Dynamic sensitivity analysis of chemical reaction systems: A variational method

An approach to the sensitivity analysis of systems governed by ordinary differential equations is presented. It is based on a variational approach and is developed here in the context of chemically reacting systems, although in principal it is more general. The linear analysis generates sensitivity indexes which are a measure of the sensitivity of an objective function to the jth reaction of a mechanism. Both instantaneous and time-averaged sensitivities can be obtained. It also gives the sensitivity to initial concentrations of reactants, or to concentration perturbations at arbitrary times. The use of an objective function permits one to obtain the sensitivity of several species simultaneously in a single analysis, in contrast to other methods where the sensitivity of one species at a time must be determined. In this work the objective functions used are norms involving an arbitrary number of dependent variables. A ranking of the relative importance of each reaction in governing the concentrations of species appearing in the objective function is obtained. Since the sensitivity indexes are time dependent, the analysis may be said to be a dynamic sensitivity analysis. The sensitivity indexes given by this method are related to other standard sensitivity indexes.