**6. Discussion**

84 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

**Figure 16.** Real variations of electromagnetic torque versus the shaft rotational speed of the WRIM

40% 30% 20% 10% Healthy

287.5 288 288.5 289 289.5 290

Shaft rotational speed [rad/s]

**20% 30% 10% 40%**

**Figure 17.** Variations of electromagnetic torque residues versus the shaft rotational speed residues of

**Healthy**


Shaft rotational speed

the WRIM

10.3



0

Electromagnetic torque

0.2

0.4

0.6

10.35

10.4

10.45

Electromagnetic torque [Nm]

10.5

Several types of representations are used in the signals processing domain, especially for the electrical machines diagnosis. We can mention the temporal representation (Figure 8 to Figure11, Figure 14 and Figure 15) and the signal frequency analysis. Although they have proved their efficiency, the state variable representations between them also show their advantages. They can be performed without mathematical transformation (Figure 16) and with mathematical transformation (Figure 12 and Figure 13).

The latter representation type and the temporal representation are confronted with the PCA method application results (Figure 14, Figure 15 and Figure 17). Only the simulation results with stator faults are presented because the global behavior of the state variables in both rotor and stator faults are almost similar.

For the temporal variations case, the rotor currents (Figure 9) and the shaft rotational speed (Figure 10) are the variables which produce the most information in presence of defaults. The defaults occur on the rotor current frequency and the shaft rotational speed magnitude.

The electromagnetic torque variations versus the shaft rotational speed also show clearly the WRIM operation zone in the presence of defaults (Figure 16). On the opposite, the representations with mathematical transformations (Figure 12 and Figure 13) do not provide significant information due to the fact that the stator currents remain almost unchanged in the presence of defaults (Figure 8).

With PCA method application, every representation type shows precisely the differences between healthy and faulted WRIM (Figure 14, Figure 15 and Figure 17). In the healthy case, residues are zero. When defaults appear, the residue representations have an effective value with an absolute value superior to zero.

In the figure 17, the healthy case is represented by a point situated on the coordinate origins. Therefore, one can show several right lines corresponding to the faulted cases. This behavior is due to the proportional characteristic of the considered faults.

PCA method proved to be very effective in electrical machines faults detection. This requires a good choice of the number of the principal components to be retained so that information contained in residues is relevant.
