Passat TDI Problems: Troubleshooting & Repair

Hello,

'In a Passat (current model) belonging to a customer, the following problem has been occurring sporadically recently:'

The car suddenly starts to vibrate. This can happen while driving, or even after it has been parked for a shorter or longer period of time, when you turn the ignition key. The vibrations seem to be coming from a hydraulic pump (?), located in the engine compartment on the left side, next to the engine cover.
'Occasionally, a message also appears inside the car indicating that the ABS/ESP is not working. When visiting the VW workshop, the error never occurs, and the error memory only shows an ESP error, if anything at all.'
What could that be?

Stefan.