### Comparison of methods for training grey-box neural network models

**Keywords:**
kinetics, model, equations, models, state, network, expression, fermentation, complex, balance, rates, mass, regression, networks, variables, kinetic, non-linear, comparison, part, methods, method, grey-box, differential, of, Rate, Functions, Neural, Indirect, Direct, Integral, Tile, Bioprocesses

### Abstract

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 tile same neural network to represent two kinetic rate expressions that are used directly in tile grey-box model. In one method(tile direct method), tile model is fitted directly on data obtained from the derivative of smoothed state variables where as the other two methods (indirect methods) use a non-linear regression algoritlun to fit the complete grey-box model ill order to derive specific kinetic rate expressions that minimise an objectivefunction made of some measured state variables, Results clearly show that indirect methods are superior to direct methods for tile prediction of state variables. However, the derived kinetic rate models are not unique. © 1999 Elsevier Science Ltd.

### Más información

Título de la Revista: | COMPUTERS & CHEMICAL ENGINEERING |

Volumen: | 23 |

Número: | SUPPL. 1 |

Editorial: | PERGAMON-ELSEVIER SCIENCE LTD |

Fecha de publicación: | 1999 |

URL: | http://www.scopus.com/inward/record.url?eid=2-s2.0-0012355497&partnerID=q2rCbXpz |