# 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
#### 4.2.1 Single-Type Fault Diagnosis Provided by the CWRU Dataset

For analyzing the fault diagnosis capabilities of the proposed methodology, SFO and FO techniques, the energy of residual signals that extracted from CWRU consisting of 1600 samples (400 data instances per class) was randomly split into training and testing subsets. Specifically, 1200 samples (300 instances per class) were used for training SVM classification algorithms, whereas the remaining previously unobserved 400 samples (100 instances per class) were utilized for the testing process. In the first step, we investigate the fault diagnosis capabilities of the proposed method, SFO, and FO on four different crack-variant CWRU datasets, when the torque load remains fixed. The fault diagnosis results and the average of accuracy (ACA) are tabularized in Tables 3-6. Regarding these tables, the proposed algorithm for bearing fault diagnosis clearly outperforms the state-of-the-art techniques used for comparison in this work for all fault types. In addition, the average of fault diagnosis accuracy for the proposed method is about 98.13%, while for the SFO it is about \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** & 98\% & 98\% & 99\% & 90\% & 90\% & 87\% & 86\% & 88\% & 88\% \\
**OR Fault** & 98\% & 98\% & 99\% & 88\% & 88\% & 88\% & 86\% & 87\% & 82\% \\
**IR fault** & 98\% & 99\% & 100\% & 90\% & 91\% & 91\% & 88\% & 90\% & 89\% \\ \hline
**ACA** & 98.5\% & 98\% & 99.5\% & 92\% & 92.3\% & 91.5\% & 90\% & 91.3\% & 89.8\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The single fault diagnosis accuracy for 1 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\% & 100\% & 100\% & 100\% \\
**Ball Fault** & 97\% & 97\% & 100\% & 90\% & 92\% & 94\% & 89\% & 91\% & 92\% \\
**OR Fault** & 88



93.5%, and for the FO is 90.3%. Moreover, the proposed method outperforms the SFO, yielding average performance accuracy increases of about 4.7%, 4%, and 5.1% for 0.007-inch, 0.014-inch, and 0.021-inch crack sizes, respectively. In addition, the proposed method outperforms the FO, yielding average performance accuracy increases of about 7.9%, 6.9%, and 8.8% for 0.007-inch, 0.014-inch, and 0.021-inch crack sizes, respectively. To test the robustness, the CWRU dataset with load variation is used. The fault diagnosis results are tabularized in Table 7.

Regarding this table, the average fault diagnosis accuracy in the presence of load variation for the proposed method is about 97.5%, for the SFO it is about 90.3%, and for the FO it is 86%. Moreover, the proposed method for fault diagnosis outperforms the SFO, yielding average performance accuracy increases of about 7.8%, 5.7%, and 4.8% for 0.007-inch, 0.014-inch, and 0.021-inch crack sizes, respectively. Furthermore, the proposed method outperforms the FO, yielding average performance accuracy increases of about 11%, 11.2%, and 11% for 0.007-inch, 0.014-inch, and 0.021-inch crack sizes, respectively. Therefore, the proposed method is more robust than the other two methods for single-type fault diagnosis in bearings. #### 4.2.2 Multi-Type Fault Diagnosis Provided by the SHSE Lab Dataset

In this section, we discuss the fault diagnosis capabilities of the proposed method, SFO, and FO on crack-variant datasets when the torque speeds remain fixed.