摘要
对于线性系统中频响函数的估计问题,文章提出一种新的非参数辨识法-局部多项式法.与其它基于加窗策略的非参数辨识法相比较可知,在不使用周期输入激励信号下,局部多项式法在应用离散傅里叶变换时可有效地降低泄露误差的影响.将频响函数和泄露项围绕某中心频率处的窄窗展开成两个局部多项式模型,局部参数的估计可通过多个局部最小二乘问题来求解.当考虑相邻频率处多项式系数间的约束时,对局部多项式法做改进得到约束局部多项式法.改进后的约束局部多项式法通过多目标最小二乘准则来求解,并可降低频响函数估计的均方误差.最后用仿真算例验证文章辨识方法的有效性.
Here we propose a new nonparametric identification method which is called the local polynomial method to solve the problem of estimating the frequency response function in the linear system. Compared with other nonparametric identification methods based on the windowing strategies, this new identification method can be remarkably efficient in reducing the effect caused by the leakage error when the discrete Fourier transform is used under non period input excited signal. Considering the constraints between the coefficients of the polynomials at neighbor frequencies, we modify the proposed local polynomial method to get one constrained local polynomial method. The modified local polynomial method reduces the mean square error about the frequency response function and the estimation of the frequency response func- tion is identified by one multi-objective least squares criterion. Finally, the simulation example results confirm the identification theoretical results.
作者
王建宏
熊朝华
许莺
徐欣
WANG Jianhong XIONG Zhaohua XU Ying XU Xin(Science and Technology on Information Systems Engineering Laboratory, Nanjing 210007)
出处
《系统科学与数学》
CSCD
北大核心
2016年第11期1815-1824,共10页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(61402426)资助课题
关键词
频响函数
非参数辨识
局部多项式法
误差分析
Frequency response function, nonparametric identification, local poly-nomial methods, error analysis.
