what do you mean by structure, in this context?
Generally, Aikido has a classroom structure of everyone doing exercises, technique, working with partners, etc., that is *generally* followed/accomodated throughout the art. Within that general format are a number of already-existing exercises that were originally used for ki/kokyu development, even though those exercises have become ritualistic, muscular, technique-y, etc., almost across the board. It would be a far simpler matter to insert bona fide ki/kokyu training into Aikido than it would into most of the other parodies of Asian arts that flourish in the West. Karate, for example, has for the most part become a muscular parody of the southern Shaolin arts that it derived from.
Taiji (Tai Chi), Xingyi, most of the Chinese martial arts don't follow a generally standardized method of teaching. It's difficult to find any 2 teachers that have classes resembling each others and the theories have become wild, non-standardized guesses that run the spectrum of fantasy and science fiction.
So what I'm saying is that Aikido is like a car body pretty much ready for the engine to be dropped in. Most other arts are just bits and pieces that don't have a waiting coherent structure. One of the most interesting experiments at the moment in the US, in my opinion, is the Itten Dojo and how they attempt to transition to a ki-based Aikido... and not in the flowery sense; in the practical sense.
There may be others attempting the transition out of Dan Harden's methodology (or Akuzawa, Ushiro, and some others that I am being negligent in not mentioning), but I don't have much of a feel what their approach is or how complete the syllabus is, etc., so I can't comment intelligently. If any art can do it, though, it will almost certainly have to be Aikido.