Sensitivity Analysis of Random Linear Dynamical Models Using System Norms

We consider linear dynamical systems with a single output, where the systems include random parameters to perform an uncertainty quantification. Using the concept of polynomial chaos, a linear stochastic Galerkin system of higher dimension with multiple outputs is arranged. Quadratic combinations of the outputs yield approximations of time-dependent indices in global sensitivity analysis, which indicate the influence of each random parameter. We investigate system norms for the quadratic outputs, because these norms generate time-independent sensitivity measures. Numerical results are presented for a model of an electric circuit.