## 3 Proposed Approach for the Bearing Failure Diagnosis  
In the industrial environment, TIMs are subject to different operational situations, such as load torque variations, unbalanced supply voltage, installation in a harsh environment, and electrical and/or mechanical defects, among others [1; 3]. Proper monitoring to identify incipient failures related to these machines provides significant benefits to industrial processes, such as reduction of unscheduled downtime, reduced maintenance costs and more reliable machine operation. Two TIMs were tested to simulate harsh operating conditions (Motor 1 of 0.74 kW and Motor 2 of 1.48 kW). The motors operated in steady-state, with and without bearing failures. These failures were created to emulate the process of bearing degradation through overuse, under lubrication and overload. First, the bearing was cleaned, and then an abrasive slurry was used in place of the lubrication to wear the parts. Then, the motor was run for the previously set times of 15, 30, 60, and 90 min to produce the bearing's degradation. This way, four classes of faults were obtained, one for each time of operation. Once the degradation of the bearings was produced, they were cleaned and lubricated to acquire the data properly. The two TIMs were tested fed by two different inverters Siemens Sinamics G110 (G110), and Siemens MicroMaster 440 (MM440). To emulate situations common in an industrial environment, the coupled mechanical load and the supply frequency were varied. For the tests carried out with Motor 1, 808 samples were acquired, varying the load torque at 0.5 N.m intervals, from 0.5 N.m to 5.0 N.m. For Motor 2, 771 samples were collected with the load varying from 1.0 N.m to 9.0 N.m, in 1.0 N.m intervals. For both TIMS, the supply frequency varied from 20% to 100% of the nominal value at 10% intervals. These conditions were considered for each level class of bearing failure. Figure 1 shows the experimental workbench used to perform the experimental data. This workbench was designed to monitor electrical and mechanical measurements, such as voltage, current, vibration, torque and speed. In addition, it is possible to emulate many of the operating conditions mentioned above. The workbench allows the variation of the supply frequency and a mechanical torque imposition on the shaft because the TIM is connected to a direct current generator. Moreover, there is a torque meter with an integrated speed sensor that can read torque and speed signals. Hall sensors are responsible for collecting and conditioning the stator current signals transferred to the data acquisition board's analog inputs connected to a microcomputer. An algorithm developed in MATLAB software using the concepts described in Section 2.1 extracts relevant information from the collected data and reduces the number of inputs to the pattern classifiers. Figure 2 shows the procedures of the stages of acquisition, processing, and classification of signals used in this work. Since the signals of the analyzed currents are out of phase, the delayed version of the mutual information described in the Section 2.1 is used to verify the similarity measurement. This measurement is calculated using the motor phase stator current signals, \(IA\) and \(IB\), and the displacement value \(\tau\). The phase B stator current must be shifted sample by sample until the displacement value \(\tau\) is reached. To calculate the DMI measurement, for each iteration of the algorithm, the marginal _pdf_s of the stator currents, and the joint _pdf_ between these currents must be calculated. This procedure is performed recursively until the displacement value \(\tau\) is reached. In this study, a displacement value of \(\tau\) of 150 samples because using this value, the currents are in phase for at least one cycle. Figure 3 shows phases A and B of the current for Motor 1 without bearing failures, coupled load of 5 N.m, and supply frequency of 60 Hz; Figure 4 shows the calculated MI values. Figure 1: Workbench used in the experimental tests.