Many industrial processes belong to nonlinear distributed parameter systems (DPS) with significant spatio-temporal dynamics. They often work at multiple operating points due to different production and working conditions. To obtain a global model, the direct modeling and experiments in a large operating range are often very difficult. Motivated by the multi-modeling, a fuzzy-based spatio-temporal multi-modeling approach is proposed for nonlinear DPS. To obtain a reasonable operating space division, a priori information and the fuzzy clustering are used to decompose the operating space from coarse scale to fine scale gradually. To reduce the dimension in the local spatio-temporal modeling, the Karhunen–Loève method is used for the space/time separation. Both multi-modeling and space/time separation can reduce the modeling complexity. Finally, to get a smooth global model, a three-domain (3D) fuzzy integration method is proposed. Using the proposed method, the model accuracy will be improved and the experiments become easier. The effectiveness is verified by simulations. 
A fuzzy-based spatio-temporal multi-modeling for nonlinear distributed parameter processes