# Fault Detection in Active Magnetic Bearings Using Digital Twin Technology
## 8 Results  
To determine how to figure out the efficacy of the suggestion of the digital twin model, a sequence of tests was conducted on an AMB system (which was explained in Section 6). The system was tested at different rotation speeds (3000, 6000, 9000, and 12,000 rpm) under normal conditions. Figure 15 illustrates examples of vibration images under normal conditions at different rotation speeds.  
Figure 16a illustrates the difference between the simulated signal response and the actual measured signals of the AMB system. By feeding the real-time inputs from the sensors into the simulation digital twin model, the error was minimized to achieve the most accurate update of the digital twin model, as seen in Figure 16b.  
Two categories of data failures, including imbalance and misalignment, were acquired. A total of 1000 samples was randomly chosen from each category for training purposes, while the remaining samples were used for testing (as show in Table 3). Examples of normal and imbalanced signals are presented in Figure 17.  
When testing a proposed CNN algorithm, it was observed that the precision of the test data was around 94%, although the precision of the training data was approximately 96.5%, as shown in Figure 18. The result indicates the model acts at a high level for detecting faults, proving it to be robust, efficient, and trusted. In Figure 19, the confusion matrix is shown. The expected faults are shown on the vertical axis of the matrix, the actual faults are shown on the horizontal axis, and the percentage of the prediction value is shown on the diagonal axis. The accuracy of fault detection in the AMB is greatly influenced by the decision to gather data from multiple sensors. The results of testing the digital twin model using different two-sensor combinations (x1, y1), (x1, x2), (x1, y2), (y1, x2), (y1, y2), and (x2, y2) are shown in Figure 20.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Rotation Speed (rpm)** & **Category** & **Number of Samples** & \
\begin{tabular}{c} **Number of Training** \\ **Samples** \\ \end{tabular} &
\begin{tabular}{c} **Number of Testing** \\ **Samples** \\ \end{tabular} \\ \hline \multirow{3}{*}{3000} & Normal & 11,251 & 1000 & 10,251 \\  & Imbalance & 5012 & 1000 & 4012 \\  & Misalignment & 4120 & 1000 & 3120 \\ \hline \multirow{3}{*}{6000} & Normal & 12,001 & 1000 & 11,001 \\  & Imbalance & 5743 & 1000 & 4743 \\  & Misalignment & 4490 & 1000 & 3490 \\ \hline \multirow{3}{*}{9000} & Normal & 12,256 & 1000 & 11,256 \\  & Imbalance & 6277 & 1000 & 5277 \\  & Misalignment & 5295 & 1000 & 4295 \\ \hline \multirow{3}{*}{12,000} & Normal & 9501 & 1000 & 8501 \\  & Imbalance & 3420 & 1000 & 2420 \\ \cline{1-1}  & Misalignment & 2832 & 1000 & 1832 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The AMB data used in the experiments.  
Figure 16: The comparison of the signal output between the physical system and simulation response, (**a**) before and (**b**) after the model update.  
Figure 19: The confusion matrix.  
Figure 17: Examples of normal and imbalanced signals.  
Figure 18: (**a**) Training Accuracy (**b**) Test Accuracy.