Principal components analysis in sensitivity studies of dynamic systems

Local sensitivity analysis is a modeling tool for determining the effects of single parameter variations on the output of a first order differential system. To determine the effects of multi-parameter variations, the local sensitivity matrix can be used in a first order Taylor series to approximately model the variance of the system output. For dynamic systems, a principal component analysis based on this time varying approximation reveals the evolution of the directions and magnitudes of greatest variation of the system output derived from input variability in the parameters. Such an analysis acts as a means of modeling the robustness of dynamic differential systems.