Fenced areas.......two large dogs (pit bulls) in the fenced area?
Pictures and cameras are great if you want to see who took your generator, but I can all but assure you, unless the Police recognize the thief, nothing will be done even with video and photos.
There are some very small GPS trackers available and you might be able to hide one on the generator under the side panels or gas tank and if it's stolen, have the Police meet you at it's current location.
Thieves aren't always dumb, and if they plan to steal your generator, you have to assume they will come equipped to cut any chain or lock.
I have video cameras that can alert me to motion so if someone were to enter my yard I would know even before they reached my valuables. Unfortunately in the USA it has become more of a criminal offense to defend your property, than to steal others property.
To clarify - I'm not a Predator, but one of my Generators IS
HarborFreight Predator 3500 Inverter