** & **Iteration** & **Best** & **Best** \\  & **Observed** & **Estimated** & **Observed** & **Estimated** \\ \hline
1 & 0.377380 & 0.377380 & 16 & 0.058669 & 0.058932 \\
2 & 0.254860 & 0.266290 & 17 & 0.058669 & 0.058645 \\
3 & 0.137740 & 0.137790 & 18 & 0.058669 & 0.058685 \\
4 & 0.065611 & 0.065584 & 19 & 0.058669 & 0.058689 \\
5 & 0.058669 & 0.058120 & 20 & 0.058669 & 0.058773 \\
6 & 0.058669 & 0.059034 & 21 & 0.058669 & 0.058808 \\
7 & 0.058669 & 0.058826 & 22 & 0.058669 & 0.058937 \\
8 & 0.058669 & 0.058769 & 23 & 0.058669 & 0.058980 \\
9 & 0.058669 & 0.058740 & 24 & 0.058669 & 0.059034 \\
10 & 0.058669 & 0.058748 & 25 & 0.058669 & 0.059115 \\
11 & 0.058669 & 0.587110 & 26 & 0.058669 & 0.058672 \\
12 & 0.058669 & 0.058711 & 27 & 0.058669 & 0.058672 \\
13 & 0.058669 & 0.058715 & 28 & 0.058669 & 0.058672 \\
14 & 0.058669 & 0.558560 & 29 & 0.058669 & 0.058672 \\
15 & 0.058669 & 0.057117 & 30 & 0.058669 & 0.058672 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Hyperparameters (decision trees) for Test \(C_{7}\). with an accuracy of 88.15%. At the end of the plot, it can be shown that 250 samples obtain an accuracy of 98.05%. Considering the percentage results obtained from the polynomial regression curve, additional classification tests were performed. At this stage of the experimental tests, the \(B_{6}\) displacements resulting from Test B and the best feature in Test C were considered. The accuracy percentages per class are shown in Figure 9 and have been obtained using the homogeneity texture for two different classifiers. The classification accuracy achieved is 98.16% using the Bagged decision tree and 91.4% for K-NN. Table 7 compares the proposed approach with previous works in the literature. The second column in the table presents the methods, the third column the type of faults, the fourth column the type of signal, the fifth the domain of analysis, and finally, the accuracy. The proposed method achieves an accuracy of 98.16% using fundamental and low-complexity arithmetic operations. The nature of the proposed algorithm allows for parallelization of the computations to speed up the processing. However, authors in [31] achieved a 100% accuracy in induction motor classification of HLT, 1 BRB, and 2 BRB. This processing implies filtering the signal to perform convolutional processing, demanding high  
Figure 8: Classification results for the homogeneity texture (\(C_{7}\)) of Table 3. (**a**) Confusion matrix for \(C_{7}\). (**b**) Polynomial regression curve for decision tree. Figure 9: Confusion matrices obtained for homogeneity feature. (**a**) K-nearest neighbor. (**b**) Bagged decision tree. computational resources. The accuracy difference is irrelevant to our proposed conventional computational resource approach. Likewise, in [22], the authors initially filtered the signal; then, an analysis window was used for segmenting and detecting BRB under different motor loads. The final detection consisted of checking the presence of BRB without considering additional motor conditions and achieving a lower percentage than the proposed method. On the other hand, in [32], the authors presented a dataset obtained through an Ansys Maxwell simulator to generate synthesized signals for evaluating the signal decomposition with cross-correlation. The results are promising; however, simulated signals do not provide real motor behavior. In [33], authors developed a similar methodology to our approach for detecting HLT, 1 BRB, and 2 BRB, obtaining an accuracy of 98.3%. However, our system proposes a more robust analysis that includes nine texture features for describing motor behavior.