On the Usefulness of Grey-box Information when doing Experiment Design for System Modeling and Identification

Abstract

In this paper, the usefulness of performing optimal experiments for stochastic dynamic models is investigated. The prior partial information about the parameters of the model is given as probability distribution functions in the system parameters. The concept of information is related to entropy reduction in the parameters through Lindley’s measure of average information, and the relationship between the choice of information related criteria and some estimators (MAP and MLE) is established. Bayesian as well as non-Bayesian techniques are considered and compared using numerical methods and geometrical interpretations and the importance of employing partial prior information in design methods is discussed. The role of prior physical knowledge has also been investigated in experiment design for a continuous time model. The results show that introducing prior information in experimental design methods enables us to reach a more efficient identification especially in terms of a reduction of the experimental length. Besides, it is established that the physical knowledge of system enables us to design experiments which are informative about the physical parameters of interest.