So I am playing Armada 3 at the moment and I have noticed that the AI even on the hardest setting does not care much about military research like increased weapon damage and more hull/shields/armor. I would like to change that on my own rather than hoping the devs will do it some day. Where can I change the research behavior?
You cannot. The AI always prioritizes getting new ships, structures, colonizeable planet research over damage/hull/shield upgrades. The only way around this is to make an AI only tech that unlocks a dummy ship which has research you want the AI to acquire as a prerequisite. Otherwise the AI often waits until it has maxed out its fleet before working on those kind of research.
What GoaFan said is true, but not exactly precise. The AI is hardcoded to prioritize techs that unlock new ships and structures or are prerequisites to unlock techs, but that shouldn't stop the AI from researching other techs.
The issue I believe lies in the AI's "Research Check Frequency", which can be changed in Gameplay.constants. To confirm my suspicions, open up the mod's Gameplay.constants file in Notepad and scroll down to the line that reads "playerAISharedDef". Under that line, you'll see four sections, each starting with "table-"; (almost) all of these are "Check Frequency" values for the four AI presets. Choose up to three presets (you'll need an unchanged one for "control" purposes) and multiply the value next to "UpgradeResearch" by 10 or 100. Then, set up a game that has at least one changed preset and one unchanged preset and see if the changed presets are unlocking a lot more techs than the unchanged ones.
Based on my observations, the way AI does tech in Sins is kind of odd: every <time interval set by UpgradeResearch in Gameplay.constants>, the AI will run a "tech roulette" of sorts, where it will randomly select a tech from each tech tree (or only one tech tree at a time, I'm a bit unclear on this). It will then decide whether it wants to research that randomly selected tech or not based on calculations that I haven't discovered yet. The "tech roulette" isn't completely random though, since techs are weighted by their priority parameter (defined in the tech's .entity file) during the roulette: a tech with a priority value of 2 will be twice as likely to be selected as a tech with a priority value of 1, while a tech with a priority value of 0 will never be selected. Remember that the AI won't necessary want to research the tech it selects by random though, so increasing a tech's priority value won't make the AI want to research it more per say, it will just make sure that when the AI does want to research the tech, it is more likely to be selected. Oh yes, and this is all independent of any hardcoding: techs with hardcoded priority (colonization unlocks, interstellar travel unlock, wormhole travel unlock, ship unlocks, etc.) have their own little system that I haven't bothered to decipher in detail yet. This is why all hardcoded techs have a priority value of 0 in the unmodded game: since the AI is hardcoded to research the tech anyway, having it included in the "tech roulette" is a waste of space and inhibits the AI from selecting a non-hardcoded tech to research.
If you're interested in doing an AI modmod for Armada 3, even if it'll be for personal use only, I highly recommend you check out Section 3 of my Artificial Unintelligence post, which is essentially a giant collection of my observations about which game parameters affect the AI in what way.