| Dynamic process models are an important mathematical tool in chemical engineering and a number of other fields in science and engineering. Such models are often used to simulate situations that are otherwise difficult, dangerous, immoral, impossible, or tedious to investigate. Mathematical modeling can also be used together with experiments to improve the design of further models and experiments.;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. Such process models are often represented by a system of ordinary differential equations (ODEs). Described in this work is a new approach, based on the use of Taylor model methods, for the rigorous propagation of uncertainties through nonlinear ODE systems. The focus is on uncertainties whose distribution is not known precisely, but can be bounded by a probability box (p-box), and how to use p-boxes in the context of Taylor models. It is then possible to obtain p-box representations of the uncertainties in the state variable outputs of a nonlinear ODE model. Using this approach, rigorous probability bounds can be determined at a computational cost that is significantly less than that required by Monte Carlo analysis.;The examples presented here are used to demonstrate the potential of this approach for studying the effect of uncertainties with imprecise probability distributions. Direct examples from chemical engineering include those of reactor and control models for both chemical and biological processes. Uncertainties in the context of initial states, observed reaction rates, and/or control parameters are investigated for a number of examples including exothermic reactions, biomass production, and metabolic processes in humans.;The same tools also apply to a variety of situations considered in mathematical biology, including the fields of epidemiology and ecology. The work of a number of epidemiological studies is put together here to use a consistent notation and investigation. Population ecology models are covered theoretically with a consideration of a model that has been developed to investigate the effects of a contaminant being introduced into an ecosystem. |
