A SVM Gray-Box Model for a Solid Substrate Fermentation Process

Gray-Box models (GBM) which combine a priori knowledge of a process -e.g. first principle equations-with a black-box modeling technique are useful when some parameters of the first-principle model - normally time-variant parameters like the specific kinetics of some bioprocesses- cannot be easily determined. In this case the black-box part of the GBM can be used to model the influence of input and state variables on the evolution of those parameters. The most commonly used black-box technique for GBM is Artificial Neural Networks (ANN). However Support Vector Machine (SVM) has shown its usefulness by improving over the performance of different supervised learning methods, either as classification models or as regression models. In this paper, a kind of SVM -the Least-Square Support Vector Machine (LS-SVM)- are used to develop a GBM for a solid-substrate fermentation (SSF) batch process, the growth of the filamentous fungus Gibberella fujikuroi. SSF are well known as low water consumption processes, therefore reducing liquid effluent treatment costs. They can also use agricultural wastes as substrates. Although these advantages lack of adequate models attempts to better exploit SSF processes at an industrial level. The aim of the present work is then to build a GBM to simultaneously estimate the specific growth kinetics and the specific production kinetics. Good results confirm that SVM can be effectively used for developing GBM for SSF processes.