# 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
\begin{table}
\begin{tabular}{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** & 96\% & 98\% & 91\% & 92\% & 82\% & 81\% \\
**OR Fault** & 98\% & 98\% & 94\% & 95\% & 70\% & 73\% \\
**Ball Fault** & 98\% & 99\% & 94\% & 94\% & 72\% & 74\% \\
**IR-Ball Fault** & 98\% & 99\% & 94\% & 96\% & 79\% & 80\% \\
**OR-Ball Fault** & 98\% & 97\% & 96\% & 93\% & 80\% & 82\% \\
**IR-OR Fault** & 97\% & 97\% & 94\% & 94\% & 80\% & 81\% \\
**IR-OR-Ball Fault** & 98\% & 98\% & 96\% & 96\% & 81\% & 82\% \\ \hline
**ACA\%** & 98.3 & 98.4 & 95.1 & 95.6 & 79.6 & 80.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The multi-fault diagnosis accuracy for 300 RPM torque speed. \begin{table}
\begin{tabular}{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** & 96\% & 98\% & 91\% & 92\% & 82\% & 81\% \\
**OR Fault** & 98\% & 98\% & 94\% & 95\% & 70\% & 73\% \\
**Ball Fault** & 98\% & 99\% & 94\% & 94\% & 72\% & 74\% \\
**IR-Ball Fault** & 98\% & 99\% & 94\% & 96\% & 79\% & 80\% \\
**OR-Ball Fault** & 98\% & 97\% & 96\% & 93\% & 80\% & 82\% \\
**IR-OR Fault** & 97\% & 97\% & 94\% & 94\% & 81\% & 82\% \\
**IR-OR-Ball Fault** & 98\% & 98\% & 95\% & 96\% & 81\% & 82\% \\ \hline
**ACA\%** & 97.9 & 98.3 & 94.8 & 95 & 79.1 & 80.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The multi-fault diagnosis accuracy for 400 RPM torque speed. The SHSE acoustic emission dataset is used to test the robustness of the proposed method against motor speed variation for fault detection and diagnosis. The fault diagnosis results for the acoustic emission REB datasets provided by the SHSE Lab with motor speed variation and fixed crack sizes are tabularized in Table 12.

Table 12 shows that the average of fault diagnosis accuracy in the presence of load variation for the proposed method is about 97.95%, for the SFO is about 94.9%, and for the FO is 80.35%. Moreover, the proposed method of fault diagnosis outperforms the SFO, yielding average performance accuracy increases of about 3.4% and 2.7% for 3 mm and 6 mm crack sizes, respectively. Furthermore, the proposed fault diagnosis method outperforms the FO, yielding average performance accuracy increases of about 18% and 17.2% for 3 mm and 6 mm crack sizes, respectively. Thus, the proposed fault diagnosis method is more robust than the other two methods for multi-type fault diagnosis in bearings. ## 5 Conclusions

In this paper, a hybrid approach using the SVM-based fuzzy orthonormal-ARX adaptive fuzzy logic-structure feedback observer was developed for detection and classification of REB faults. To modeling the vibration and AE bearing signals, the fuzzy orthonormal-ARX technique is proposed. Next, signal estimation is developed in four main steps. Firstly, the feedback observer is implemented for vibration and AE signals. Secondly, the multi-structure technique is recommended to decrease the problems usually encountered with varying motor speeds. Thirdly, a TSK fuzzy procedure is suggested to decrease the estimation error. In the final step, the adaptive approach improves the reliability, robustness, and stability of the proposed signal estimation algorithm. Moreover, an SVM is used to detect and classify single-type and multi-type REB faults. Two different datasets are defined to validate the effectiveness of the proposed observer: (a) the CWRU vibration dataset, and (b) the AE signals provided by the SHSE Lab. The proposed algorithm increases the classification accuracy from 86% in the SVM-based fuzzy orthonormal-ARX feedback observer (FO) to 97.5% in single-type fault and from 80% to 98.3% in the multi-type faults.