# Detection of Broken Bars in Induction Motors Using Histogram Analysis of Current Signals
## 3 Results  
This section evaluates the proposed classification method to analyze the displacement configuration and texture that obtains the best performance. The analysis of a single-phase current in induction motors evaluates two sets of different \(\Delta\) displacements defined in Tests A and B. Moreover, the experiments are conducted using a fixed value for the analysis window \(\mathsf{W}_{s}\), nine texture features, and comparing the accuracy performance of three classifiers. To perform the tests, 30 current signals for each category were analyzed from an induction motor diagnosed with 1 BRB, 2 BRB, and Health. From these signals, 153 histograms were obtained, divided as follows: for Test A 90 vectors, for Test B 54 vectors, and nine for Test C. Table 3 shows the accuracy classification results obtained by a multiclass decision tree for the three tests performed. Decision trees offer all the advantages of any other more robust classifier. However, the disadvantages of this classifier can be reduced by compensating hyperparameters required for determining the best configuration to train the model [30]. Therefore, the complexity of training a decision tree is controlled by the parameter that governs the process. Table 4, and Figure 7a specifies the tuning parameters evaluated in each iteration to achieve the best performance. Furthermore, Table 5 shows the summary of the decision tree tuning parameters with the best performance, and Figure 7b shows the estimated objective function value. From the total samples in the dataset, 75% were selected for training and 25% were selected for validation. Thirty tests were performed, choosing the above percentage; however, the examples were randomly selected for training and validation during the experimental tests. Based on these results of Tests A and B, the best \(\Delta\) displacements are \(B_{6}\), which are used to perform the analysis in Test C. Notably, the best percentage in Test C among all the analyzed features is \(C_{7}\), corresponding to the homogeneity attribute. Test C's classification accuracy is above 80% for three texture attributes. These results show that the proposed methodology is reliable as multiple texture features can characterize the method. Furthermore, we can consider adding signals from other motor states to be analyzed for increasing the number of faults. Therefore, additional analysis using the homogeneity feature is performed using a polynomial regression curve. This analysis validates the performance of classification as the number of samples increases. The processing time of texture features depends on the number of displacements performed. We have proposed three displacement sets; therefore, the processing time differs. In this case, the processing time for feature extraction, training, and validation of the analyzed signal is shown in Table 6.  
According to the confusion matrix shown in Figure 8a, the motor state that provides the best classification result is one broken rotor bar. Moreover, Figure 8b shows the analysis history from the initial samples evaluated through a polynomial regression curve. Based on this plot, it can be noticed that the processing of 50 samples obtains an acceptable result, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Process** & **Time** & \(\mathbf{\sigma}\) \\ \hline Feature extraction & 296.20 ms & 16.10 ms \\ Training & 15.50 s & 1.97 s \\ Validation & 18.35 μs & 48.52 μs \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Process computational time for \(C_{7}\).