I tried installing aspen hysys on my system, but at 0% when it states installing sql data base, my system restarts. This has happened everytime I try it.
You'll probably get better help contacting Aspen but while I'm here, if it's using SQL Express, try installing it separately from the link. Just first confirm which version is required. If you need an earlier one, you may be able to download it from the MS site.
Remove all traces of SQL Express already installed and then try the instructions from @spicypadthai.
Also, does the installer still work if you, say, install SQL Express first (e.g. SQL Express 2012 R2 - an old version that runs with most apps when newer versions do not) and then run the installer afterwards?