频域响应函数估计的非参数辨识法

针对振动工程领域中频响函数的辨识估计，本文深入研究频响函数估计的非参数辨识法。在离散傅里叶变换中，考虑初始和终端状态带来的暂态泄露项和观测噪声谱项对频响函数估计的影响。为得到准确的频响函数估计值，联合频响函数、初始-终端状态和脉冲响应系数待辨识参数矢量，将频响函数估计问题转化为一个线性最小二乘优化问题。针对此线性最小二乘优化问题的特殊形式，提出一种可分离的求解过程。最后用仿真算例验证本文辨识方法的有效性。

A nonparametric identification method to frequency response funtion estimation

In this paper, we discuss the problem of studying a nonparametric identification method to frequency response function estimation, which can be applied to vibration engineer field. In the discrete fourier transform, we consider the effect from the initial - final conditions and observed noise spectrum on the frequency response function estimation. To obtain the more accurate frequency response function estimation value, we combine the frequency response function, the initial - final conditions and impulse response parameters as a identified parameter vector, so as to convert the former problem of frequency response function estimation to a linear least square optimum problem. Then a new separable algorithm is proposed to solve this linear least square optimum problem. Finally the simulation example results confirm the identification theoretical results.