# Low-Speed Bearing Fault Diagnosis Based on Permutation and Spectral Entropy Measures
## 5 Results  
This section shows the results obtained from the data set defined in Section 3 by application of the methodology described in Section 4. The computed values are summarized in Figures 5 and 6 for 5 and 10 rpm, respectively. Figure 5a shows the SE values for each rotation in HS, D1, and D2, along with their affine linear regression. The obtained results are in the band of 0.05 to 0.35, as the SE values are normalized. Figure 5a reveals a general pattern for each scenario, where the values for HS are on the top of the figure and the values for D2 are close to the bottom. The values for HS and D1 are significantly close in comparison to the values for D2, which are clearly separated to the aforementioned scenarios. In comparison to HS values, values for D1 and D2 are closer to 0, specially for the case with the bigger damage D2. The affine regression for each data set can help to discern the difference among scenarios which are detected visually. From Table 1, the negative slope values reveal a very slow but steady decrease trend of the values through time. The \(y\)-intercept values expose the distance of each scenario trend to 0, where HS trend is the most distant and the D2 trend the closest one. For D1, the distance is slightly smaller in comparison to HS. To better understand the obtained values in each scenario, a statistical summary is given by the boxplot in Figure 5b and the average \(\bar{x}\), median Md, and standard deviation \(s\) values for each scenario in Table 2. From Figure 5b, the lowest average and median are from D2 and the highest are from HS. The average value of D1 is higher in comparison to D2 and closer to HS, which is consistent with the visual examination of Figure 5a. The boxplot shows an overlay of the values from D1 and HS. In specific, the first two quartiles of HS are overlapped to the calculated values from D1. The standard deviation for D2 is specially higher in comparison to D1 and HS, as seen in 5b. Overall, and considering as reference the values of HS, the average values decrease for D1 (13%) and D2 (56%). For the median, a decrease is also notable for D1 (12%) and D2 (57%). Figure 4: Diagram of the signal analysis procedure. Results obtained for data at 10 rpm can be seen in Figure 5(a), where the SE values for HS, D1, and D2, along with their affine linear regression are shown. The figure shows values in the band of 0.1 to 0.3 for the normalized value of SE. In general, the values corresponding to HS are higher than those of the bearings with damage. The trend for the D1 and D2 values is significantly below the value trend for the HS bearing, which is lower when the size of circular damage is higher. Although the values from D1 can be seen as overlapping the HS values, the affine linear regression for each set of data have different slope and \(y\)-intercept values (Table 3). In contrast, the differences between data from HS and D2 are easy to observe in the figure. The linear regression highlights the disparities among the scenarios. As Table 3 shows, the slopes are negative. The \(y\)-intercept value for HS is the largest of all the values for the three scenarios, and the lowest value is for the D2 scenario. A statistical summary of the data from each scenario is shown in Figure 5(b). The average \(\bar{x}\), median Md, and standard deviation \(s\) of each scenario are shown in Table 4. From Figure 5(b), HS has the highest average value and median. As D1 and D2 have lower values of \(\bar{x}\) in comparison with HS, \(\bar{x}\) is lower when seeded damage exists. This situation also occurs for the median, which has a higher value in HS, but is lower for D1 and D2. The standard deviations for HS and D2 are similar, but for D1, the standard deviation is significantly higher than those for HS and D2. This value corresponds to the observed trend for Figure 5(a). The box plot shows an overlay of the values from HS and D1. In particular, the last three quartiles of D1 are overlapped with the values from the SE calculation for the HS.