*5.3. Follow-Up*

The follow-up starts at iteration 11 to iteration 90 for the 5 *GV*, Calinski and Davies–Bouldin index, density, contour and distance, Figure 10. The behavior of these variables was di fferent and remained similar to the behaviors established during the simulation. The Calinski index increased with the size of defects. At iteration 65, the index had an exponential evolution in the mathematical form *GV*1 = 161.13*e*0.084*<sup>k</sup> R*<sup>2</sup> = 0.982 , Figure 10a. The Davies–Bouldin index decreased proportionally with the fault, Figure 10b. In this case, a linear regression *GV*2 = −0.0107*k* + 0.947 *R*<sup>2</sup> = 0.994 was proposed. The density decreased with the increasing amplitude values to attend around zero from signal number sixty to ninety, the mathematical model was *GV*3 = 197.15. exp(−0.095*k*) *R*<sup>2</sup> = 0.940 . The distance curve was increasing with the increasing of the amplitude values. The evolution was exponential *GV*4 = 0.225*e*0.039*<sup>k</sup> R*<sup>2</sup> = 0.828 . However the monotony was not relevant. There was a lot of variability around the average trend, Figure 10d. The contour shows two trends, Figure 10e. The contour evolved proportionally for the first 60 iterations with a low slope, *GV*5 = 0.014*k* − 0.0697 *R*<sup>2</sup> = 0.934 . From the 60th iteration onwards, the evolution remained linear but increased sharply, *GV*5 = 0.4791*k* − 3.518 *R*<sup>2</sup> = 0.904 .

(**a**) (**b**)

**Figure 10.** Follow-up of the detected cluster: evolution of (**a**) Calinski index, (**b**) Davies–Bouldin index. (**c**) Density, (**d**) distance and (**e**) contour.

By comparing the evolution of these indicators, the Calinski index and the contour showed some singularities in the evolution at iteration 60 corresponding to defect 5. These parameters indicate the severity degradation stage in the rolling bearing. The Davies-Bouldin index was the index most correlated to the number of iteration ( *R*<sup>2</sup> = 0.994). In general, these indicators allowed us to make a prognosis on the evolution of these parameters with the iterations.
