A self-organizing fuzzy neural network with hybrid learning algorithm for nonlinear system modeling

Fuzzy neural networks (FNNs) integrating the advantages of fuzzy systems and neural networks are useful techniques for nonlinear system modeling. However, how to determine the structure and parameters to guarantee satisfactory modeling performance still remains a challenge. In this study, a self-organizing FNN with hybrid learning algorithm (SOFNN-HLA) is developed for nonlinear system modeling. First, a growing-and-pruning constructive scheme is proposed based on the network learning accuracy and the rule firing strength. New fuzzy rules can be developed with appropriate initial parameters based on the idea of an error-correction algorithm to improve the learning performance. Meanwhile, some redundant rules with low firing strength would be pruned to ensure a compact structure. Second, a hybrid learning algorithm combining an improved second-order algorithm and the least square method is developed for parameter adjustment. In this hybrid learning algorithm, linear parameters and nonlinear parameters are tackled separately to enhance the learning efficiency. Finally, the effectiveness of SOFNN-HLA is validated by two benchmark simulations and one real problem from wastewater treatment pro-cesses. The results show that the proposed SOFNN-HLA can achieve desirable generalization performance with a compact structure for nonlinear system modeling.