Automatic adjustment of the transition between local models in a hierarchical structure identification algorithm

This article addresses the adjustment of overlaps between local models in hierarchical local model networks. A comparison with flat model structures exposes the advantages of the hierarchical approach. The objective is to identify a smooth global model with validity functions that have a local and unimodal interpretation in the input space. The difficulty in achieving appropriate local model overlaps is solved with a new algorithm for automatic transition adjustment. It overcomes the problem that an a-priori smoothness fixation is disadvantageous because of the primary unknown number of hierarchy levels of the identified model. The universal approximation characteristic will get lost if too large overlaps of newly added local models prevent an improvement of the global model. An illustration of this effect is given by a simple demonstration example. Furthermore an example of a practical application is presented with the torque modeling of a combustion engine map.