基于偏差补偿递推最小二乘的Hammerstein-Wiener模型辨识

Identification of Hammerstein-Wiener Models Based on Bias Compensation Recursive Least Squares

许多实际系统可以表示成一种中间为线性动态环节、输入输出端为非线性静态环节的Hammerstein-Wiener模型.针对含过程噪声的Hammerstein-Wiener模型,提出一种改进在线两阶段辨识方法.第一步采用偏差补偿递推最小二乘法在线辨识含原系统参数乘积项的参数向量.通过在递推最小二乘算法中引入一个修正项,补偿过程噪声引起的估计偏差.第二步采用基于张量积逼近的奇异值分解法分离出原系统各参数的值.通过引入两个矩阵的张量积逼近加权最小二乘的权系数,提高参数分离精度.理论分析和计算机仿真验证了本文方法的有效性.

Many actual systems can be represented by the Hammerstein-Wiener model, where a linear dynamic system is surrounded by two static nonlinearities at its input and output. An improved on-line two stage identification algorithm is proposed to identify the Hammerstein-Wiener model with process noise. Firstly, the bias compensation recursive least squares is adopted to identify the parameter vector containing the product of the original system parameters. The estimation bias is compensated by introducing a correction term in the recursive least squares estimate. Secondly, the singular value decomposition method based on the tensor product approach is adopted to separate each parameter value from the original system. The accuracy of parameter separation is improved by introducing the tensor product of two matrixes to approach the weight coefficient of the weighted least squares. Theoretical analysis and computer simulation validate the effectiveness of the proposed algorithm.