Type-2 fuzzy instrumental variable algorithm for evolving neural-fuzzy modeling of nonlinear dynamic systems in noisy environment

Abstract

In neural-fuzzy modeling, dealing with dynamic systems in a noisy environment is a relevant issue due to uncertainties in the experimental data. In this sense, a type-2 fuzzy instrumental variable based learning algorithm for evolving neural-fuzzy modeling is proposed in this paper. For antecedent adaptation, an Extend Kalman Filter based evolving type-2 fuzzy algorithm is adopted, where the participatory concept is used to mitigate the effects of outliers in the data flow. For consequent estimation, a type-2 fuzzy instrumental variable based subspace identification method is proposed. From the data flow, the instrumental variables are computed via recursive singular spectral analysis and used to estimate the fuzzy Markov parameters. From Markov parameters, the linear state-space matrices are obtained, recursively. Results illustrate the efficiency of the proposed methodology compared to other prominent approaches in the literature for identifying a nonlinear dynamic system with discontinuous function corrupted by colored noise and online identification of a 2DoF helicopter with correlated noise.