Comparison of methods for training grey-box neural network models

Due to its inherent plasticity, neural network models are well suited to represent complex functions such as those encountered in bioprocesses. In this paper, neural networks were used to model kinetic rate expressions that form an integral part of a grey-box model. A grey-box model normally consists of a phenomenological part (differential equations of heat and/or mass balances) and an empirical part (a neural network in this paper). The objective of this investigation is to compare three different methods to come up with the same neural network to represent two kinetic rate expressions that are used directly in the grey-box model. In one method (the direct method), the model is fitted directly on data obtained from the derivative of smoothed state variables whereas the other two methods (indirect methods) use a non-linear regression algorithm to fit the complete grey-box; model, in order to derive specific kinetic rate expressions that minimise an objective function made of some measured state variables. Results clearly show that indirect methods are superior to direct methods for the prediction of state variables. However, the derived kinetic rate models are not unique.