Optimal experiment design for static polynomial approximation of nonlinear systems

Most real systems do not belong to a known model class and thus identification boils down to approximation. Universal approximators are often used, e.g. polynomial nonlinear models whose number of parameters tends to increase very fast with the model complexity. In view of the potentially high number of parameters to be identified and more in general to the nonlinearity, choosing the appropriate excitation is not trivial but indispensable. In this paper, we consider a simplified setup limited to static polynomial systems. We show the limits of classical design of experiments (DOE) in terms of prediction error even for this simple case. Against this background, we first suggest to use a more suitable optimization criterion based on the prediction error and show that it is a generalization of the well-known V-optimality criterion, if the system belongs to the model class. Second, we show that it makes sense to design the excitation on the basis of a higher degree model than the one to be identified. NO x emission measurements from a BMW 2-liter Diesel engine are used to confirm this approach.