Energy-based model order reduction for linear stochastic Galerkin systems of second order

TL;DR

This paper develops an energy-based model order reduction technique for large stochastic Galerkin systems derived from second-order linear ODEs with random variables, focusing on stability, passivity, and energy dissipation.

Contribution

It introduces an energy-based MOR approach tailored for stochastic Galerkin systems of second order, emphasizing properties like stability and energy preservation.

Findings

The MOR maintains stability and passivity of the original system.

Numerical results demonstrate effective reduction of a mass-spring-damper model.

Energy dissipation properties are preserved in the reduced model.

Abstract

We consider a second-order linear system of ordinary differential equations (ODEs) including random variables. A stochastic Galerkin method yields a larger deterministic linear system of ODEs. We apply a model order reduction (MOR) of this high-dimensional linear dynamical system, where its internal energy represents a quadratic quantity of interest. We investigate the properties of this MOR with respect to stability, passivity, and energy dissipation. Numerical results are shown for a system modelling a mass-spring-damper configuration.