# Fault Detection in Active Magnetic Bearings Using Digital Twin Technology
## 6 Vibration Image  
The fault diagnosis process may be considered a problem of identification of patterns, where the extraction of features plays an important part in recognizing these patterns. The selection of the methodology used to characterize faults adequately significantly influences the precision of fault identification. The displacement sensors used by the AMB serve two primary purposes: first, to provide feedback about any deviations in the control loop, and second, to monitor the operational status of the AMB. Figure 9 illustrates the spatial locations of sensors denoted as X1, Y1, X2, and Y2. Both X1/Y1 and X2/Y2 are placed in orthogonal orientations. The points X1/X2 and Y1/Y2 are situated on the same axis line of the rotor. In order to get a vibration image, two channels of vibration signals (X1/Y1, X2/Y2) captured by different sensors are combined. Pairs of vibration signals, occurring simultaneously, are then represented as point pairings inside orthogonal coordinates. The trajectory is formed by collecting all point pairings, with the vertical and horizontal coordinates represented by both channels. The trajectory in the given coordinates is often referred to as a vibration image, while the specific places along this trajectory are denoted as vibration locations. This trajectory is called a shaft orbit. A shaft orbit is a useful tool for describing problems and is often used in monitoring since its form changes depending on the operational status of the rotating machinery. As seen in Figure 10, the vibration image exhibits different features than the conventional shaft orbit approach. In its normal condition, the conventional approach typically displays an approximately circular pattern, but the vibration image showcases a variety of patterns.  
Figure 8: The design of the digital twin model for the AMB.  
Figure 9: Sensor’s arrangement in the AMB.  
In cases when the number of signal channels exceeds two, the construction of the vibration image involves the arbitrary selection of two channels. Consequently, this process allows for the generation of many vibration images. Four sensors within the implemented AMB system are capable of generating six vibration images. Every vibration image is handled to get its features. Before the vibration image could be utilized in machine learning, it was necessary to convert it to a discretized representation and convert one dimension (1D) into a composite signal with two dimensions (2D). The region of the vibration image is split into L\({}^{2}\) grids. The active area, denoted by a value of 1, is defined as the region where the signal points interact. Conversely, the inactive area, represented by a value of 0, covers the remainder of the area. The representation of the vibration image can be shown as a binary image consisting of L\({}^{2}\) pixels, forming a matrix with values of 1 and 0. Figure 11 illustrates the mechanism by which the vibration image is formed.  
As such, vibration images may be analyzed using a wide range of currently available image processing and description technologies. The vibration image shows the relationship between the two signal channels. Putting the two channels together makes it easier to show the phase and amplitude of the vibration image as well as their relationship, which is not possible when they are kept separate.