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一种基于组合赋权法的小波去噪质量评价方法

李晋斐 赵冬青 王栋民 蔡聪聪 贾晓雪 张乐添

李晋斐,赵冬青,王栋民,等. 一种基于组合赋权法的小波去噪质量评价方法[J]. 北京航空航天大学学报,2023,49(3):718-725 doi: 10.13700/j.bh.1001-5965.2021.0303
引用本文: 李晋斐,赵冬青,王栋民,等. 一种基于组合赋权法的小波去噪质量评价方法[J]. 北京航空航天大学学报,2023,49(3):718-725 doi: 10.13700/j.bh.1001-5965.2021.0303
LI J F,ZHAO D Q,WANG D M,et al. A quality evaluation method for wavelet denoising based on combinatorial weighting method[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(3):718-725 (in Chinese) doi: 10.13700/j.bh.1001-5965.2021.0303
Citation: LI J F,ZHAO D Q,WANG D M,et al. A quality evaluation method for wavelet denoising based on combinatorial weighting method[J]. Journal of Beijing University of Aeronautics and Astronautics,2023,49(3):718-725 (in Chinese) doi: 10.13700/j.bh.1001-5965.2021.0303

一种基于组合赋权法的小波去噪质量评价方法

doi: 10.13700/j.bh.1001-5965.2021.0303
基金项目: 国家自然科学基金(41774037)
详细信息
    通讯作者:

    E-mail:dongqing.zhao@hotmail.com

  • 中图分类号: V249.3; P227.9

A quality evaluation method for wavelet denoising based on combinatorial weighting method

Funds: National Natural Science Foundation of China (41774037)
More Information
  • 摘要:

    针对传统质量评价指标在小波阈值去噪中理论依据不足的问题,提出了一种基于组合赋权法的小波去噪质量评价方法,能够为小波去噪参数的选择提供有效评价。通过分析在真值未知情况下均方根误差(RMSE)、信噪比(SNR)、平滑度等单项指标的特点,选取RMSE与平滑度作为小波去噪指标,对其进行归一化处理,采用信息熵权与变异系数的方法进行组合赋权,将归一化指标与对应权值线性组合,得到一种新的指标即为复合评价指标,其值越小,说明去噪效果越好,所选参数越优。仿真实验表明,在真值已知情况下,该评价指标具有更高的准确性,能够适用于不同的分解层数与小波基函数,具有比传统方法更好的适用性;实测数据表明,所提方法得出的小波去噪峰值域更加光滑,波形更加平稳,去噪效果更佳。

     

  • 图 1  真值已知的多普勒信号的单一评价指标趋势

    Figure 1.  Trends of single evaluation index of Doppler signal with known truth value

    图 2  真值未知的陀螺输出数据的单一评价指标趋势

    Figure 2.  Trends of single evaluation index of gyro output data with unknown truth value

    图 3  原始信号与降噪信号时域曲线

    Figure 3.  Time-domain curves of original signal and denoising signal

    图 4  原始信号与降噪信号频谱曲线

    Figure 4.  Spectrum curves of original signal and denoising signal

    图 5  原始信号与降噪信号功率谱密度图

    Figure 5.  Power spectral density diagram of original signal and denoising signal

    表  1  真值未知时评价指标特点

    Table  1.   Characteristics of evaluation indexes when truth value is unknown

    评价指标关注信息与分解层数相关性
    RMSE细节信息正相关
    SNR细节信息负相关
    平滑度近似信息负相关
    下载: 导出CSV

    表  2  不同分解层数利用sym4小波基处理的评价指标

    Table  2.   Evaluation indexes of sym4 wavelet basis processing for different decomposition layers

