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.

翻译：本文提出了一种新型神经模糊模型，称为模糊递归随机配置网络（F-RSCN），用于工业数据分析。与原始递归随机配置网络（RSCN）不同，所提出的F-RSCN由多个子储备池构建而成，每个子储备池与一条Takagi-Sugeno-Kang（TSK）模糊规则相关联。通过这种混合框架，首先，通过引入模糊推理将先验知识嵌入网络，增强了模型的可解释性。其次，该神经模糊模型的参数由递归随机配置（RSC）算法确定。该方案不仅保证了所构建模型的通用逼近特性和快速学习速度，还克服了非线性动态建模中的不确定性问题，如未知动态阶次、任意结构确定以及学习参数敏感性等。最后，利用投影算法对输出权重进行在线更新，并给出了学习参数的收敛性分析。通过将TSK模糊推理系统集成到RSCN中，F-RSCN具备强大的模糊推理能力，并能实现优异的学习与泛化性能。综合实验表明，所提出的F-RSCN优于其他经典的神经模糊及非模糊模型，在复杂工业系统建模方面展现出巨大潜力。