Sensitivity analysis of random linear dynamical systems using quadratic outputs

In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with quantity interest as output. Our objective to analyse the sensitivity output respect A variance-based approach generates partial variances and indices. expand using generalised polynomial chaos. The Galerkin method yields larger system equations. represent quadratic outputs this system. examine norms formulation obtain measures. Furthermore, we apply model order reduction balanced truncation, which allows for an efficient computation guaranteed error bounds. Numerical results shown test example.