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.

翻译：我们考虑一个包含随机变量的二阶线性常微分方程组。随机伽辽金方法生成一个规模更大的确定性线性常微分方程组。我们对该高维线性动力系统应用模型降阶，其中系统内能代表一个二次型关注量。我们从稳定性、无源性及能量耗散角度研究了该模型降阶方法的特性。数值结果展示了一个质量-弹簧-阻尼系统的建模实例。