Towards a global modelling of the Camembert-type cheese ripening process by coupling heterogeneous knowledge with dynamic Bayesian networks

Food processes are systems featuring a large number of interacting microbiological and/or physicochemical components, whose aggregate activities are nonlinear and are responsible for the changes in food properties. As a result of time limits, financial constraints and scientific and technological obstacles, knowledge regarding food processes may be obtained from various sources of know-how such as expert operators, scientific theory, experimental trials etc. Faced with this fragmented and heterogeneous knowledge, it is difficult to implement mathematical models in the form of equations capable of representing and simulating all different phenomena that occur during the process. It is necessary to develop practical mathematical tools capable of integrating and unifying the knowledge puzzle in order to have a better understanding of the whole food process. With this aim in mind, the concept of dynamic Bayesian networks (DBNs) provides a practical mathematical formalism that makes it possible to describe complex dynamical systems tainted with uncertainty. It relies on probabilistic graphical models where the graphical structure of network defines highly-interacting sets between variables and probabilities take uncertainty pertaining to the system into account. To illustrate our approach, we focused on cheese ripening that still remains an ill-known and complicated process to control where capitalised knowledge is fragmented and incomplete. Based on the available knowledge, we propose a global representation/modelling and an explicit overview of the whole ripening process by means of dynamic Bayesian networks. That means we define a model allowing to describe a network of interactions taking place between variables at different scales (i.e. microbial behaviour as well as sensory development) during the ripening. Model has been tested with new experimental trials not available in the learning database. Simulated results are close to experimental data presenting an average adequacy rate of about 85% according to the admitted errors provided by experts highlighting its predictive character. The established model then presents the ability to predict the dynamics of sensory properties from the predicted microbial behaviour.