The smarttools are available on the shell/console, e.g.
smartctl -H /dev/hda or smartctl -H /dev/sda
will print the health status of the drive, according to the drive's SMART status.
smartctl can do other tests too, but it all relies on the drive being honest and stable enough for the results to be trustworthy.
the badblocks program actually reads the disk and will tell you if any sectors are unreadable/unrecoverable.
You can do a readonly test of your disk while Astaro is running: (as root) badblocks -sv /dev/disk/by-label/storage (storage partition only)
or, the entire drive: badblocks -sv /dev/sda (SCSI/SATA) or badblocks -sv /dev/hda (IDE/PATA)
This should be completely safe, but always BACKUP your config first! If your disk is bad, running something like this should expose it. A read/write test (-nsv) would be better, but cannot be run online. (use RIP or Knoppix or other bootable distro)