北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (9): 1722-1728.doi: 10.13700/j.bh.1001-5965.2014.0693

• 论文 • 上一篇    下一篇

基于多尺度径向基函数的时变系统辨识

刘青, 李阳   

  1. 北京航空航天大学 自动化科学与电气工程学院, 北京 100191
  • 收稿日期:2014-11-11 出版日期:2015-09-20 发布日期:2015-09-29
  • 通讯作者: 李阳(1980—),男,湖南邵阳人,副教授,liyang@buaa.edu.cn,主要研究方向为复杂系统建模、信号处理与机器学习. E-mail:liyang@buaa.edu.cn
  • 作者简介:刘青(1991—),女,河北沧州人,硕士研究生,lqyueming_2009@163.com
  • 基金资助:
    国家自然科学基金(61403016); 高等学校博士学科点专项科研基金(20131102120008); 教育部留学回国人员科研启动基金 (60300002014103001); 中央高校基本科研业务费专项资金(YWF-14-ZDHXY-020)

Identification of time-varying systems using multi-scale radial basis function

LIU Qing, LI Yang   

  1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2014-11-11 Online:2015-09-20 Published:2015-09-29

摘要: 应用非平稳时间序列的时变系统建模方法进行了参数随时间变化的线性系统参数的辨识.通过引入多尺度径向基函数(MRBF)将非平稳过程的辨识问题转化为线性时不变过程的辨识,结合粒子群优化算法(PSO)获得时变系统参数估计的最优径向基函数(RBF)尺度.由于RBF具有良好的局部特性且尺度可以调整,采用RBF作为基函数可以更好地识别具有多种动态过程的时变系统参数.通过对时变系数包含多种波形的二阶时变自回归模型进行仿真辨识,与采用传统的递推最小二乘法和勒让德多项式作为基函数展开式方法相比,提出的方法对于时变系统参数具有更好的跟踪能力,验证了辨识方法的有效性.

关键词: 时变自回归模型, 递归最小二乘算法, 勒让德基函数, 多尺度径向基函数, 粒子群优化算法, 参数辨识

Abstract: A time-varying autoregressive model with time-varying coefficients was investigated to identify linear system parameters from nonstationary time series. The basis function of multi-scale radial basis function (MRBF) was employed, and the identification of nonstationary modeling problem was then simplified to a linear time-invariant modeling problem. Particle swarm optimization (PSO) algorithm was applied to search the optimal RBF scales for the estimation of time-varying system parameters. The basis functions of RBF can better estimate time-varying parameters with a variety of dynamic process because optimal different RBF scales with good local properties can be effectively adjusted by the PSO algorithm. One simulation example of second-order time-varying autoregressive model with time-varying parameters involved different waveform was presented to show the effectiveness of the proposed method. Compared with classical approaches of time-varying parametric estimations such as recursive least square algorithms and the expansion approach of Legendre polynomial basis function, the identification results of time-varying parameters can be more accurately estimated which validates the effectiveness of the proposed time-varying modeling method.

Key words: time-varying autoregressive model, recursive least squares algorithm, Legendre basis function, multi-scale radial basis function, particle swarm optimization, parameter identification

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