同元次分数阶模型的一种具有稳定约束的频域辨识算法  

Identifying a Commensurate Fractional Order Model from Frequency Domain Data with Stable Constraints

作　　者：苏密勇[1] 谭永红[2] 王子民[3] 秦建华[4] 

机构地区：[1]西安电子科技大学电子工程学院,陕西西安710071 [2]上海师范大学信息与机电工程学院,上海201418 [3]桂林电子科技大学电子工程与自动化学院,广西桂林541004 [4]北京邮电大学电子工程学院,北京100876

出　　处：《四川大学学报（工程科学版）》2012年第2期130-134,共5页Journal of Sichuan University (Engineering Science Edition)

基　　金：国家自然科学基金资助项目(60971004)

摘　　要：为了进一步提高同元次分数阶模型的辨识精度与可靠性,提出一种具有稳定约束的可分离非线性最小二乘法(SC-SNLS)来优化频域均方误差指标函数。模型中线性参数与非线性参数分别用最小二乘法与Levenberg-Marquardt(LM)法来交替迭代估计。通过对线性参数估计值的扰动分析,揭示了优化算法的4种不稳定因素,并在迭代中加以约束与处理,从而增强优化算法的稳定性与收敛性。仿真结果表明,该辨识算法性能优于相关的算法,具有更高的辨识精度与收敛速度。In order to improve the identification accuracy and reliability of Commensurate Fractional Order Model（CFOM）,a Separable Nonlinear Least Squares algorithm with Stable Constraints（SC-SNLS） was presented to optimize the mean square error evaluation criterion.Considering that the CFOM is linear in its numerator polynomial coefficients and are nonlinear in its common fractional derivative order and the denominator polynomial coefficients,the LS and LM algorithms were alternately and iteratively used to estimate the linear and non-linear parameters,respectively.Four unstable factors were revealed in the estimation procedure through perturbation analysis of the estimation of linear parameter.Then the stability and convergence of optimization procedure were improved through tackle the unstable factors.Simulation results showed that the proposed algorithm has a fast convergence speed and provides more accurate estimation compared to relative approaches.

关 键 词：分数阶模型 频域辨识 可分离非线性最小二乘法 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]