# Nonlinear Extended-state ARX-Laguerre PI Observer Fault Diagnosis of Bearings
## 5 Results and Analysis
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithms** & \multicolumn{2}{c}{**Proposed Method**} & \multicolumn{2}{c}{**ALPIO**} \\ \hline
**Crack Diameters (mm)** & 3 & 6 & 3 & 6 \\
**Normal Stat** & 100\% & 100\% & 80\% & 80\% \\
**IR Fault** & 95\% & 96\% & 67\% & 73\% \\
**OR Fault** & 95\% & 97\% & 72\% & 80\% \\
**Ball Fault** & 96\% & 100\% & 78\% & 74\% \\
**IR-Ball Fault** & 93\% & 98\% & 80\% & 81\% \\
**OR-Ball Fault** & 97\% & 97\% & 82\% & 82\% \\
**IR-OR Fault** & 98\% & 98\% & 78\% & 82\% \\
**IR-OR-Ball Fault** & 97\% & 97\% & 78\% & 81\% \\
**Average** & 96.1\% & 97.9\% & 77.6\% & 79.4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fault diagnosis results using dataset 1 with the proposed method and ARX-Laguerre proportional integral observation (ALPIO) when the torque speed is 300 RPM. Figure 19: Residual signal for the inner-outer-ball faulty condition, normal, ball, inner, outer, inner-ball, outer-ball, and inner-outer thresholds with a crack width of 6 mm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithms** & \multicolumn{2}{c}{**Proposed Method**} & \multicolumn{2}{c}{**ALPIO**} \\ \hline
**Crack Diameters (mm)** & 3 & 6 & 3 & 6 \\
**Normal Stat** & 100\% & 100\% & 80\% & 80\% \\
**IR Fault** & 95\% & 96\% & 67\% & 73\% \\
**IR Fault** & 95\% & 96\% & 70\% & 73\% \\
**OR Fault** & 96\% & 97\% & 72\% & 82\% \\
**Ball Fault** & 97\% & 99\% & 78\% & 79\% \\
**IR-Ball Fault** & 94\% & 98\% & 80\% & 84\% \\
**OR-Ball Fault** & 97\% & 97\% & 83\% & 83\% \\
**IR-OR Fault** & 98\% & 100\% & 78\% & 82\% \\
**IR-OR-Ball Fault** & 97\% & 98\% & 79\% & 80\% \\
**Average** & 96.8\% & 98.2\% & 78.3\% & 81.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fault diagnosis results using dataset 2 with the proposed method and ARX-Laguerre proportional integral observation (ALPIO) when the torque speed is 400 RPM. ARX-Laguerre PI observer fault diagnosis method efficiently identifies single and composite faults in an induction motor. To analyze the false alarm in the proposed algorithm, the confusion matrix using dataset 2 is illustrated in Tables 6 and 7. Based on Table 6, for normal condition, apart from the precision is 100% but recall is 97.1% because proposed method cannot predict all normal case correctly. The main target to design the classifier is improving the performance of recall and precision, as well. Regarding Tables 6 and 7, the overall accuracy for 3 mm crack size is 95.07% and for 6 mm crack size is 98.13%. In this experiment, the bearing data are collected under four different motor speeds, as shown in Table 1. Using the proposed method, this system is modeled by the ARX-Laguerre method. The proposed method is robust even if the motor speed changes. When the motor speed changes, the system model is changed, and the proposed observer detects the model change. This technique is robust, and the speed variation is defined as an uncertainty condition. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithms** & **Proposed Method** & \multicolumn{2}{c}{**ALPIO**} \\ \hline
**Crack Diameters (mm)** & 3 & 6 & 3 & 6 \\
**Normal Stat** & 100\% & 100\% & 88\% & 88\% \\
**IR Fault** & 97\% & 97\% & 75\% & 78\% \\
**OR Fault** & 97\% & 98\% & 76\% & 82\% \\
**Ball Fault** & 97\% & 99\% & 82\% & 82\% \\
**IR-Ball Fault** & 95\% & 98\% & 83\% & 84\% \\
**OR-Ball Fault** & 97\% & 98\% & 84\% & 84\% \\
**IR-OR Fault** & 98\% & 99\% & 80\% & 82\% \\
**IR-OR-Ball Fault** & 97\% & 97\% & 79\% & 81\% \\
**Average** & 97.3\% & 98.8\% & 79.6\% & 82.4\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fault diagnosis results using dataset 3 with the proposed method and ARX-Laguerre proportional integral observation (ALPIO) when the torque speed is 450 RPM.