基于小波和非线性含输入自回归模型的系统辨识算法

System Identification Based on Wavelet and Nonlinear Autoregressive with Exogenous Inputs Model

提出了一种结合小波理论和非线性含输入自回归(NARX)模型的系统辨识新算法.该算法利用小波函数有效的逼近能力避免了应用NARX模型系统辨识时确定模型结构的复杂过程,消除了通常小波网络辨识算法由于输入变量之间可能存在巨大差别而引入的严重失真,构成了一个通用、有效、不依赖于系统先验信息的非线性辨识框架.两则数据仿真表明,对于高度非线性系统,该算法可使系统估计的均方误差减少60%以上.

A new approach to system identification was proposed, which combined wavelet theory and nonlinear autoregressive with exogenous (NARX) model properly. The approach utilized the efficient approximation power of wavelet functions to remove the complicated processes of model structure determination using NARX model in system identification. It avoided potential serious distortion caused by great difference among the input variables in the universal identification algorithm based on wavelet networks and could achieve a more accurate estimation of system. It constructed a universal and efficient framework of nonlinear identification without depending on a priori information. For serious nonlinear systems, two simulation examples show that the mean of square errors of output estimation caused by the universal wavelet network algorithms can be reduced more than 60% by the proposed approach.