A structured modeling approach for dynamic hybrid fuzzy-first principles models

Hybrid fuzzy-first principles models can be attractive if a complete physical model is difficult to derive. These hybrid models consist of a framework of dynamic mass and energy balances, supplemented with fuzzy submodels describing additional equations, such as mass transformation and transfer rates. In this paper, a structured approach for designing this type of model is presented. The modeling problem is reduced to several simpler problems, which are solved independently: hybrid model structure and subprocess determination, subprocess behavior estimation, identification and integration of the submodels to form the hybrid model. The hybrid model is interpretable and transparent. The approach is illustrated using data from a (simulated) fed-batch bioreactor.