How to batch-rename long file names into short ones under Linux?

I have a lot of data with file name (just for example):

dt_upd_global_merged_madt_uv_20100801_20100801_20110721.bil
dt_upd_global_merged_madt_uv_20100802_20100802_20110721.bil
dt_upd_global_merged_madt_uv_20100803_20100803_20110721.bil

What should I do if I want to rename that files into the following?

20100801.bil
20100802.bil
20100803.bil