二阶系统基于奇异值的保结构模型降阶方法  

Structure-preserving Model Reduction for Second-order Systems Based on Singular Values

作　　者：解礼 欣肖志 华金辉 XIE Lixin;XIAO Zhihua;JIN Hui(School of Information and Mathematics,Yangtze University,Jingzhou,Hubei,434023,P.R.China)

机构地区：[1]长江大学信息与数学学院,湖北荆州434023

出　　处：《数学进展》2024年第2期425-440,共16页Advances in Mathematics（China）

基　　金：Supported by NSFC(Nos.61803046,62273059)。

摘　　要：本文提出了一种二阶系统基于奇异值的保结构模型降阶方法.该方法通过脉冲响应的移位勒让德多项式展开系数直接计算得到二阶系统的可控和可观格拉姆矩阵的低秩因子.然后基于二阶系统的奇异值结构,构造相应的平衡系统,进而通过截断较小奇异值对应的状态得到保结构的降阶系统.最后,通过两个数值实验展示了所提方法的有效性.In this paper,a structure-preserving model order reduction method for second-order systems based on singular values is proposed.This method calculates the low-rank factors of the controllability and observability Gramians of the second-order system directly by using the shifted Legendre polynomial-expansion coefficients of the impulse response.Then,based on the singular values’structure of the second-order systems,a corresponding balanced system is constructed.After that the structure-preserving reduced-order systems can be obtained by truncating the states corresponding to the small singular values.In the end,the validity of our methods are shown by two numerical examples.

关 键 词：模型降阶 平衡截断 奇异值 移位勒让德多项式 格拉姆矩阵 

分 类 号：O231.1[理学—运筹学与控制论]