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.