  This paper presents a novel neuro-fuzzy model, termed fuzzy recurrent
stochastic configuration networks (F-RSCNs), for industrial data analytics.
Unlike the original recurrent stochastic configuration network (RSCN), the
proposed F-RSCN is constructed by multiple sub-reservoirs, and each
sub-reservoir is associated with a Takagi-Sugeno-Kang (TSK) fuzzy rule. Through
this hybrid framework, first, the interpretability of the model is enhanced by
incorporating fuzzy reasoning to embed the prior knowledge into the network.
Then, the parameters of the neuro-fuzzy model are determined by the recurrent
stochastic configuration (RSC) algorithm. This scheme not only ensures the
universal approximation property and fast learning speed of the built model but
also overcomes uncertain problems, such as unknown dynamic orders, arbitrary
structure determination, and the sensitivity of learning parameters in
modelling nonlinear dynamics. Finally, an online update of the output weights
is performed using the projection algorithm, and the convergence analysis of
the learning parameters is given. By integrating TSK fuzzy inference systems
into RSCNs, F-RSCNs have strong fuzzy inference capability and can achieve
sound performance for both learning and generalization. Comprehensive
experiments show that the proposed F-RSCNs outperform other classical
neuro-fuzzy and non-fuzzy models, demonstrating great potential for modelling
complex industrial systems.
