Late reply, but might help future visitors.
I had this problem - it would shriek for a while, then stop shrieking with a 'chirp'. The noise also stopped abruptly when I cut the power. Aquastream provided two new cartridges (fortunately under warranty) but there was no improvement.
It was finally fixed by replacing the motor / pump assembly (Bosch branded) with a new (unbranded) one.
If it's out of warranty it'll cost you about £100 for the part.
Richard, February 2014