title: How to be a gray box: dynamic semi-physical modeling.
abstract: A general methodology for gray-box, or semi-physical, modeling is presented. This technique is intended to combine the best of two worlds: knowledge-based modeling, whereby mathematical equations are derived in order to describe a process, based on a physical (or chemical, biological, etc.) analysis, and black-box modeling, whereby a parameterized model is designed, whose parameters are estimated solely from measurements made on the process. The gray-box modeling technique is very valuable whenever a knowledge-based model exists, but is not fully satisfactory and cannot be improved by further analysis (or can only be improved at a very large computational cost). We describe the design methodology of a gray-box model, and illustrate it on a didactic example. We emphasize the importance of the choice of the discretization scheme used for transforming the differential equations of the knowledge-based model into a set of discrete-time recurrent equations. Finally, an application to a real, complex industrial process is presented.
authors.affiliation: Ecole Supérieure de Physique et de Chimie Industrielles de la Ville de Paris, Laboratoire d'Electronique, France. yacine.oussar@espci.fr
authors.forename: Y
authors.initials: Y
authors.lastname: Oussar
authors.forename: G
authors.initials: G
authors.lastname: Dreyfus
mesh_terms: D000465:Algorithms; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics; D055585:Physical Phenomena; D010825:Physics