# Bearing Anomaly Recognition Using an Intelligent Digital Twin Integrated with Machine Learning
## 3 Experimental Results and Discussion
### Classification Analysis  
To test the power of the proposed method for FPRCI, the combination of the proposed digital twin integrated with the SVM (hence called MS-HRKF+SVM) is compared with the  
Figure 14: The frequency response of power spectral density estimation for NS, RFS, IFS, and OFS using the proposed method. Figure 15: RMS resampled residual signal using the proposed digital twin (MS-HRKF) algorithm when the motor torque loads vary from 0 to 3 hp; moreover, the crack sizes for abnormal conditions are 0.007, 0.014, and 0.021 inch. combination of the MS-RKF with SVM (hence called MS-RKF+SVM) and the combination of the MS-KF with SVM (hence called MS-KF+SVM). Figures 16-18 illustrate the confusion matrices for 10 experiments to show the accuracy of the fault pattern recognition (FPR) in the proposed digital twin integrated with SVM (MS-HRKF+SVM), the MS-RKF+SVM, and the MS-KF+SVM. In the combination of the MS-KF with SVM, the nonlinear signal modeling algorithm is integrated with the linear estimation algorithm. This algorithm has two important challenges: linear estimator and robustness. To improve the robustness the combination of the MS-RKF with SVM is recommended. Based on Figures 17 and 18, the combination of the MS-RKF with SVM improves the accuracy of FPR in the combination of the MS-KF with SVM by around 4.9%. To solve the challenge of the linear estimator in the combination of the MS-RKF with SVM and the combination of the MS-RKF with SVM, the proposed digital twin integrated with SVM (MS-HRKF+SVM) is suggested. Based on these figures, the average FPR 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, respectively, are 99.5%, 87%, and 82.1%. Thus, the proposed digital twin integrated with SVM (MS-HRKF+SVM) improves the accuracy of FPR in the combination of the MS-RKF with SVM and the combination of the MS-KF with SVM by 12.55% and 17.4%, respectively. Moreover, Figure 19 shows the impact 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 Figure 19, due to the boxplot, the resistance of the proposed digital twin integrated with SVM (MS-HRKF+SVM) is higher than the others. Regarding this figure, the impact of the high-order variable structure technique (HVS) is clear in the proposed digital twin integrated with SVM (MS-HRKF+SVM) and the combination of the MS-RKF with SVM compared to the combination of the MS-KF with SVM. Tables 4-6 demonstrate the power of the proposed digital twin integrated with SVM (MS-HRKF+SVM), the combination of the MS-RKF with SVM (MS-RKF+SVM), and the combination of the MS-KF with SVM (MS-KF+SVM) for crack size identification (CSI). Table 4 shows the impact 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 ball CSI when the crack sizes are 0.007, 0.014, and 0.021 inch. Based on this table, the average ball CSI accuracies are 98.7%, 88.9%, and 77.7%, respectively, using the proposed digital twin integrated with SVM (MS-HRKF+SVM), the combination of the MS-RKF with SVM, and combination of the MS-KF with SVM. Thus, the proposed digital twin integrated with SVM (MS-HRKF+SVM) improves the average ball CSI in the combination of the MS-RKF with SVM and the combination of the MS-KF with SVM by 9.8% and 21%, respectively. Figure 19: Boxplots of the average FPRA metrics over 10 experiments for the proposed digital twin integrated with SVM (MS-HRKF+SVM), the MS-RKF+SVM, and the MS-KF+SVM to test the power of robustness. Table 5 illustrates the impact 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 inner CSI when the crack sizes are 0.007, 0.014, and 0.021 inch.