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

北京航空航天大学学报 ›› 2018, Vol. 44 ›› Issue (6): 1312-1320.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

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

收稿日期:2017-07-05 出版日期:2018-06-20 发布日期:2018-06-28
通讯作者: 李阳.E-mail:liyang@buaa.edu.cn E-mail:liyang@buaa.edu.cn
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。
基金资助:
国家自然科学基金（61671042，61403016）；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）

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

LEI Mengying¹, WEI Yanzhao¹, LI Yang¹, 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

Received:2017-07-05 Online:2018-06-20 Published:2018-06-28

摘要/Abstract

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。

关键词: 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.

Key words: non-stationary time-varying system, multi-wavelet basis function, regularized orthogonal least squares (ROLS), parametric estimation, time-frequency analysis of electroencephalography (EEG) signals

中图分类号:

N945.14

雷梦颖, 魏彦兆, 李阳, 王丽娜. 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.

LEI Mengying, WEI Yanzhao, LI Yang, WANG Lina. 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 A, 2018, 44(6): 1312-1320.

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稀疏多小波时变系统辨识及脑电信号时频分析

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

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