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电路测试响应信号的GP-KSVD稀疏重构算法

聂静 苏东林 李红裔 赵迪

聂静, 苏东林, 李红裔, 等 . 电路测试响应信号的GP-KSVD稀疏重构算法[J]. 北京航空航天大学学报, 2017, 43(7): 1336-1347. doi: 10.13700/j.bh.1001-5965.2016.0518
引用本文: 聂静, 苏东林, 李红裔, 等 . 电路测试响应信号的GP-KSVD稀疏重构算法[J]. 北京航空航天大学学报, 2017, 43(7): 1336-1347. doi: 10.13700/j.bh.1001-5965.2016.0518
NIE Jing, SU Donglin, LI Hongyi, et al. Circuitry test response signal reconstruction based on GP-KSVD algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(7): 1336-1347. doi: 10.13700/j.bh.1001-5965.2016.0518(in Chinese)
Citation: NIE Jing, SU Donglin, LI Hongyi, et al. Circuitry test response signal reconstruction based on GP-KSVD algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(7): 1336-1347. doi: 10.13700/j.bh.1001-5965.2016.0518(in Chinese)

电路测试响应信号的GP-KSVD稀疏重构算法

doi: 10.13700/j.bh.1001-5965.2016.0518
基金项目: 

国家自然科学基金 61379001

详细信息
    作者简介:

    聂静 女, 博士研究生。主要研究方向:系统级电磁兼容性评估

    苏东林 女, 博士, 教授, 博士生导师。主要研究方向:系统级电磁兼容

    李红裔 女, 博士, 教授, 博士生导师。主要研究方向:矩阵理论与应用、多复变与几何

    赵迪 男, 博士, 教授, 博士生导师。主要研究方向:矩阵理论与应用、多复变与几何

    通讯作者:

    赵迪, E-mail:zdzz@buaa.edu.cn

  • 中图分类号: V219+.3;TB553;O29

Circuitry test response signal reconstruction based on GP-KSVD algorithm

Funds: 

National Natural Science Foundation of China 61379001

More Information
  • 摘要:

    电路系统测试响应信号具有周期性强、分布较稀疏的特点,针对电路系统测试响应信号的压缩重构问题进行了研究,提出了基于梯度方向追踪的K奇异值分解(GP-KSVD)稀疏重构算法。结合单一响应信号以及混合信号其自身特点进行字典训练,利用更新后字典对含噪信号进行梯度追踪稀疏表征,通过对含噪信号的重构,实现了去噪的目的,算法计算复杂度低,储存量小,具有较好的重构效果。仿真中将GP-KSVD表征与使用随机字典、离散余弦字典(DCT)的表征进行比较,从信噪比(SNR)以及相对均方误差(RMSE)2项指标中得出使用KSVD字典具有更好的重构去噪效果;此外将GP-KSVD稀疏重构算法与正交匹配追踪正交匹配追踪(OMP)-KSVD、预处理共轭梯度追踪(PCGP)算法进行比较,得出GP-KSVD的计算时间最短、重构精度更高的结论,并且进行了实测验证。算法可用来对测试响应信号进行预处理,为电路系统设备性能的评估分析提供了理论依据。

     

  • 图 1  GP-KSVD对5 Hz正弦信号的重构

    Figure 1.  GP-KSVD reconstruction of 5 Hz sine signal

    图 2  正弦信号1 kHz以及KSVD字典基原子

    Figure 2.  1 kHz sine signal and basic atom of KSVD dictionary

    图 3  GP-KSVD对1 kHz正弦信号的重构以及系数表征

    Figure 3.  1 kHz sine signal reconstruction and coefficient representation by GP-KSVD

    图 4  不同字典处理正弦信号的SNR以及RMSE指标的比较

    Figure 4.  Comparison of index of SNR and RMSE of sine signal processed with different dictionaries

    图 5  几种不同算法对正弦信号的重构对比

    Figure 5.  Comparison of sine signal reconstruction among different algorithms

    图 6  15 MHz正切信号以及KSVD字典基原子

    Figure 6.  15 MHz tangent signal and basic atom of KSVD dictionary

    图 7  GP-KSVD对15 MHz正切信号的重构以及系数表征

    Figure 7.  15 MHz tangent signal reconstruction and coefficient representation by GP-KSVD

    图 8  不同字典处理正切信号的SNR以及RMSE指标的比较

    Figure 8.  Comparison of indices of SNR and RMSE of tangent signal processed with different dictionaries

    图 9  几种不同算法对正切信号的重构对比

    Figure 9.  Comparison of tangent signal reconstruction among different algorithms

    图 10  GP-KSVD对混合信号的重构

    Figure 10.  Reconstruction of mixed signal by GP-KSVD

    图 11  文献[9]中的干净TwinSine信号以及含噪信号

    Figure 11.  Clean and noisy TwinSine signal in Ref. [9]

    图 12  对TwinSine信号的重构比较

    Figure 12.  Comparison of reconstruction of TwinSine signal

    图 13  对文献[9]中Cusp信号的重构比较

    Figure 13.  Comparison of reconstruction of Cusp signal in Ref. [9]

    图 14  GP-KSVD对电磁辐射信号的去噪重构

    Figure 14.  Denoising reconstruction of electromagnetic radiation signal by GP-KSVD

    图 15  电磁辐射信号实测现场图

    Figure 15.  Field measurement of electromagnetic radiation signal

    表  1  算法复杂度和存储量

    Table  1.   Algorithms complexity and storage

    算法计算复杂度存储量
    OMP-Cholesky2D+3n2+3M+(D+N)n (n+1) /2+(D+M+2n+N)
    GPD+n+3M+(D+N)M+(D+M+2n+N)
    下载: 导出CSV

    表  2  对正弦信号不同算法的SNR指标以及运行时间

    Table  2.   Index of SNR and running time of different algorithms on sine signal

    算法SNR/dB信噪比增值/dB运行时间/s
    PCGP12.77.20.162 89
    OMP-KSVD11.05.50.205 86
    GP-DCT7.11.60.111 33
    GP-KSVD12.97.40.097 656
    下载: 导出CSV

    表  3  对正切信号不同算法的SNR指标以及运行时间

    Table  3.   Index of SNR and running time of different algorithms on tangent signal

    算法SNR/dB信噪比增值/dB运行时间/s
    PCGP10.67.70.008 984 4
    OMP-KSVD9.36.40.014 063
    GP-DCT4.41.50.069 531
    GP-KSVD10.67.70.005 468 7
    下载: 导出CSV

    表  4  GP-KSVD算法与文献[9]中算法对TwinSine信号的运行时间对比

    Table  4.   Comparison of running time on TwinSine signal between GP-KSVD and algorithms in Ref. [9]

    算法MOF[9]MP[9]BP[9]GP-KSVD
    运行时间/s0.218 750.078 120.468 750.066 41
    下载: 导出CSV

    表  5  GP-KSVD算法与文献[9]中算法对Cusp信号的运行时间对比

    Table  5.   Comparison of running time on Cusp signal between GP-KSVD and algorithms in Ref. [9]

    算法MOF[9]MP[9]BP[9]GP-KSVD
    运行时间/s3.890 60.031 254.234 40.005 47
    下载: 导出CSV
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出版历程
  • 收稿日期:  2016-06-15
  • 录用日期:  2016-09-21
  • 刊出日期:  2017-07-20

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