The structural index of sensitivity equation systems

Abstract

ABSTRACTThis work presents a new methodology for computing parameter sensitivities of differential algebraic system of equations with higher differential index. This methodology is particularly adequate for performing sensitivity analysis of object-oriented models described by modern universal modelling languages. By employing the same concepts and tools adopted by these languages for structural analysis of systems of equations, it is shown that the computational graphs of a differential algebraic system of equations and its corresponding sensitivity equation are structurally isomorphic. As a consequence, the structural index of both systems of equations are proven to be equal. Based on this result, an efficient strategy for index reduction of sensitivity equations is designed.