Probability bounds analysis for nonlinear dynamic process models

Abstract

Dynamic process models frequently involve uncertain parameters and inputs. Propagating these uncertainties rigorously through a mathematical model to determine their effect on system states and outputs is a challenging problem. In this work, we describe a new approach, based on the use of Taylor model methods, for the rigorous propagation of uncertainties through nonlinear systems of ordinary differential equations (ODEs). We concentrate on uncertainties whose distribution is not known precisely, but can be bounded by a probability box (p-box), and show how to use p-boxes in the context of Taylor models. This allows us to obtain p-box representations of the uncertainties in the state variable outputs of a nonlinear ODE model. Examples having two to three uncertain parameters or initial states and focused on reaction process dynamics are used to demonstrate the potential of this approach. Using this method, rigorous probability bounds can be determined at a computational cost that is significantly less than that required by Monte Carlo analysis. © 2010 American Institute of Chemical Engineers AIChE J, 2011