  In this paper, we establish an iterative data-driven approach to derive
guaranteed bounds on nonlinearity measures of unknown nonlinear systems. In
this context, nonlinearity measures quantify the strength of the nonlinearity
of a dynamical system by the distance of its input-output behaviour to a set of
linear models. First, we compute a guaranteed upper bound of these measures by
given input-output samples based on a data-based non-parametric set-membership
representation of the ground-truth system and local inferences of nonlinearity
measures. Second, we propose an algorithm to improve this bound iteratively by
further samples of the unknown input-output behaviour.
