A while back i had a UPS that started making a rather loud and strange humming sound when running on battery.
It turned out to be 1 of the mosfets failing, the switching waveform wasn't right and that was causing the sound in the transformer.
If the hum your hearing doesn't sound like general 50hz hum then it could be something similar.
The hum i got really didn't sound good, so it was pretty obvious something wasn't right.
The UPS still worked though, but i suspect it wouldnt have handled full load.
It was under warranty so i didn't bother trying to fix it, just sent it back.