| 引用本文: | 景绍学,李正明.Wiener系统的变聚点样条逼近递推贝叶斯算法[J].控制理论与应用,2017,34(1):13~21.[点击复制] |
| JING Shao-xue,LI Zheng-ming.Variable knots spline approximation recursive Bayesian algorithm for identification ofWiener systems[J].Control Theory and Technology,2017,34(1):13~21.[点击复制] |
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| Wiener系统的变聚点样条逼近递推贝叶斯算法 |
| Variable knots spline approximation recursive Bayesian algorithm for identification ofWiener systems |
| 摘要点击 2904 全文点击 2232 投稿时间：2016-03-23 修订日期：2016-07-23 |
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| DOI编号 10.7641/CTA.2017.60158 |
| 2017,34(1):13-21 |
| 中文关键词 参数估计 Wiener系统 过程噪声 三样条函数 递推贝叶斯算法 可变聚点 |
| 英文关键词 parameter estimation Wiener system process noise cubic spline function recursive Bayesian algorithm variable knots |
| 基金项目 国家自然科学基金项目(51477070), 江苏大学研究生科研创新项目(KYXX 0003)资助. |
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| 中文摘要 |
| 为了辨识过程噪声干扰的Wiener非线性系统, 提出了一种基于三样条函数逼近的递推贝叶斯算法. 众所周
知, 传统的多项式逼近具有不能外推、高阶易震荡等缺点. 为了克服这些缺点, 首先利用三样条函数对Wiener系统
的非线性反函数进行逼近, 在此基础上将待辨识系统参数化为伪线性回归系统. 然后把估计到的噪声方差融入算
法, 接着使用递推贝叶斯算法对参数进行了估计. 为了提高三样条函数对非线性反函数的逼近能力, 一种基于均值
的变聚点选择方法被应用于算法. 文中还对算法的收敛性进行了分析, 并用数值仿真和案例建模验证了算法的有
效性. |
| 英文摘要 |
| To estimate the Wiener nonlinear systems with process noise, a recursive Bayesian algorithm based on cubic
spline approximation is proposed. It’s well known that the polynomial approximation does not extrapolate well and
high degree polynomials have oscillatory behavior, etc. To overcome these drawbacks, a cubic spline function is used to
approximate the inverse function of the output nonlinearity. And then the original Wiener system is parameterized to be a
pseudo-linear regression model. The estimated variance of the noise is also integrated in the algorithm to estimate the parameters.
In order to approximate the inverse nonlinearity, a mean-value based variable knot-selection method is employed.
After the convergence is analyzed, a numerical simulation and a case study validate the algorithm. |