基于时域误差限的大规模系统自适应模型降阶

发布时间：2018-01-26 09:19

本文关键词： SVD-Krylov空间法大规模动态系统时域误差限自适应模型降阶　出处：《数学的实践与认识》2017年09期 　论文类型：期刊论文

【摘要】：为满足解大规模动态系统常微分方程组对精度和速度权衡的要求,提出了一种基于误差限的大规模系统自适应模型降阶方法,其中方法的误差分析基于时域最大误差限,降阶方法基于SVD-Krylov子空间的方法.方法既考虑了算法的复杂性,又保证了算法的精度.通过对典型实例分析,结果表明该方法在给定相对误差限10~(-4)下得出的降阶阶数在不同频率下都能给出很好的近似精度,低频1~10Hz平均相对误差为1.1812×10~(-5),高频1~10GHz平均相对误差为5.6408×10~(-5),即在很宽的频率范围内都能满足精度要求.
[Abstract]:In order to meet the requirements of accuracy and speed tradeoff for solving ordinary differential equations of large-scale dynamic systems, an adaptive model reduction method for large-scale dynamic systems based on error limits is proposed. The error analysis of the method is based on the time domain maximum error limit, and the order reduction method is based on the method of SVD-Krylov subspace. Through the analysis of typical examples, the results show that the order reduction obtained by this method under the given relative error limit of 10 / 10 ~ (-4) can give good approximate accuracy at different frequencies. The average relative error of low frequency is 1.1812 脳 10 ~ (10) GHz and that of high frequency is 5.6408 脳 10 ~ (-5). That is, in a wide range of frequency can meet the accuracy requirements.
【作者单位】：哈尔滨工业大学航天学院;哈尔滨工业大学威海校区;
【基金】：国家青年科学基金(61201307)
【分类号】：O175
【正文快照】： 1 引言随着科学的不断进步,处理的问题的复杂度越来越大,这使得对于系统的模拟、控制和性能分析变得越来越困难,而模型降阶是缩减大规模系统复杂性的有效方法.降阶方法主要分为两类:Krylov子空间法;奇异值分解法.Krylov子空间的方法主要有两类组成:基于Lanczos过程的降阶算

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