## 4 Result and Discussion
### Fault Related Feature Evaluation  
The proposed technique for the detection of BRB in LS-PMSM includes two steps: first, the characteristic pattern of LSH, which is shown in Figure 4, is calculated, and second, the entropy features are computed. In the first stage, knowing the value of the motor slip is compulsory for LSH calculation. Therefore, the speed of the tested motor was measured and the slip was calculated. Figure 16 presents the behavior of LSH determined using Equation (2), where s and f are slip and fundamental frequency, respectively. These values are obtained from measuring the motor speed for both faulty and fault-free motors when there is no starting load and when there is a starting load equal to 1.5 Nm. As is clear in this figure, the frequency of the LSH will change between the fundamental frequency (s = 1), zero frequency (s = 1/2) and again near the fundamental frequency (s \(\approx\) 0) when the motor reaches a steady state. From this figure, it should be noted that there is a shift between the faulty and fault-free motor under the same level of load that is also created by the effect of BRB. The second stage is the quantitative approach, which begins with applying the wavelet transforms to the startup current signal. By applying wavelet transform to the signal, sets of wavelet signals are obtained based on the approximation and detail coefficient. The method is to track the evolution of the LSH. As the LSH changes in the range of 50-0-80 Hz, its evolution is reflected by the wavelet signals and covers the frequencies lower than the fundamental frequency and, hence, cancels their effects. The alternative variant proposed for detecting this evolution is to perform the signal decomposition in a number of levels that result in two approximations and one detail signal and covers the aforementioned frequency range. The number of levels that lead to such a result with their type of coefficients is marked in Figure 15. The next step, in this stage, involves entropy computation to quantify failure in LS-PMSM. Two different features introduced in the previous section are then applied in these three frequency bands (A6, A7 and D7). After all data have been analysed, the result is investigated with trend and boxplot graphs. Figure 17 illustrates the trend and boxplot graphs for entropy features used as a fault feature in this study. A number of interesting conclusions can be drawn from the analysis of these figures. The most significant is that the trends are dissimilar for all the conditions, and thus each individual case must be studied and analyzed independently. The trend graph for Shannon entropy shows an overlap between the healthy and faulty states at different levels of starting load for approximation and detail of decomposition level seven (Figure 17b,c). The trend graph for Shannon entropy in the approximation of level six indicates that there is no overlapping between the healthy and faulty states at various levels of starting load. However, by looking at the boxplot graph, there is an overlap for each condition in the same load (Figure 17a).The trend graph for log-energy entropy shows an overlapping between the healthy situation and faulty state at various levels of starting load for an approximation  
Figure 16: The behavior of LSH from experimental data. of level seven (Figure 17e). The trend graphs for log-energy entropy in the approximation of level six and detail of level seven indicate that there is no overlapping between the healthy and faulty states at various levels of starting load (Figure 17d,f). Figure 17: _Cont._  
Figure 17: Trend and boxplot for entropy features under different levels of starting load. (**a**) Shannon entropy (A6); (**b**) Shannon entropy (A7); (**c**) Shannon entropy (D7); (**d**) log-energy entropy (A6); (**e**) log-energy entropy (A7); (**f**) log-energy entropy (D7).