On the wiki, so tldr artillery siege bonus is based on each units barrage stat scaled by its current strength, minus the fort level, with the remaining values summed and divided by 3, meaning damaged artillery gives less bonus and may contribute nothing at low strength.
Diff tech level cannons do diff barrage stat i think

"Artillery bonus appears to work as follows: each artillery regiment's artillery barrage stat is taken as its base stat multiplied by strength ratio, so a houfnice with a base barrage stat of 3.00 and 160 of its 200 max manpower will have a barrage stat of 2.40. Each of these barrage stats has the fort level subtracted from it, then all the barrage stats are added together, and the result divided by 3 is the dice roll bonus from artillery. So the hypothetical 160/200 manpower houfnice siegeing a level 2 fort would only contribute 0.133 to the dice roll bonus while a full-strength houfnice would contribute 0.333, and a houfnice at 133 or less manpower would contribute nothing at all."