Abstract:

Based on approximate least absolute deviation and principal component analysis, the partial approximate least absolute deviation for non-linear system identification is carried out aiming at multivariable Hammerstein model with linear correlation of input signals. An approximate least absolute deviation objective function is established by introducing a deterministic function to replace the absolute value under certain situations. The proposed method can overcome the disadvantage of large square residual of least square criterion when the identification data is disturbed by the impulse noise which obeys symmetrical alpha stable (SαS) distribution. By adopting principal component analysis to eliminate the linear correlation among the elements of data vector of nonlinear systems, the unique solution of model parameters can be easily acquired by the proposed method. The simulation shows that the proposed method has stronger robustness than the partial least square (PLS) method in the identification of multivariable Hammerstein model with white noise and impulse noise under the above situation.

Key words: parameter identification, principal component analysis, multivariable Hammerstein model, partial least absolute deviation, dynamic simulation, impulse noise

摘要：

基于近似最小一乘准则和主成分分析，针对输入信号线性相关的多变量Hammerstein模型，进行了近似偏最小一乘非线性系统辨识算法的推导。本文算法用确定性可导函数近似代替残差绝对值，可以抑制满足SαS分布的尖峰噪声，且具有目标函数可导、计算简单的优点。同时，通过主成分分析去除非线性系统数据向量矩阵之间的相关性，可以得出模型参数的唯一解。仿真实验表明，本文算法可以对输入信号存在相关性的多变量Hammerstein模型进行直接辨识，抑制了尖峰噪声对辨识结果的影响，具有优良的稳健性。

关键词: 参数辨识, 主成分分析, 多变量Hammerstein模型, 偏最小一乘, 动态仿真, 尖峰噪声