# 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** & **Proposed Method** & \multicolumn{2}{c}{**ALPIO**} \\ \hline
**Crack Diameters (mm)** & 3 & 6 & 3 & 6 \\
**Normal Stat** & 100\% & 100\% & 90\% & 90\% \\
**IR Fault** & 97\% & 97\% & 81\% & 83\% \\
**OR Fault** & 98\% & 98\% & 78\% & 82\% \\
**Ball Fault** & 97\% & 99\% & 82\% & 84\% \\
**IR-Ball Fault** & 97\% & 97\% & 83\% & 85\% \\
**OR-Ball Fault** & 98\% & 99\% & 85\% & 85\% \\
**IR-OR Fault** & 98\% & 99\% & 82\% & 82\% \\
**IR-OR-Ball Fault** & 97\% & 98\% & 82\% & 83\% \\
**Average** & 99.9\% & 99.1\% & 81.2\% & 84.6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Fault diagnosis results of dataset 4 using the proposed method and ARX-Laguerre proportional integral observation (ALPIO) when the torque speed is 500 RPM. Tables 8 and 9 present the fault diagnosis accuracy for variable motor speeds (e.g., 300 RPM, 400 RPM, 450 RPM, and 500 RPM) in different crack sizes (e.g., 3 mm and 6 mm), various conditions (normal, ball fault, inner fault, outer fault, inner-outer fault, inner-ball fault, outer-ball fault, and inner-outer-ball fault) of the proposed method and PIO. Dataset 4 is used to calculate the threshold value for different types of faults and two crack sizes. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Predict Class** & **Normal** & **Ball** & **IR** & **OR** & **IR-Ball** & **OR-Ball** & **IR-OR** & **IR-OR-Ball** & **Precision** \\ \hline Normal & 100\% & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 100\% \\ Ball & 1\% & 97\% & 0 & 0 & 1\% & 1\% & 0 & 0 & 97\% \\ IR & 0 & 1\% & 95\% & 2\% & 1\% & 0 & 1\% & 0 & 5\% \\ OR & 0 & 0 & 1\% & 96\% & 3\% & 0 & 0 & 0 & 96\% \\ IR-Ball & 0 & 0 & 0 & 4\% & 94\% & 1\% & 1\% & 0 & 94\% \\ OR-Ball & 1\% & 1\% & 0 & 1\% & 0 & 97\% & 0 & 0 & 97\% \\ IR-OR & 1\% & 0 & 0 & 0 & 1\% & 0 & 98\% & 0 & 2\% \\ IR-OR-Ball & 0 & 0 & 0 & 0 & 0 & 0 & 3\% & 97\% & 3\% \\ Recall & 97.1\% & 97.9\% & 99\% & 93.2\% & 94\% & 97.9\% & 95.1\% & 100\% & 95.07\% \\
2.9\% & 2.1\% & 1\% & 6.8\% & 6\% & 2.1\% & 4.9\% & 0\% & 4.93\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Confusion matrix using dataset 2 with the proposed method when the torque speed is 400 RPM and the crack size is 3 mm. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Predict Class** & **Normal** & **Ball** & **IR** & **OR** & **IR-Ball** & **OR-Ball** & **IR-OR** & **IR-OR-Ball** & **Precision** \\ \hline Normal & 100\% & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 100\% \\ Ball & 0 & 99\% & 0 & 1\% & 0 & 0 & 0 & 0 & 1\% \\ IR & 0 & 0 & 96\% & 3\% & 0 & 0 & 1\% & 0 & 4\% \\ OR & 0 & 0 & 2\% & 97\% & 1\% & 0 & 0 & 0 & 97\% \\ IR-Ball & 0 & 2\% & 0 & 0 & 98\% & 0 & 0 & 0 & 98\% \\ OR-Ball & 1\% & 2\% & 0 & 0 & 0 & 97\% & 0 & 0 & 97\% \\ IR-OR & 0 & 0 & 0 & 0 & 0 & 0 & 100\% & 0 & 0 \\ IR-OR-Ball & 0 & 0 & 1\% & 0 & 0 & 0 & 1\% & 98\% & 2\% \\ Recall & 99\% & 96.1\% & 97\% & 96\% & 99\% & 100\% & 98\% & 100\% & 98.13\% \\  & 1\% & 3.9\% & 3\% & 4\% & 1\% & 0\% & 2\% & 0\% & 1.87\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Confusion matrix using dataset 2 with the proposed method when the torque speed is 400 RPM and the crack size is 6 mm.