How to check the health of a SSAS database? And of its backups?
I don't think you can verify an SSAS database isn't corrupt apart from querying it. If you query it and you get errors it's corrupt.

If your database ends up corrupt the only sure way to recover is to restore the last known good backup, even though sometimes you can get away with messing in the .xml files or the data folder structure there is no guarantee and it's certainly not automated.

You can test an OLAP backup using msmdsrv.exe on the server (located in &lt;driveletter&gt;:\Program Files\Microsoft SQL Server\&lt;instance&gt;\OLAP\bin).

For example executing 

C:\Program Files\Microsoft SQL Server\MSAS10_50.MSSQLSERVER\OLAP\bin&gt;msmdsrv -j -b "f:\backup\olap\olap.abf"


on the server I'm currently on yields this:


  Backup file f:\backup\olap\olap.abf contains database with the Name
  of OLAP and  Id of OLAP consisting of 179 files with the total size of
  100632864 bytes All files were successfully tested


If you are using encryption you need to use the -k switch to provide the password

If the backup is invalid I don't know of any automated method to fix it apart from creating a new backup.