An adaptive-node broad learning based incremental model for time-varying nonlinear distributed thermal processes

Distributed parameter systems (DPSs) widely exist in industrial thermal processes. Modeling of such processes is challenging for the following reasons: (1) nonlinear spatiotemporal coupling dynamics, (2) model uncertainty, and (3) time-varying dynamics. To address these problems, an adaptive-node broad learning (AN-BL) based incremental spatiotemporal model is developed for nonlinear time-varying DPSs. First, incremental kernel Karhunen–Loève (IK-KL) decouples nonlinear spatio-temporal coupling dynamics and derives adaptive spatial basis functions to represent the nonlinear time-varying dynamics in the spatial domain. The application of kernel method can better deal with nonlinear spatio-temporal characteristics. Second, a broad learning (BL) based on pruning strategy was developed to estimate the unknown time-varying dynamics in the time domain. The adaptive pruning strategy greatly reduced the redundancy of the network structure and reduce computational burden. The proposed online modeling scheme can adaptively adjust the model structure and parameters under streaming data environments, which makes it promising for dealing with time-varying DPSs.