# 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
The sampling rate of the record data is 12 kHz under four different motor torque loads (0 to 3 horsepower (hp)) under different rotation velocities from 1730 rpm to 1790 rpm. Table 1 shows the data classification of the CWRU bearing dataset. Furthermore, the CWRU vibration signals have three different crack sizes: 0.007, 0.014, and 0.021 inches in diameter [5; 21]. #### 4.1.2 Smart Health, Safety, Environment (SHSE) Lab Acoustic Emission (AE) Bearing Dataset

The SHSE acoustic emission dataset is used to test the effectiveness of the proposed algorithm using AE multi-crack faults. An AE sensor is used to collect data in various conditions including normal conditions, ball faults, inner (IR) faults, outer (OR) faults, inner-ball (IR-Ball) faults, inner-outer (IR-OR) faults, and inner-outer-ball (IR-OR-Ball) faults. The sampling rate of the record data is 250 kHz under four different rotational velocities (300 rpm, 400 rpm, 450 rpm, and 500 rpm) for two crack sizes: 3 and 6 millimeters in diameter. Figure 5 illustrates the bearing data collection testbench. Table 2 shows the SHSE Lab acoustic emission bearing dataset [10]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Conditions** & **Load (hp)** & **Crack Sizes (in)** \\ \hline \multirow{4}{*}{Dataset I} & Normal & 0 & \\  & Ball & 0 & \\  & IR & 0 & \\  & OR & 0 & \\ \hline \multirow{4}{*}{Dataset II} & Normal & 1 & \\  & Ball & 1 & \\  & IR & 1 & \\  & OR & 1 & \\ \hline \multirow{4}{*}{Dataset III} & Normal & 2 & \\  & Ball & 2 & \\  & IR & 2 & \\  & OR & 2 & \\ \hline \multirow{4}{*}{Dataset IV} & Normal & 3 & \\  & Ball & 3 & \\ \cline{1-1}  & IR & 3 & \\ \cline{1-1}  & OR & 3 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The Case Western Reserve University (CWRU) datasets to test the activity of the proposed algorithm in normal and abnormal bearing conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Fault Types** & **Rotational Speed (RPM)** & **Crack Sizes (mm)** \\ \hline \multirow{8}{*}{**Dataset I**} & Normal & 300 & \\  & IR & 300 & \\  & OR & 300 & \\  & Ball & 300 & \\  & IR-OR & 300 & \\  & IR-Ball & 300 & \\  & OR-Ball & 300 & \\  & IR-OR-Ball & 300 & \\ \hline \multirow{8}{*}{**Dataset II**} & Normal & 400 & \\  & IR & 400 & \\  & OR & 400 & \\ \cline{1-1}  & Ball & 400 & \\ \cline{1-1}  & IR-OR & 400 & \\ \cline{1-1}  & IR-Ball & 400 & \\ \cline{1-1}  & OR-Ball & 400 & \\ \hline \multirow{8}{*}{**Dataset III**} & Normal & 450 & \\ \cline{1-1}  & IR & 450 & \\ \cline{1-1}  & OR & 450 & \\ \cline{1-1}  & Ball & 450 & \\ \cline{1-1}  & IR-OR & 450 & \\ \cline{1-1}  & IR-Ball & 450 & \\ \cline{1-1}  & OR-Ball & 450 & \\ \cline{1-1}  & IR-OR-Ball & 450 & \\ \hline \multirow{8}{*}{**Dataset IV**} & Normal & 500 & \\ \cline{1-1}  & IR & 500 & \\ \cline{1-1}  & OR & 500 & \\ \cline{1-1}  & Ball & 500 & \\ \cline{1-1}  & IR-OR & 500 & \\ \cline{1-1}  & IR-Ball & 500 & \\ \cline{1-1}  & OR-Ball & 500 & \\ \cline{1-1}  & IR-OR-Ball & 500 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The Smart Health Safety Environment (SHSE) acoustic emission datasets to test the activity of the proposed algorithm in normal and abnormal bearing conditions. Figure 5: Block diagram of the bearing data collection testbench. ### Results

The effectiveness of fault diagnosis using the SVM-based fuzzy orthonormal-ARX adaptive fuzzy logic-structure feedback observer (proposed method) is validated against two state-of-the-art approaches, namely, the SVM-based fuzzy orthonormal-ARX structure feedback observer (SFO) and the SVM-based fuzzy orthonormal-ARX feedback observer (FO), to test single-type and multi-type fault diagnosis using vibration and AE datasets (the CWRU dataset and the SHSE Lab dataset). To test the robustness of these techniques, two different conditions are analyzed in each case study--crack-variant and load-variant.