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Interpolatory model reduction for quadratic-bilinear systems using error estimators

机译：二次双线性系统使用误差估计的插值模型约简

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摘要

Purpose The purpose of this paper is to propose an interpolation-based projection framework for model reduction of quadratic-bilinear systems. The approach constructs projection matrices from the bilinear part of the original quadratic-bilinear descriptor system and uses these matrices to project the original system.Design/methodology/approach The projection matrices are constructed by viewing the bilinear system as a linear parametric system, where the input associated with the bilinear part is treated as a parameter. The advantage of this approach is that the projection matrices can be constructed reliably by using an a posteriori error bound for linear parametric systems. The use of the error bound allows us to select a good choice of interpolation points and parameter samples for the construction of the projection matrices by using a greedy-type framework.Findings The results are compared with the standard quadratic-bilinear projection methods and it is observed that the approximations through the proposed method are comparable to the standard method but at a lower computational cost (offline time).Originality/value In addition to the proposed model order reduction framework, the authors extend the one-sided moment matching parametric model order reduction (PMOR) method to a two-sided method that doubles the number of moments matched in the PMOR method.
机译：目的本文的目的是为二次双线性系统的模型简化提出基于插值的投影框架。该方法从原始二次-双线性描述符系统的双线性部分构造投影矩阵，并使用这些矩阵投影原始系统。设计/方法/方法通过将双线性系统视为线性参数系统来构造投影矩阵，其中与双线性部分关联的输入被视为参数。这种方法的优点是可以通过使用线性参数系统的后验误差边界来可靠地构造投影矩阵。使用误差边界使我们可以使用贪心类型的框架来选择用于构建投影矩阵的插值点和参数样本的良好选择。结果与标准二次双线性投影方法进行了比较，得出观察到，通过提出的方法进行的近似值可与标准方法进行比较，但计算成本较低（脱机时间）。原始数据/值除了提出的模型阶数减少框架之外，作者还扩展了单侧矩匹配参数模型阶数减法（PMOR）方法变为双面方法，该方法使PMOR方法中匹配的矩数加倍。

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