## 3 Proposed Approach for the Bearing Failure Diagnosis
Figure 3: Stator current signals of Motor 1, without bearing faults, coupled load of 5 N.m. and supply frequency of 60 Hz. Figure 2: Block diagram of signal acquisition, data processing, and classification of the three-phase induction motor (TIM) bearing diagnosis system. The DMI signatures for all samples collected in the experimental tests were obtained using this feature extraction tool. These DMI curves are similar regardless of the machine's operating conditions. Figures 5 and 6 illustrate the behavior of the DMI values with the evolution of bearing defects. It is analyzed that the characteristic patterns of the DMI are similar regardless of the load in the axis of the machines. Firstly, Figure 5 was obtained for signals for Motor 1 with a supply frequency of 60 Hz and with a coupled load torque of 0.5 N.m. In this figure, it is possible to notice that the evolution of wear on the machine's bearings causes an increase in mutual information's maximum value. In conclusion, as the fault progresses, the peak of the DMI increases. These characteristic patterns are also similar and can be analyzed as the machine's load torque changes. Figure 6 shows the DMI curves for Motor 1 with a supply frequency of 60 Hz and a load torque of 5.0 N.m. Again, there is a similar behavior observed in Figure 5. With the evolution of the defect, there is an increase in the maximum values of DMI signatures. All the previous analyses were also performed for Motor 2, and the same behavior presented in Figures 5 and 6 was observed regardless of the machine's supply frequency. Once calculated, the DMI values were normalized using the maximum of the mutual information (\(MI_{max}\)) found in all TIM operating situations. Then, the most relevant attributes of mutual information were selected using the ABC algorithm to reduce the input matrix of the C4.5 and MLP ANN classifiers. The ABC algorithm was selected because it is widely employed in pattern classification problems, as [PERSON] and [PERSON] [27] and [PERSON] et al. [28]. It was also observed that the ABC algorithm could optimize the data matrix more efficiently, considering that this matrix has been reduced with a smaller amount of data. Figure 4: Delayed mutual information signature of Motor 1, without bearing faults, coupled load of 5 N.m. and supply frequency of 60 Hz. In the step of attribute selection using the ABC algorithm, this tool employs the Correlation Feature Selector (CFS) algorithm, a technique that correlates the data set attributes based on a heuristic function. This algorithm also considers each attribute's individual predictive ability and the correlation degree between those attributes, including the class [37]. This methodology evaluates a subset of attributes, using the concept of relevance and redundancy. The relevance of an attribute is measured by the correlation of that attribute with the class, and the redundancy is measured by the correlation of that attribute with the other attributes of the subset. These concepts are intuitive, and they use the two main objectives of selecting attributes: choosing attributes with greater predictive power and decreasing the dimensionality by removing attributes with redundant information. Thus, the CFS method seeks to choose attributes with greater relevance and less redundancy. The implementation is carried out using a local search strategy named forward, which only adds an attribute A to a subset S if there is no other attribute belonging to this set that has a greater correlation with class C than the attribute A. Therefore, the search for subsets of attributes is completed when the addition of attributes does not improve the  
Figure 5: Delayed mutual information signatures change with the evolution of the bearing faults-Motor 1 with a supply frequency of 60 Hz and coupled load of 0.5 N.m.  
Figure 6: Delayed mutual information signatures change with the evolution of the bearing faults-Motor 1 with a supply frequency of 60 Hz and coupled load of 5 N.m.  
assessment value than the current best subset.