# Bearing Anomaly Recognition Using an Intelligent Digital Twin Integrated with Machine Learning
## 3 Experimental Results and Discussion
### Classification Analysis
Based on this table, the average inner CSI accuracies are 100%, 90.1%, and 77.7%, respectively, using the proposed digital twin integrated with SVM (MS-HRKF+SVM), the combination of the MS-RKF with SVM. Hence, the proposed digital twin integrated with SVM (MS-HRKF+SVM) improves the average inner CSI in the combination of the MS-RKF with SVM and the combination of the MS-KF with SVM by 9.9% and 22.3%, respectively. Table 6 proves the effect of the proposed digital twin integrated with SVM (MS-HRKF+SVM), the combination of the MS-RKF with SVM, and the combination of the MS-KF with SVM for the outer CSI when the crack sizes are 0.007, 0.014, and 0.021 inch. Based on this table, the average outer CSI accuracies are 100%, 90.7%, and 80.8%, respectively, using the proposed digital twin integrated with SVM (MS-HRKF+SVM), the combination of the MS-RKF with SVM, and the combination of the MS-KF with SVM. Henceforth, the proposed digital twin integrated with SVM (MS-HRKF+SVM) modifies the average outer CSI in the combination of the MS-RKF with SVM and the combination of the MS-KF with SVM by 9.3% and 19.2%, respectively. Based on Tables 4-6, the power of the CSI in the proposed digital twin integrated with SVM (MS-HRKF+SVM) is better than the other two methods. Thus, the proposed digital twin integrated with SVM (MS-HRKF+SVM) is more reliable than the other two methods for the ball, inner, and outer CSI. Furthermore, Figure 12 demonstrates the effect of the robustness in the proposed digital twin integrated with SVM (MS-HRKF+SVM), the combination of the MS-RKF with SVM, and the combination of the MS-KF with SVM for 10 experiments. Based on this figure, due to the boxplot, the resistance of the proposed digital twin integrated with SVM (MS-HRKF+SVM) for the outer, inner, and ball CSI is better than the other two approaches. Thus, based on Figures 8-10, the accuracy of the proposed digital twin integrated with SVM (MS-HRKF+SVM) is significantly better than the combination of the MS-RKF with SVM and the combination of the MS-KF with SVM for bearing FPR. In addition, based on Figure 11, the proposed digital twin integrated with SVM (MS-HRKF+SVM) is more robust than the combination of the MS-RKF with SVM and the combination of the MS-KF with SVM for bearing FPR. Tables 4-6 and Figure 20 show \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Outer Crack Sizes (inch)** & **0.007** & **0.014** & **0.021** & **Average** \\ \hline MS-HRKF+SVM (\%) & 100 & 100 & 100 & 100 \\ MS-RKF+SVM (\%) & 95 & 83.8 & 93.5 & 90.7 \\ MS-KF+SVM (\%) & 77.3 & 80 & 85.3 & 80.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Average accuracy of the outer CSI using the proposed MS-HRKF+SVM, the MS-RKF+SVM, and the MS-KF+SVM. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Ball Crack Sizes (inch)** & **0.007** & **0.014** & **0.021** & **Average** \\ \hline MS-HRKF+SVM (\%) & 100 & 97 & 99 & 98.7 \\ MS-RKF+SVM (\%) & 88.8 & 82.5 & 95.5 & 88.9 \\ MS-KF+SVM (\%) & 78.2 & 73 & 81.8 & 77.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average accuracy of the ball CSI using the proposed MS-HRKF+SVM, the MS-RKF+SVM, and the MS-KF+SVM. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Ball Crack Sizes (inch)** & **0.007** & **0.014** & **0.021** & **Average** \\ \hline MS-HRKF+SVM (\%) & 100 & 97 & 99 & 98.7 \\ MS-RKF+SVM (\%) & 88.8 & 82.5 & 95.5 & 88.9 \\ MS-KF+SVM (\%) & 78.2 & 73 & 81.8 & 77.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Average accuracy of the inner CSI using the proposed MS-HRKF+SVM, the MS-RKF+SVM, and the MS-KF+SVM. that the impact (accuracy and robustness) of the proposed digital twin integrated with SVM (MS-HRKF+SVM) for the bearing CSI is better than the combination of the MS-RKF with SVM and the combination of the MS-KF with SVM.