Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error can be bounded by residual-based methods, which are typically known to be highly pessimistic in the sense of largely overestimating the true error. This work applies two improved error bounding techniques, namely (a) a hierarchical error bound and (b) an error bound based on an auxiliary linear problem, to the case of port-Hamiltonian systems. The approaches rely on a second approximation of (a) the dynamical system and (b) the error system. In this paper, these methods are for the first time adapted to port-Hamiltonian systems by exploiting their structure. The mathematical relationship between the two methods is discussed both, theoretically and numerically. The effectiveness of the described methods is demonstrated using a challenging three-dimensional port-Hamiltonian model of a classical guitar with fluid-structure interaction.

翻译：基于投影的动力系统模型降阶通常会在高保真模型与低维模型之间引入误差。这种未知误差可通过残差法进行界定量化，但经典方法往往因过度估计真实误差而过于悲观。本文将两种改进的误差界技术——（a）分层误差界和（b）基于辅助线性问题的误差界——应用于端口-哈密顿系统。这两种方法分别依赖于对（a）动力系统或（b）误差系统的二次逼近。本文首次通过利用端口-哈密顿系统的结构特性，将这两种方法适配至该类系统。从理论与数值两个维度探讨了两种方法间的数学关联性。通过一个包含流固耦合的三维古典吉他端口-哈密顿挑战性模型，验证了所述方法的有效性。