Multiphase Bioreactor Design

develop a process model with the desirable accuracy. In this situation data-driven

modelling can be used to improve the accuracy of the model. In many industrial plants

the relevant cause/effect mechanisms have been registered for many years in the form

of process input/output data. Some of these mechanisms have been at least observed

by the people operating the plant, but many of them have been just recorded in process

data files and passed completely unaware. The modelling of unknown parts of the

process can be made using the so-called black box methods, namely time-series and

artificial neural networks (ANN). A very complete survey of black-box modelling in

system identification is given by Sjöberg et al. (1995). In particular ANNs have been

getting a great deal of attention from researchers in the last years. They prove to be

extremely flexible in representing complex non-linear relationships (e.g. Cybenko,

1989; Hornik et al., 1989; Poggio and Girosi, 1990) without requiring any kind of

knowledge concerning the structure of the underlying model. Several important results

have been published concerning the application of ANNs for dynamical system

identification and control (e.g. Hunt et al., 1992; Pollard et al., 1992; Narendra and

Parthasarathy, 1990).

Efficient knowledge fusion

The preceding analysis leads naturally to the questions of knowledge utilisation,
knowledge fusion and hybrid solutions. There are two types of hybrid modular structures:

1. modular complementary (Figure 3.4a), where different kinds of information for the
   sub-system complement themselves (Schubert et al., 1994b); the case depicted in
   Figure 4a shows the combination of an Artificial Neural Network (ANN) kinetic
   model (black-box model) with a mechanistic mass balance equation (white-box
   model). and


2. modular competitive (Figure 3.4b) where different forms of information about the
   same sub-system are available for possible utilisation; in the example, a
   mechanistic/empirical-Monod type-kinetic model (white-box module), a fuzzy kinetic
   model (grey-box module) and an ANN kinetic model (black-box module).

In competitive hybrid model structures, a mechanism for dynamical weighting of each
single model is necessary (Figure 3.4b). This mechanism should obey to the criterion that
for the current set of inputs the best model should have a higher weight for the final
output while the worst model should have the lowest weight.

Multiphase bioreactor design 72