论文标题
参数系统的基于结构化优化的模型订单降低
Structured Optimization-Based Model Order Reduction for Parametric Systems
论文作者
论文摘要
我们开发了一种基于优化的算法，用于线性时间流动动力系统的参数模型订购（PMOR）。我们的方法旨在最小化$ \ Mathcal {h} _ \ infty \ otimes \ Mathcal {l} _ \ infty $近似错误，通过优化减少订单模型（ROM）矩阵，在频率和参数域中的近似错误。最先进的PMOR方法通常计算出不同参数样本的几个非参数ROM，然后将其组合到单个参数ROM中。但是，这些参数ROM在使用的样品点之间的精度较低。相反，我们基于优化的PMOR方法最大程度地减少了整个参数域中的近似误差。此外，由于我们直接优化系统矩阵的灵活方法，我们可以在整个参数域中在ROM中执行诸如port-hamiltonian结构之类的优惠功能。 我们的方法是最近开发的Sobmor-Algorithm到参数系统的扩展。我们将ROM参数化和自适应采样过程扩展到参数情况。在与其他PMOR方法进行比较时，几个数值示例证明了我们方法的有效性和高精度。
We develop an optimization-based algorithm for parametric model order reduction (PMOR) of linear time-invariant dynamical systems. Our method aims at minimizing the $\mathcal{H}_\infty \otimes \mathcal{L}_\infty$ approximation error in the frequency and parameter domain by an optimization of the reduced order model (ROM) matrices. State-of-the-art PMOR methods often compute several nonparametric ROMs for different parameter samples, which are then combined to a single parametric ROM. However, these parametric ROMs can have a low accuracy between the utilized sample points. In contrast, our optimization-based PMOR method minimizes the approximation error across the entire parameter domain. Moreover, due to our flexible approach of optimizing the system matrices directly, we can enforce favorable features such as a port-Hamiltonian structure in our ROMs across the entire parameter domain. Our method is an extension of the recently developed SOBMOR-algorithm to parametric systems. We extend both the ROM parameterization and the adaptive sampling procedure to the parametric case. Several numerical examples demonstrate the effectiveness and high accuracy of our method in a comparison with other PMOR methods.
