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稀疏多小波时变系统辨识及脑电信号时频分析

雷梦颖 魏彦兆 李阳 王丽娜

雷梦颖, 魏彦兆, 李阳, 等 . 稀疏多小波时变系统辨识及脑电信号时频分析[J]. 北京航空航天大学学报, 2018, 44(6): 1312-1320. doi: 10.13700/j.bh.1001-5965.2017.0449
引用本文: 雷梦颖, 魏彦兆, 李阳, 等 . 稀疏多小波时变系统辨识及脑电信号时频分析[J]. 北京航空航天大学学报, 2018, 44(6): 1312-1320. doi: 10.13700/j.bh.1001-5965.2017.0449
LEI Mengying, WEI Yanzhao, LI Yang, et al. Sparse multi-wavelet-based identification of time-varying system with applications to EEG signal time-frequency analysis[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(6): 1312-1320. doi: 10.13700/j.bh.1001-5965.2017.0449(in Chinese)
Citation: LEI Mengying, WEI Yanzhao, LI Yang, et al. Sparse multi-wavelet-based identification of time-varying system with applications to EEG signal time-frequency analysis[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(6): 1312-1320. doi: 10.13700/j.bh.1001-5965.2017.0449(in Chinese)

稀疏多小波时变系统辨识及脑电信号时频分析

doi: 10.13700/j.bh.1001-5965.2017.0449
基金项目: 

国家自然科学基金 61671042

国家自然科学基金 61403016

北京市自然科学基金 4172037

闽江学院福建省重点实验室开放课题基金 MJUKF201702

详细信息
    作者简介:

    雷梦颖  女, 硕士研究生。主要研究方向:信号处理与机器学习

    李阳  男, 博士, 副教授, 博士生导师。主要研究方向:复杂系统建模、信号处理与机器学习

    通讯作者:

    李阳, E-mail:liyang@buaa.edu.cn

  • 中图分类号: N945.14

Sparse multi-wavelet-based identification of time-varying system with applications to EEG signal time-frequency analysis

Funds: 

National Natural Science Foundation of China 61671042

National Natural Science Foundation of China 61403016

Beijing Natural Science Foundation, China 4172037

Open Fund Project of Fujian Provincial Key Laboratory in Minjiang University MJUKF201702

More Information
  • 摘要:

    通过时变参数建模算法对非平稳时变系统的辨识问题进行了研究,并将其应用于脑电(EEG)信号时频特征提取分析。首先,将时变系统参数用具有良好局部逼近能力的多小波基函数进行展开,时变系统建模问题简化为时不变回归模型估计。其次,进一步结合正则化正交最小二乘(ROLS)算法,既降低模型复杂度,又避免模型过拟合问题,从而实现了时变参数的快速准确估计。仿真实例结果表明,与传统递归最小二乘(RLS)算法、经典正交最小二乘(OLS)算法结果相比,所提稀疏多小波建模算法能够更加准确跟踪时变参数的变化。最后,该算法用于运动想象任务下采集的真实EEG信号的时频特征分析,能够有效地得到α节律下高时频分辨率的事件相关去同步(ERD)及事件相关同步(ERS)分析结果,验证了本文算法的应用性。

     

  • 图 1  基于3种算法的参数辨识结果

    Figure 1.  Parameter identification results based on three algorithms

    图 2  预处理后EEG信号时域波形

    Figure 2.  Time domain waveform of preprocessed EEG signals

    图 3  5阶时变自回归模型估计结果与真实EEG信号对比

    Figure 3.  Comparison between estimation results from TVAR(5) time-varying autoregressive model and real EEG signal

    图 4  不同任务下C3、C4通道相对时频能量变化图

    Figure 4.  Relative time-frequency power spectrum of channel C3 and C4 during motor imagery

    图 5  各类任务下不同时间点相对能量头皮地形图

    Figure 5.  Topographic maps of time-dependent power during motor imagery tasks

    表  1  3种辨识算法估计结果对比

    Table  1.   Comparison of estimation results among three identification algorithms

    辨识算法估计参数MAERMSE
    RLS算法a1(t)0.044 80.142 7
    a2(t)0.042 20.263 4
    b1(t)0.011 40.149 6
    b2(t)0.017 60.107 7
    B样条-OLS估计法a1(t)0.040 60.101 0
    a2(t)0.037 70.178 9
    b1(t)0.008 90.121 7
    b2(t)0.016 80.102 4
    B样条-ROLS建模算法a1(t)0.039 20.097 5
    a2(t)0.035 00.136 5
    b1(t)0.007 90.099 0
    b2(t)0.015 40.102 0
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出版历程
  • 收稿日期:  2017-07-05
  • 录用日期:  2017-09-05
  • 网络出版日期:  2018-06-20

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