Fuzzy Recurrent Stochastic Configuration Networks for Industrial Data Analytics

TL;DR

Fuzzy recurrent stochastic configuration networks (F-RSCNs) address the challenges of modelling nonlinear, uncertain industrial processes by embedding Takagi–Sugeno–Kang fuzzy rules into a multi-subreservoir recurrent framework. The model guarantees universal approximation and provides online weight updates via a projection-based algorithm, while maintaining interpretability through fuzzy inference. Theoretical results establish the echo-state property, convergence, and robustness of the online learning, with empirical validation across nonlinear system identification and two industrial applications demonstrating superior accuracy and stability over conventional neuro-fuzzy and ESN variants. The work advances practical industrial analytics by marrying fast, lightweight learning with principled fuzzy reasoning and rigorous convergence analysis.

Abstract

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.

Figures (10)

• Figure 1: Architecture of the fuzzy RSCN.
• Figure 2: Prediction fitting curves and error values of different models for nonlinear system identification task.
• Figure 3: The testing NRMSE surface map of the F-RSCN with different number of fuzzy rules and reservoir sizes on the nonlinear system identification task.
• Figure 4: The fire strength of the F-RSCN for different testing samples on the nonlinear system identification task (Q=5).
• Figure 5: Flowchart of debutanizer column.