Identification of quasi-ARX neurofuzzy model with an SVR and GA approach

The quasi-ARX neurofuzzy (Q-ARX-NF) model has shown great approximation ability and usefulness in nonlinear system identification and control. It owns an ARX-like linear structure, and the coefficients are expressed by an incorporated neurofuzzy (InNF) network. However, the Q-ARX-NF model suffers from curse-of-dimensionality problem, because the number of fuzzy rules in the InNF network increases exponentially with input space dimension. It may result in high computational complexity and over-fitting. In this paper, the curse-of-dimensionality is solved in two ways. Firstly, a support vector regression (SVR) based approach is used to reduce computational complexity by a dual form of quadratic programming (QP) optimization, where the solution is independent of input dimensions. Secondly, genetic algorithm (GA) based input selection is applied with a novel fitness evaluation function, and a parsimonious model structure is generated with only important inputs for the InNF network. Mathematical and real system simulations are carried out to demonstrate the effectiveness of the proposed method.