At what stage of Appian Delivery Methodology we repeatedly do backlog refinement. Is it the Build or the Optimize stage or am I missing something?
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If you're using the Scrum flavor of Agile then backlog refinement is conducted in parallel with the Build stage. You can imagine the backlog as a "hopper" of work that is being used to feed a production line. You don't want the hopper to become empty otherwise you have to stop the production line. So the team will spend some of their working week developing the User Stories for the current Sprint, and some of the same working week refining Stories in the backlog so that the "Ready to Play" "hopper" is kept topped up. Then when you plan for the next Sprint there is a set of User Stories that are ready that you can pull into the next Sprint backlog.
I suspect "Build" and "Optmiize" are the same thing, just with a different focus. Every application that gets delivered crosses over into the "Optimize" stage but the methodology is the same.