A small thump at power up is likely normal/ok. Not exactly desirable, but I would personally not be too worried about that.
Now, a BUZZ is a different story. That is most likely a problem, and could be a serious problem.
Now, is it a BUZZ or a (60Hz) HUM?
If you say that you hear it on 2 different subs, then it is most likely a Hum. And, the most likely cause for a hum is a poor ground and/or a ground loop. These things can be difficult to find and eliminate, but it is not impossible.
If it is a buzz, then you may be headed towards a component failure, it could even be a dramatic component failure!