Quantification of overestimation in interval simulations of uncertain systems

In this paper, the properties of a criterion to quantify the overestimation arising in both interval evaluation of multidimensional nonlinear multivariate functions and interval simulation of dynamical systems are discussed. Computationally efficient, easy-to-implement consistency tests which are based on this criterion are developed for static as well as dynamic nonlinearities to find tight guaranteed enclosures of all possible results. The efficiency of these consistency tests is demonstrated for steady-state analysis of an electrical bridge circuit and for dynamical simulation of an activated sludge process in biological wastewater treatment under consideration of parameter uncertainties.