This article proposes a novel randomized neuro-fuzzy model called fuzzy stochastic configuration networks (F-SCNs), which integrates the Takagi–Sugeno (T–S) fuzzy inference system into SCNs to enhance its fuzzy inference capability. Unlike original SCNs, the hidden layer in SCNs is replaced by the T–S fuzzy inference module, which is responsible for fuzzifying the input data and performing fuzzy reasoning. The fuzzy rules generated by the fuzzy module are directly connected to the output layer of the network. In addition, an enhancement layer is added between the fuzzy module's output and the output layer of the network to extract nonlinear information contained in fuzzy rules. The parameters of fuzzy systems are determined by the distribution characteristics of the input-output data of the network, which enhances the interpretability of the model. Moreover, the parameters of the neuro-fuzzy model are learned by stochastic configuration algorithms. Therefore, the model inherits the fast learning speed and universal approximation capability of SCNs. A series of simulation experiments are carried out, including nonlinear dynamic system identification, sequence prediction, and benchmark data modeling from the real world to verify the feasibility and effectiveness of the proposed method. Finally, a soft sensing model for the effluent total phosphorus concentration in wastewater treatment processes is developed based on the proposed F-SCNs. The results show that the proposed method has good potential for nonlinear system modeling tasks compared to some classical neuro-fuzzy and nonfuzzy models.

Stochastic configuration networks (SCNs) have been widely used as predictive models to model complex nonlinear systems due to their advantages in terms of easy-to-implement, fast learning speed, and universal approximation property. In many fields, however, the data generated by nonlinear systems are often characterized by dynamic time series and nonstationary, which result in the learner model with poor generalization performance. This article presents an online self-learning stochastic configuration network to improve the continuous learning ability of SCNs to model nonstationary data streams. The method can autonomously adjust the parameters and structure of the network according to the real-time arriving data streams. Specifically, we use a recursive learning mechanism to update the network parameters online based on the data acquired in real time. In addition, the structure of the SCNs is dynamically adjusted by sensitivity analysis and stochastic configuration algorithm to improve the adaptive and continuous learning capability of the network. A series of comparisons are carried out over two benchmark datasets and one practical industrial case from the wastewater treatment process to verify the effectiveness of the proposed method. Experimental results demonstrate that the proposed method has good potential for nonstationary data stream analysis.