## 2 Theoretical Background  
### Bearing Faults in Electric Motors  
The rotating movement of the electrical machines, such as IM, is produced by means of the bearing elements; therefore, its proper operation ensures the availability of such electric machines [14]. The occurrence of failures in bearings may be to different sources; indeed, different types of failures may appear in bearings; in this sense, the most studied faults in bearings are related to problems that appear in the inner race, outer race, cage, and balls. Although the common occurrence of faults in bearings can be produced by overloads, the electrical discharge is also considered a critical issue that can lead to the appearance of faults in bearings [15].  
This issue is also known as electrical erosion, and it is considered as a phenomenon produced by the current leakage; specifically, this phenomenon produces a micro-scaling of the rolling surfaces [39]. Thereby, the current leakage usually occurs during the IM operation generating small craters on the bearing surfaces (outer and/or inner races), and this damage appears since the leakage of currents travels through the rolling elements (bearing balls) from the outer race to the inner race, as shown in Figure 1a. Subsequently, on the contact surfaces, a similar process to the electric arc welding arises, that is, a high current density on small contact surfaces, as Figure 1b depicts. Then, as shown in Figure 1c, the material is heated to high temperatures, where the bearing material may experiment with a temperature ranging from the temper level to the melt level. As a consequence, the appearance of discolored areas and the appearance of craters occur in those areas where the material has been melted and removed due to the rotation of the rolling element. Finally, the excess material that adhered to the rolling elements of the bearing wears away, as shown in Figure 1d.  
In this sense, electric erosion is considered one of the main causes of the gradual degradation of bearings in electric machines such as IMs; indeed, such phenomenon may produce the sudden appearance of damages on the outer and/or inner races of the bearing [13]. Although, initially, the failures produced on the outer and/or inner races may not affect the operation of the electric machines; the quick evolution of the bearing degradation can cause several issues in electric machines, even their unexpected breakdown. Thereby, in real applications, when craters are produced in the outer race and/or the inner race of the bearing, the generation of impacts when the rolling elements pass through them is produced. In fact, as it is known and according to the theoretical basis of bearings operation, when they are working under the influence of defects in the inner-race and/or outer-race, it affects the whole bearing system due to the influence of the induced impacts that result from balls coming into contact with the damaged area during the rotating operation of bearings. Even though these impacts are usually generated at intervals of time that are influenced by the severity (size) and shape of the fault, its occurrence may or may not appear depending on the severity of the damage [40].