基于改进最小角回归算法的Hammerstein模型辨识

Identification for Hammerstein models based on a modified least angle regression algorithm

中文关键词  Hammerstein模型  稀疏系统辨识  最小角回归算法  模型选择准则  时滞估计

英文关键词  Hammerstein model  sparse system identification  least angle regressive algorithm  model selection criterion  time-delay estimation

中文摘要

      针对一类未知时滞和阶次的Hammerstein模型的辨识问题, 本文提出一种基于绝对角度停止准则最小角回归(AS-LAR)的稀疏辨识方法, 该方法可以同时辨识出Hammerstein模型的时滞、阶次和参数. 首先, 通过引入最大非线性阶次和输入回归长度, 将系统表示成具有稀疏参数向量的高维辨识模型; 然后, 提出一种绝对角度停止准则, 对最小角回归算法进行改进, 并基于改进的AS-LAR算法获得稀疏参数向量的估计; 最后, 基于参数向量稀疏结构, 估计出系统的时滞和阶次, 并从估计的参数向量中提取和分离出系统线性部分和非线性部分的参数估计值. 数值仿真和水箱实例结果表明, 提出的辨识方法有效, 且与其它辨识方法相比, 具有估计精度高、计算量小、速度快等特点.

英文摘要

      For the identification of a class of Hammerstein models with unknown time-delays and orders, this paper proposes a sparse system identification method based on the absolute angle stopping criteria least angle regression (AS-LAR) algorithm, which can simultaneously estimate the time-delays, orders and parameters of the Hammerstein model. Firstly, a high-dimensional sparse identification model is derived by introducing a maximum nonlinear order and a maximum input regression length. Then a new absolute angle stopping criteria is presented to modify the least angle regression algorithm, and the sparse parameter vector is identified based on the new AS-LAR algorithm. Finally, the time-delays and system orders are estimated based on the sparse structure of the estimated parameter vector, and the parameters of the nonlinear and linear part are extracted and separated from the estimated parameter vector. A numerical simulation and a water tank example show that the proposed algorithm is effective and has the features of high accuracy of parameter estimation, low computational effort and fast speed.