Piecewise polynomial nonlinear model reduction
Piecewise polynomial nonlinear model reduction
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DOI：
10.1145/775832.775957
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发表时间：
2003-06
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影响因子：
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通讯作者：
Ning Dong;J. Roychowdhury
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作者：
Ning Dong;J. Roychowdhury
提出了一种结合了全局逼近和局部逼近性质的非线性系统模型降阶的新方法。首先将非线性系统近似为多个区域上的分段多项式，然后利用多项式模型降阶方法对每个区域进行降阶。我们的方法，称为PWP，推广了最近的分段线性方法，并将它们与基于多项式的MOR联系在一起，从而结合了它们的优点。特别是，我们的方法得到的简化模型很好地再现了小信号失真和互调特性，同时在大摆幅和大信号分析中保持了保真度，例如瞬时模拟。因此，我们简化的模型可以用来替代具有小或大激励的时域和频域模拟。通过利用系统多项式系数的稀疏性，我们能够使多项式约简过程在原始系统的大小中线性。我们给出了实现细节，并用一个例子说明了PWP。
We present a novel, general approach towards model-order reduction (MOR) on nonlinear systems that combines good global and local approximation properties. The nonlinear system is first approximated as piecewise polynomials over a number of regions, following which each region is reduced via polynomial model-reduction methods. Our approach, dubbed PWP, generalizes recent piecewise linear approaches and ties them with polynomial-based MOR, thereby combining their advantages. In particular, reduced models obtained by our approach reproduce small-signal distortion and intermodulation properties well, while at the same time retaining fidelity in large-swing and large-signal analyses, e.g., transient simulations. Thus our reduced models can be used as drop-in replacements for time-domain as well as frequency-domain simulations, with small or large excitations. By exploiting sparsity in system polynomial coefficients, we are able to make the polynomial reduction procedure linear in the size of the original system. We provide implementation details and illustrate PWP with an example.