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Greyhole
Greyhole uses Samba to create a storage pool of all your available hard drives, and allows you to create redundant copies of the files you store.
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snapraid
A backup program for disk arrays. It stores parity information of your data and it recovers from up to six disk failures
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InfluxDB
Power Real-Time Data Analytics at Scale. Get real-time insights from all types of time series data with InfluxDB. Ingest, query, and analyze billions of data points in real-time with unbounded cardinality.
It looks like greyhole added a checksum checksum verification feature (see line 90 here: https://github.com/gboudreau/Greyhole/blob/master/USAGE). I don't know whether it offers the ability to heal bad copies from good.
NOTE:
The number of mentions on this list indicates mentions on common posts plus user suggested alternatives.
Hence, a higher number means a more popular project.