    分解层数真值已知真值未知TSH
    RMSESNRRMSEr
    20.581 113.861 70.778 10.103 00.866 50.890 30.899 5
    30.465 015.796 90.844 70.069 70.212 30.256 60.193 3
    40.416 216.761 30.856 80.065 40.132 80.233 30.105 9
    50.406 216.970 80.866 20.064 60.128 80.122 30.097 9
    60.400 617.093 40.867 20.064 50.127 50.146 20.096 2
    70.405 616.985 40.869 90.064 40.130 60.109 70.098 3
    80.405 516.986 00.869 90.064 40.130 60.116 40.098 3
    90.418 716.876 80.870 40.064 40.131 20.132 00.098 7
    100.410 116.888 80.872 10.064 30.133 50.100 5
    下载: 导出CSV

    表  3  不同分解层数利用db5小波基处理的评价指标

    Table  3.   Evaluation indexes of db5 wavelet basis processing for different decomposition layers

    分解层数真值已知真值未知TSH
    RMSESNRRMSEr
    20.541114.48050.82190.08080.85930.89250.8933
    30.456 115.965 50.883 30.050 00.236 90.267 80.219 0
    40.414 916.788 00.895 50.045 70.156 10.248 90.129 6
    50.382 517.492 80.905 70.044 40.140 30.157 40.108 7
    60.375 817.648 30.909 40.044 10.139 70.119 50.106 5
    70.375 217.662 20.910 30.044 00.140 00.109 50.10627
    80.379 517.562 90.910 70.044 00.140 10.108 70.106 3
    90.379 717.558 60.910 90.044 00.140 70.107 50.106 5
    100.380 217.546 30.911 00.044 00.144 50.106 7
    下载: 导出CSV

    表  4  不同小波基对应的最优分解层数

    Table  4.   Number of optimal decomposition layers corresponding to different wavelet bases

    小波基最优分解层数
    真值已知本文方法文献[9]文献[10]
    db39996
    db46667
    db57767
    db66657
    db76656
    db86866
    sym39996
    sym46665
    Sym56557
    Sym66665
    Sym77767
    Sym86656
    coif36665
    coif46666
    coif55665
    下载: 导出CSV

    表  5  SPAN-ISA-100C陀螺仪Allan方差分析结果

    Table  5.   Allan variance analysis results of SPAN-ISA-100C gyroscope

    坐标轴角度随机游走/
    $({(^\circ )}\cdot{ {\text{h} }^{-\frac{ {1} }{ {2} } } })$
    零偏不稳定性/
    $((^\circ) \cdot{\text{h} }^{-1})$
    角速率随机游走/
    $((^\circ )\cdot{ {\text{h} }^{-\frac{ {3} }{ {2} } } })$
    x0.030 40.045 50.054 2
    y0.026 90.120 80.185 7
    z0.025 40.043 00.057 9
    下载: 导出CSV

    表  6  MP-M39陀螺仪Allan方差分析结果

    Table  6.   Allan variance analysis results of MP-M39 gyroscope

    坐标轴角度随机游走/
    $({(^\circ )}\cdot{ {\text{h} }^{-\frac{ {1} }{ {2} } } })$
    零偏不稳定性/
    $((^\circ) \cdot{\text{h} }^{-1})$
    角速率随机游走/
    $((^\circ )\cdot{ {\text{h} }^{-\frac{ {3} }{ {2} } } })$
    x0.199 39.504 128.599 4
    y0.136 34.198 714.920 2
    z0.186 87.591 229.389 7
    下载: 导出CSV

    表  7  陀螺数据对应的最优分解层数

    Table  7.   Number of optimal decomposition layers corresponding to gyro data

    方法陀螺数据
    x1y1z1x2y2z2
    本文455555
    文献[9]444444
    下载: 导出CSV

    表  8  陀螺数据对应的最佳小波基函数

    Table  8.   Optimal wavelet basis functions corresponding to gyro data

    陀螺数据x1y1z1x2y2z2
    小波基sym6sym4db8db7db7db7
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-06-07
  • 录用日期:  2021-07-18
  • 网络出版日期:  2021-09-24
  • 整期出版日期:  2023-03-30

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