A hybrid representation approach for modelling complex dynamic bioprocesses

This paper considers the use of hybrid models to represent the dynamic behaviour of biotechnological processes. Each hybrid model consists of a set of non linear differential equations and a neural model. The set of differential equations attempts to describe as much as possible the phenomenology of the process whereas neural networks model predict some key parameters that are an essential part of the phenomenological model. The neural model is obtained indirectly, that is, using the prediction errors of one or more state variables to adjust its weights instead of successive presentations of input-output data of the neural network. This approach allows to use actual measurements to derive a suitable neural model that not only represents the variation of some key parameters but it is also able to partly include dynamic behaviour unaccounted for by the phenomenological model. The approach is described in detail using three test cases: (1) the fermentation of glucose to gluconic acid by the micro-organism Pseudomonas ovalis, (2) the growth of filamentous fungi in a solid state fermenter, and (3) the propagation of filamentous fungi growing on a 2-D solid substrate. Results for the three applications clearly demon- strate that using a hybrid model is a viable alternative for modelling complex biotechnological bioprocesses.