The batteries in this UPS lasted less than a year. It was because those battery were "no name" batteries, or because they were connected in series directly to the AC after the transformer? Shouldn't they have a rectifier and condenser before that? It seems that in this way the battery is connected to AC 24/7
I'm fairly sure batteries can't be directly connected to AC or they wouldn't charge in the first place. It'd just heat them up. So if they charged at some point, there has to be something else going on.
What is the make and model? Since it uses a full size transformer instead of switch mode supplies I'm going to guess its old and should be retired. Its old and inefficient, always consuming power to keep that large set of magnetics energized.
As an electrical engineer I would advise you to recycle it. How much did you save buying no brand vs how much is the equipment you connected to it worth? How long would it take you to rebuild the connected equipment if the UPS threw out too much voltage and blew up everything downstream.? In my opinion the risk isn't worth the savings, don't cheap out on power equipment.
Thats a transformer, it's outputting dc power. My main concern is that the batteries are sitting on end like that. They're filled with water, so if there's an air gap at the end the battery is not going to work as well.