A Dynamic Interval Type-2 Fuzzy Stochastic Configuration Network for Nonlinear System Modeling

To tackle the insufficient representation of uncertainty and weak structural adaptability in nonlinear system modeling, a dynamic interval type-2 fuzzy stochastic configuration network (DIT2FSCN) is proposed, synergistically integrating fuzzy rule initialization and dynamic sparse interpolation rule growth. First, a k-means clustering algorithm based on density peaks (BDPKA) is introduced to initialize the parameters of DIT2FSCN. The limitations of traditional clustering methods, such as sensitivity to initial centers and the requirement to predefine the number of rules, can be overcome by fusing density peak detection with k-means clustering, enabling data-driven fuzzy rule generation. Second, a two-stage modeling framework incorporating interval type-2 fuzzy inference and stochastic configuration-based dynamic optimization is designed. The uncertainty modeling capability of an interval type-2 fuzzy logic system (IT2FLS) and the incremental learning ability of stochastic configuration networks are jointly harnessed, allowing for dynamic characterization of complex system behaviors. Third, a dynamic sparse interpolation rule growth strategy based on the blankness score is proposed. The blankness scoring mechanism that accounts for both inter-rule spacing and local data distribution is designed to facilitate adaptive rule bases expansion via sparse region identification and dynamic interpolation, capturing the coupling relationships in nonlinear systems. Finally, the effectiveness of DIT2FSCN is validated through simulation experiments, including sequence prediction, benchmark dataset modeling, and two real-world industrial process applications. The experimental results demonstrate that the proposed DIT2FSCN has better performance than its peers in accuracy and generalization capability.