# Bearing Anomaly Recognition Using an Intelligent Digital Twin Integrated with Machine Learning
## 3 Experimental Results and Discussion
### Digital Twin Test and Analysis  
Figure 3 shows the original RAW signal for the bearing for the NS, RFS, IFS, and OFS when the crack sizes are 0.007, 0.014, and 0.021 inch in four different motor torque loads from 0 to 3 hp.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **Training Samples** & **Testing Samples** \\ \hline \multirow{4}{*}{RFS} & 0.007 inch & 300 & 100 \\ \cline{2-4}  & 0.014 inch & 300 & 100 \\ \cline{2-4}  & 0.021 inch & 300 & 100 \\ \cline{2-4}  & 0.007 inch & 300 & 100 \\ \cline{2-4}  & 0.021 inch & 300 & 100 \\ \cline{2-4}  & 0.007 inch & 300 & 100 \\ \cline{2-4}  & OFS & 0.014 inch & 300 & 100 \\ \cline{2-4}  & 0.021 inch & 300 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 3: _Cont._In Figure 3, when the crack sizes are 0.007 inch, the IFS and OFS overlap which can increase the rate of misclassification. Besides, when the crack size is 0.014 inch, the challenge of classification between OFS, IFS, and RFS increases sharply. In addition, when the crack size is 0.21 inch, the challenge of misclassification is increased between RFS and INS. Thus, the original RAW signals cannot be used for the bearing FPRCI. To improve the performance of the bearing FPRCI, in the first step, digital twin-based modeling was recommended in this study. Figure 4 shows the original normal RAW signal and modeled signal using the proposed digital twin signal modeling (MS) scheme. Based on Figure 4, the power of RAW signal modeling using proposed digital twin signal modeling (MS) scheme is very good.  
Figure 5 illustrates the bearing modeling in normal conditions using four algorithms: the proposed digital twin signal modeling (MS) scheme, the SAL technique, the AUT-LAG technique, and the AUT method.  
Figure 4: The original normal RAW signal and the modeled signal using proposed (MS) scheme.  
Figure 3: The CWRUD bearing vibration signals for NS, RFS, IFS, and OFS 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.  
Based on Figure 5, the error of normal signal modeling of the bearing for the digital twin using the proposed scheme is less than the others. Thus, the accuracy and robustness of the proposed (MS) digital twin modeling approach is better than the others. Moreover, the covariance power spectral density estimation of the normal signal and the modeled signal using MS technique is illustrated in Figure 6 to describe the distribution of power into the frequency components composing those signals. Regarding this figure, the distribution of the signal's power into the frequency for normal signal and the estimated normal signal is very close.  
Figures 7 and 8 show the bode plot for the original normal signal and modeled normal signal. Regarding these figures, the bode plot for the original normal signal and modeled normal signal are very similar.  
Figure 5: The error of the bearing normal signal modeling for the digital twin using four algorithms: AUT method, AUT-LAG technique, SAL approach, and proposed (MS) scheme.  
Figure 6: The frequency response of original normal signal and modeled normal signal using covariance power spectral density estimation.  
To test the power of signal modeling against some external change, impulse response is suggested for original normal signal and modeled normal signal. Figures 9 and 10 illustrate the impulse response for original normal signal and modeled normal signal.  
Figure 8: Bode plot for modeled normal signal.  
Figure 7: Bode plot for original normal signal.  
Figure 9: Impulse response estimated plot for original normal signal.