Several types of vibration probes are used. Probably the most common is the induction type. An AC electrical signal is sent to the coil in the probe and the current of the excitation signal is monitored to determine relative position. The closer the sensing probe is to the shaft or thrust plate the greater the current as more current is induced into the metal shaft/plate when it is closer to the probe.
Radial displacement sensors provide "X" & "Y" location of the shaft. Axial displacement gives the "Z" location.
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If the software can detect, compensate, avoid, or correct an anomalous condition in the system, it is, by definition, a software problem-regardless of the root cause. In the long run, for most classes of problems, it is cheaper to fix it in the SW