## 2 The ProbPlot via IR-AVPCA Technique for Bearing Fault Detection and Diagnosis (BFDD)
### Discussion  
#### 3.3.1 Under Constant Speed Environment  
Table 3 shows that the AVPCA could detect the different bearing faults with a 78.67%, 97.33%, and 100% success rate (i.e., fault detection rate) for the features (images) generating method using the raw vibration signal, the generating method after capturing the FFT of the vibration signal, and the generating method using the proposed ProbPlot technique, respectively. However, the classical PCA could detect the different bearing faults with only a 68%, 86.67%, and 89.33% success rate, respectively. A similar result was obtained for the fault diagnosis; the average success rates with the AVPCA were 76.89%, 96.44%, and 98.22%, and with the classical PCA they were 63.56%, 80.44%, and 84.43%, respectively. Thus, using the AVPCA improves both fault detection and diagnosis capability. Furthermore, these results show clearly the advantage of generating the features (images) using the proposed ProbPlot technique (100% success rate for fault detection and 98.22% success rate for fault diagnosis) compared to the FFT of the vibration signal (97.33% success rate for fault detection and \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**PC Number** & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline Eigenvalues & \(11.4\times 10^{9}\) & \(4.63\times 10^{-3}\) & \(3.49\times 10^{-4}\) & \(8.04\times 10^{-5}\) & \(4.51\times 10^{-6}\) & \(3.67\times 10^{-6}\) \\ CPV (\%) & 99.76 & 99.83 & 99.87 & 99.91 & 99.94 & 99.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: CPV precision of the eigenvalues. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Constant Speed**} & \multicolumn{4}{c}{**Variable Speed**} \\ \hline \multirow{3}{*}{**Method**} & **Task** & **Fault** & \multirow{3}{*}{**Fault**} & \multirow{3}{*}{**Fault Diagnosis**} & \multicolumn{2}{c}{**Fault**} & \multirow{3}{*}{**Fault**} & \multirow{3}{*}{**Diagnosis**} \\  & & & & & & & & Detection & \\ \cline{3-8}  & Features (images) are & BFF & ORF & IRF & BBF & BFF & ORF & IRF & BBF \\ \cline{3-8}  & obtained from the raw & \multirow{3}{*}{**68**} & 68 & 62.67 & 60 & \multirow{3}{*}{**49.33**} & 40 & 38.67 & 34.67 \\ \cline{3-8}  & vibration data signal & & & & & & Average: & **37.78** \\ \cline{3-8}  & Features are captured & BFF & ORF & IRF & BBF & BFF & ORF & IRF & BBF \\ \cline{3-8}  & after the FFT of the vibration signal & \multirow{3}{*}{**86.67**} & 82.67 & 78.67 & 80 & - & - & - & - \\ \cline{3-8}  & Features are generated & \multirow{3}{*}{BFF} & \multirow{3}{*}{ORF} & \multirow{3}{*}{IRF} & \multirow{3}{*}{BBF} & \multirow{3}{*}{BFF} & \multirow{3}{*}{ORF} & \multirow{3}{*}{IRF} & \multirow{3}{*}{BBF} \\  & using the proposed & \multirow{3}{*}{**89.33**} & 85.33 & 82.67 & \multirow{3}{*}{**81.33**} & & 77.33 & 78.67 & 72 \\ \cline{3-8}  & ProbPlot technique & \multirow{3}{*}{**89.33**} & \multirow{3}{*}{Average: **84.43**} & & \multicolumn{3}{c}{Average: **76**} \\ \cline{3-8}  & Features (images) are & BFF & ORF & IRF & BBF & ORF & IRF & BBF \\ \cline{3-8}  & obtained from the raw & \multirow{3}{*}{**78.67**} & 78.67 & 76 & 76 & \multirow{3}{*}{**68**} & 72 & 62.67 & 65.33 \\ \cline{3-8}  & vibration data signal & & & & & Average: & **66.67** \\ \cline{3-8}  & Features are captured & BFF & ORF & IRF & BBF & ORF & IRF & BBF \\ \cline{3-8}  & after the FFT of the vibration signal & \multirow{3}{*}{**97.33**} & 98.67 & 96 & 94.67 & - & - & - & - \\ \cline{3-8}  & Features are generated & \multirow{3}{*}{BFF} & \multirow{3}{*}{ORF} & \multirow{3}{*}{IRF} & \multirow{3}{*}{BBF} & \multirow{3}{*}{BFF} & \multirow{3}{*}{ORF} & \multirow{3}{*}{IRF} & \multirow{3}{*}{BBF} \\  & using the proposed & \multirow{3}{*}{ProbPlot technique} & \multirow{3}{*}{**100**} & \multirow{3}{*}{100} & \multirow{3}{*}{97.33} & \multirow{3}{*}{97.33} & \multirow{3}{*}{**98.67**} & \multirow{3}{*}{**98.67**} & \multirow{3}{*}{Average: **95.56**} \\ \cline{3-8}  & ProbPlot technique & & & & & & Average: & **95.56** \\ \hline \hline \end{tabular}
\end{table}