ABSTRACT Correct selection of spatial basis functions is crucial for model reduction for nonlinear distributed parameter systems in engineering applications. To construct appropriate reduced models, modelling accuracy and computational costs must be balanced. In this paper, empirical Gramian-based spatial basis functions were proposed for model reduction of nonlinear distributed parameter systems. Empirical Gramians can be computed by generalizing linear Gramians onto nonlinear systems, which results in calculations that only require standard matrix operations. Associated model reduction is described under the framework of Galerkin projection. In this study, two numerical examples were used to evaluate the efficacy of the proposed approach. Lower-order reduced models were achieved with the required modelling accuracy compared to linear Gramian-based combined spatial basis function- and spectral eigenfunction-based methods.

中文翻译：

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用于非线性分布参数系统模型约简的基于经验 Gramian 的空间基函数

摘要 正确选择空间基函数对于工程应用中非线性分布参数系统的模型简化至关重要。为了构建适当的简化模型，必须平衡建模精度和计算成本。在本文中，提出了基于经验格拉姆的空间基函数用于非线性分布参数系统的模型约简。经验 Gramians 可以通过将线性 Gramian 推广到非线性系统来计算，这导致计算只需要标准矩阵运算。在伽辽金投影的框架下描述了相关的模型缩减。在这项研究中，两个数值例子被用来评估所提出的方法的有效性。