Remove characters preceding the second underscore in file names
Bash can figure out where the last underscore is using a regular expression match, then you can use its substring extraction to get the part of the filename that you care about. Something like this:

#!/bin/bash

file="021_D05_53715-F.ab1"
pos=`expr "$file" : '^.*_'`
newfile=${file:$pos}
echo "$file -&gt; $newfile"