Spatial Construction for Modeling of Unknown Distributed Parameter Systems

Many industrial processes are distributed parameter systems that require complete spatial information for decisions and control. For modeling unknown distributed parameter systems (DPSs), a spatial construction method is proposed to preserve the spatial information between sensing locations. With the help of the spatial construction method, continuous spatial basis functions (SBFs) can be constructed to capture the spatial information lost in the time-space separation. The corresponding temporal dynamics can be identified using the generalized radial basis function network with the orthogonal least-squares (OLS) algorithm. After the time-space synthesis, the constructed spatiotemporal model can provide continuous modeling in the spatial domain with satisfactory performance. Convergence analysis proves that the proposed method can guarantee bounded errors. Finally, the experiments on a linear thermal process and a nonlinear catalytic process validate the effectiveness of the proposed method under limited sensors and its robustness when one of the sensors fails.