# Hybrid Fault Diagnosis of Bearings: Adaptive Fuzzy Orthonormal-ARX Robust Feedback Observer
## 3 Anomaly Diagnosis Based on Proposed Hybrid Algorithm
### Fault Detection and Fault Classification
For analyzing the fault diagnosis capabilities of the proposed methodology, SFO and FO techniques, the energy of residual signals that extracted from SHSE Lab dataset consisting of 3200 samples (400 data instances per class) was randomly split into training and testing subsets. Specifically, 2400 samples (300 instances per class) were used for training SVM classification algorithms, whereas the remaining previously unobserved 800 samples (100 instances per class) were utilized for the testing process. The fault diagnosis results and the average of accuracy (ACA) for the acoustic emission REB datasets provided by the SHSE Lab with various crack diameters (3 mm and 6 mm) and fixed torque speed conditions are tabularized in Tables 8-11. These tables show that the proposed method outperforms the SFO, yielding average performance accuracy increases of about 3.2% and 2.93% for 3 mm and 6 mm crack sizes, respectively. In addition, the proposed method outperforms the FO, yielding average performance accuracy increases of about 18.75% and 17.78% for 3 mm and 6 mm crack sizes, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Algorithms** & **PM (Proposed Method)** & \multicolumn{3}{c}{**SFO**} & \multicolumn{3}{c}{**FO**} \\ \hline
**Crack Diameters (in)** & 0.007 & 0.014 & 0.021 & 0.007 & 0.014 & 0.021 & 0.007 & 0.014 & 0.021 \\
**Normal** & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% \\
**Ball Fault** & 97\% & 98\% & 100\% & 91\% & 90\% & 90\% & 85\% & 86\% & 86\% \\
**OR Fault** & 97\% & 97\% & 100\% & 88\% & 86\% & 89\% & 83\% & 84\% & 86\% \\ IR **fault** & 96\% & 98\% & 100\% & 93\% & 95\% & 95\% & 85\% & 86\% & 88\% \\ \hline
**ACA** & 97.5\% & 98.3\% & 100\% & 93\% & 92.3\% & 93.5\% & 88.3\% & 89\% & 90\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The single fault diagnosis accuracy for 3 hp torque load. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Algorithms** & **PM (Proposed Method)** & \multicolumn{3}{c}{**SFO**} & \multicolumn{3}{c}{**FO**} \\ \hline
**Crack Diameters (in)** & 0.007 & 0.014 & 0.021 & 0.007 & 0.014 & 0.021 & 0.007 & 0.014 & 0.021 \\
**Normal** & 100\% & 100\% & 100\% & 100\% & 100\% & 100\% & 96\% & 96\% & 96\% \\
**Ball Fault** & 97\% & 97\% & 98\% & 82\% & 86\% & 88\% & 80\% & 82\% & 82\% \\
**OR Fault** & 88\% & 95\% & 95\% & 80\% & 85\% & 88\% & 78\% & 81\% & 82\% \\
**IR fault** & 94\% & 98\% & 98\% & 90\% & 96\% & 96\% & 85\% & 86\% & 87\% \\ \hline
**ACA** & 95.8\% & 97.5\% & 97.8\% & 88\% & 91.8\% & 93\% & 84.8\% & 86.3\% & 86.8\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The single fault diagnosis accuracy in the presence of load variation. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithms** & **PM (Proposed Method)** & \multicolumn{2}{c}{**SFO**} & \multicolumn{2}{c}{**FO**} \\ \hline
**Crack Diameters (mm)** & 3 & 6 & 3 & 6 & 3 & 6 \\
**Normal** & 100\% & 100\% & 100\% & 100\% & 88\% & 90\% \\
**IR Fault** & 98\% & 99\% & 93\% & 94\% & 80\% & 80\% \\
**OR Fault** & 99\% & 98\% & 95\% & 96\% & 74\% & 75\% \\
**Ball Fault** & 98\% & 98\% & 94\% & 94\% & 75\% & 76\% \\
**IR-Ball Fault** & 97\% & 97\% & 94\% & 95\% & 78\% & 80\% \\
**OR-Ball Fault** & 97\% & 98\% & 95\% & 95\% & 80\% & 81\% \\
**IR-OR Fault** & 99\% & 99\% & 94\% & 94\% & 80\% & 82\% \\
**IR-OR-Ball Fault** & 98\% & 98\% & 95\% & 96\% & 81\% & 82\% \\ \hline
**ACA\%** & 98.1 & 98.5 & 95 & 95.1 & 79.3 & 80.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The multi-fault diagnosis accuracy for 450 RPM torque speed.