Hierarchical Evolving Fuzzy System: A Method for Multidimensional Chaotic Time Series Online Prediction

Evolving fuzzy system (EFS), a special adaptive model with Takagi–Sugeno fuzzy rules that can adaptively update internal parameters based on data streams, has been widely used in online learning scenarios. However, current EFSs are mainly single-layer models, which cannot adequately capture hidden information in multidimensional chaotic time series. To perform online prediction of multidimensional chaotic time series, a novel evolving fuzzy system, called hierarchical evolving fuzzy system with kernel conjugate gradient (HEFS-KCG), is proposed in this article. HEFS-KCG excavates and captures latent evolutionary patterns concealed within dynamic systems through a layer-by-layer processing of multidimensional information. HEFS-KCG performs structural evolution based on data distribution in the antecedent part, and combines the sparse learning strategy and kernel conjugate gradient to update the consequent parameters. Subsequently, we provide a theoretical analysis of HEFS-KCG, ensuring its convergence when applied to online prediction. The simulation results demonstrate that HEFS-KCG outperforms existing EFSs and other models for multidimensional chaotic time series online prediction.