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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2025, Vol. 42 ›› Issue (5): 875-888.doi: 10.3969/j.issn.1005-3085.2025.05.006cstr: 32411.14.cjem.CN61-1269/O1.2025.05.006

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基于Laguerre函数的大规模二阶系统平衡截断模型降阶

解礼欣1,  肖志华1,  代  柳2   

  1. 1. 长江大学信息与数学学院，荆州 434023

    2. 荆楚理工学院数理学院，荆门 448000

  • 收稿日期:2022-12-18 接受日期:2023-06-07 出版日期:2025-10-15 发布日期:2025-12-15
  • 通讯作者: 肖志华 E-mail: zhxiao@yangtzeu.edu.cn
  • 基金资助:
    国家自然科学基金 (62273059; 61803046).

Balanced Truncation Model Reduction of Large-scale Second-order Systems via Laguerre Functions

XIE Lixin1,   XIAO Zhihua1,  DAI Liu2   

  1. 1. School of Information and Mathematics, Yangtze University, Jingzhou 434023
    2. School of Mathematics and Physics, Jingchu University of Technology, Jingmen 448000
  • Received:2022-12-18 Accepted:2023-06-07 Online:2025-10-15 Published:2025-12-15
  • Contact: Z. Xiao. E-mail address: zhxiao@yangtzeu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (62273059; 61803046).

摘要：

提出了一种基于Laguerre函数的大规模二阶系统平衡截断模型降阶方法。该方法首先利用Laguerre函数所张成空间中的矩阵指数函数的近似展开来计算系统Gram矩阵的低秩分解，然后根据二阶系统的奇异值结构构造相应的平衡系统。接着，通过截断较小奇异值对应的状态，得到降阶后的二阶模型。最后，通过数值实验验证了所提方法的有效性。

关键词: 模型降阶, 二阶系统, Laguerre函数, 矩阵指数函数, 平衡截断

Abstract:

This study considers a balanced truncation model order reduction method of large-scale second-order systems via Laguerre functions. The proposed method uses the matrix exponential functions in the space spanned by Laguerre functions to compute the low-rank decomposition. The corresponding balanced system is constructed by the singular values structure of the second-order system.  Then, the reduced second-order model is obtained by truncating the states corresponding to the small singular values. Finally, the validity of the proposed method is shown by a given numerical example.

Key words: model order reduction, second-order systems, Laguerre functions, matrix exponential function, balanced truncation

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