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

doi:10.13700/j.bh.1001-5965.2017.0449

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

雷梦颖¹,
魏彦兆¹,
李阳^1, ,,
王丽娜^{2, 3}

1.
北京航空航天大学自动化科学与电气工程学院, 北京 100083
2.
宇航智能控制技术国家级重点实验室, 北京 100854
3.
北京航天自动控制研究所, 北京 100854

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
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- 被引次数: 0
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

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

LEI Mengying¹,
WEI Yanzhao¹,
LI Yang^{1
, ,},
WANG Lina^{2, 3}

1.
School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
2.
National Laboratory of Aerospace Intelligent Control Technology, Beijing 100854, China
3.
Beijing Aerospace Automatic Control Institute, Beijing 100854, China

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

Corresponding author: LI Yang, E-mail:liyang@buaa.edu.cn

摘要

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。
- 非平稳时变系统 /
- 多小波基函数 /
- 正则化正交最小二乘(ROLS) /
- 参数估计 /
- 脑电(EEG)信号时频分析
Abstract:
The problem of identification in non-stationary time-varying system is investigated based on a time-varying parametric modelling algorithm, and is applied to time-frequency feature extraction analysis of electroencephalography (EEG) signals. The multi-wavelet basis function which has proved efficient for tracking the transient local changes in signals, is employed to approximate the time-varying coefficients, and thus the initial time-varying modelling problem is then simplified into a time-invariant regression model estimation problem. In addition, the regularized orthogonal least squares (ROLS) algorithm is used to construct a parsimonious model structure and estimate the model parameters effectively, which not only reduces the model complexity, but also avoids the overfitting problem. The simulation results show that, compared with traditional recursive least squares (RLS) algorithm and classical orthogonal least squares (OLS) algorithm, the proposed sparse multi-wavelet-based modelling method is capable of estimating time-varying parameters more accurately. Furthermore, the application of the proposed method to the real EEG signals during motor imagery has proven to have powerful tracking capabilities, and a time-frequency analysis is introduced based on the identified time-varying model. The high time-frequency resolution of the proposed method enables the characterizations of event-related desynchronization (ERD) and event-related synchronization (ERS) in alpha band precisely, and validates the applicability of the proposed modelling algorithm.

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图 1 基于3种算法的参数辨识结果

Figure 1. Parameter identification results based on three algorithms

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图 2 预处理后EEG信号时域波形

Figure 2. Time domain waveform of preprocessed EEG signals

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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

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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

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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

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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	MAE	RMSE
RLS算法	a₁(t)	0.044 8	0.142 7
	a₂(t)	0.042 2	0.263 4
	b₁(t)	0.011 4	0.149 6
	b₂(t)	0.017 6	0.107 7
B样条-OLS估计法	a₁(t)	0.040 6	0.101 0
	a₂(t)	0.037 7	0.178 9
	b₁(t)	0.008 9	0.121 7
	b₂(t)	0.016 8	0.102 4
B样条-ROLS建模算法	a₁(t)	0.039 2	0.097 5
	a₂(t)	0.035 0	0.136 5
	b₁(t)	0.007 9	0.099 0
	b₂(t)	0.015 4	0.102 0

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