An Online Self-organizing Neuro-Fuzzy System from training data

In this paper, we design a novel Online Self-constructing Neuro-Fuzzy System (OSNFS) based on the proposed generalized ellipsoidal basis functions (GEBF). Due to the flexibility and dissymmetry of the GEBF, the partitioning made by GEBFs in the input space is more flexible and more economical, and therefore results in a parsimonious neuro-fuzzy system (NFS) with high performance under the online learning algorithm. The geometric growing criteria and the error reduction ratio (ERR) method are used as growing and pruning strategies respectively to realize the structure learning algorithm which implements an optimal and compact network structure. The proposed OSNFS starts with no fuzzy rules and does not need to partition the input space a priori. In addition, all the free parameters in premises and consequents are adjusted online based on the ε-completeness of fuzzy rules and the linear least square (LLS) approach, respectively. The performance of the proposed OSNFS is compared with other well-known algorithms on a benchmark problem in nonlinear dynamic system identification. Simulation results demonstrate that the proposed OSNFS approach can facilitate a compact and economical NFS with better approximation performance.