System identification using hierarchical fuzzy neural networks with stable learning algorithms

Hierarchical fuzzy neural networks can use less rules to model nonlinear system with high accuracy. But the structure is very complex, the normal training for hierarchical fuzzy neural networks is difficult to realize. In this paper we use backpropagation-like approach to train the membership functions. The new learning schemes employ a time-varying learning rate that is determined from input-output data and model structure. Stable learning algorithms for the premise and the consequence parts of fuzzy rules are proposed. The calculation of the learning rate does not need any prior information such as estimation of the modeling error bounds. The new algorithms are very simple, we can even train each sub-block of the hierarchical fuzzy neural networks independently.