Strategy for dynamic process modeling based on neural networks in macroscopic balances

Gray box models combine the short development time of data-driven black box models with extrapolation properties of knowledge-driven first principles models (white box), which in (bio)chemical engineering are always based on macroscopic balances. By modeling the inaccurately known terms in a macroscopic balance with a black box model, one naturally obtains a so-called serial gray box model configuration. The identification data must cover only the input-output space of the inaccurately known terms, and the accurately known terms can be used for reliable extrapolation. In this way, the serial gray box configuration results in accurate models with known extrapolation properties with a limited experimental effort. This strategy is demonstrated for the modeling and control of a pressure vessel using real-time experiments. For this case, the strategy is superior to a black box modeling approach that requires much more data and to a parallel gray box approach that results in a model with poor extrapolation properties. Moreover neural networks are an accurate and convenient modeling tool for the black part in gray box model configurations, because a very fast noniterative training algorithm is used for training neural neural works.