Sorry for the delay. Identification should be mostly done by the production department for technical training because they are well-versed in the production area, along with Maintenance and Quality departments.
The second identification should come from the PMS (Performance Management System) and skill matrix. For example, if I am working in the production area, my production supervisor knows well about that area, not HR. HR's role is to assist the production department and the plant head in identifying training needs, creating calendars, and making training arrangements.
Soft skills training, such as behavior and other skills, are identified by HR.