This is for SCOM 2007.
get-alert -criteria 'ResolutionState=''0'' AND IsMonitorAlert=''False''' |where {$_.LastModified -le (Get-Date).addhours(-24)} | resolve-alert -comment "Close old alerts generated by rules" | out-null
This will look for alerts with a New resolution state and coming from a rule, where the last modification to this alert was more than 24 hours ago, and close that alert with a small comment.
