We investigate linear dynamical systems of second order. Uncertainty quantification is applied, where physical parameters are substituted by random variables. A stochastic Galerkin method yields a linear dynamical system of second order with high dimensionality. A structure-preserv\-ing model order reduction (MOR) produces a small linear dynamical system of second order again. We arrange an associated port-Hamiltonian (pH) formulation of first order for the second-order systems. Each pH system implies a Hamiltonian function describing an internal energy. We examine the properties of the Hamiltonian function for the stochastic Galerkin systems. We show numerical results using a test example, where both the stochastic Galerkin method and structure-preserving MOR are applied.

翻译：本文研究二阶线性动力系统，并应用不确定性量化方法，以随机变量替代物理参数。随机伽辽金方法生成高维二阶线性动力系统，而保结构模型降阶技术则再次得到一个小型二阶线性动力系统。我们为这些二阶系统构造了一阶关联端口-哈密顿形式。每个端口-哈密顿系统均隐含描述内部能量的哈密顿函数，并进一步考察随机伽辽金系统的哈密顿函数特性。通过测试算例展示数值结果，其中同时应用了随机伽辽金方法与保结构模型降阶技术。