First welcome to the website!
I assume you have an LTZ model AV....the pump will make a noise at start up to test system then quiet down. If it constantly runs you may have a leak or problem with your suspension. You should read the older threads about the LTZ suspension for info and tips. Most members hate the expense of replacement with GM parts but it gives less problems with error codes being set off. Others use a replacement system by Arnott. Some try to replace with stock shocks but that usually leads to an inferior ride and error codes appearing in your dash.