Online Three-Dimensional Fuzzy Multi-Output Support Vector Regression Learning Modeling for Complex Distributed Parameter Systems

Complex distributed parameter systems (DPSs) are prevalent in numerous industrial processes. However, the nonlinear spatiotemporal dynamics inherent in DPS present significant challenges for accurate modeling. In this paper, an innovative online three-dimensional (3D) fuzzy multi-output support vector regression learning method is proposed for DPS modeling. The proposed method employs spatial fuzzy basis functions from the 3D fuzzy model as kernel functions, enabling direct construction of a comprehensive fuzzy rule base. Parameters C and ε in the 3D fuzzy model adaptively adjust according to data sequence variations, effectively responding to system dynamics. Furthermore, a stochastic gradient descent algorithm has been implemented for real-time updating of learning parameters and bias terms. The proposed method was validated through two typical DPS and an actual rotary hearth furnace industrial system. The experimental results show the effectiveness of the proposed modeling method.