There's an easy method for extracting hard disk S.M.A.R.T. testing logs using the CLI. This is useful if you require support on Synology and need an easier method to get the data (other than creating screenshots from your web-browser), and if more detailed data is needed.
Before getting the logs from the CLI, first run an extended SMART analysis from the DSM. This will take a while (usually several hours). Running the analysis on multiple disks is possible and can be done concurrently, but it needs to be initiated manually for each disk.
Once tests have completed, log onto the CLI (using your favourite SSH client, such as PuTTY) using the "admin" or "root" account.