Since updating to 5.1 on my 4S, I have pages upon pages of diagnostic logs pertaining to "awdd" in the Diagnostics & Usage Data area of the About screen. There's gotta be 200 of them here, over the last 18 hours. Any idea what's up? I did a full install (DFU mode) rather than a delta update & restore from my 5.0.1 backup. Considering a "new phone" install because my battery life doesn't seem so great either. 40% dead in 6 hours of standby with extremely light usage.
I think your problem may just be the backup, since it saved all logs and everything from a previous backup.
My advice to you is to do a full reinstall from factory, not using a backup. Maybe there is something in your backup that drains battery life and gives you those diagnostics.