基于结构自适应滤波方法的非线性系统辨识

针对非线性系统辨识中定结构参数辨识局限性高和辨识率低的问题，将结构自适应引入辨识的优化，提出一种基于子系统的结构自适应滤波（SSAF）方法。该方法的模型由若干子系统级联而成，每一个子系统均为线性-非线性混合结构。子系统的线性部分是一个一阶或二阶可选的无限脉冲响应滤波器（IIR），非线性部分则是一个静态的非线性函数。初始化中，子系统的参数随机产生，生成的若干子系统按照设定的连接规则进行随机连接，而不含反馈的连接机制确保了非线性系统的有效性。采用一种自适应多精英引导的复合差分进化（AMECoDEs）算法用于自适应模型循环优化，直至找到最优的结构和参数，即全局最优。实验结果表明，SSAF方法在非线性测试函数以及真实数据集上的表现优异，辨识率高且收敛性好，与聚焦时滞递归神经网络（FTLRNN）相比，它所用参数的个数仅为FTLRNN的1/10，且适应值精度提高了7%，验证了所提方法的有效性。

Nonlinear systems identification based on structural adaptive filtering method

In order to solve the problems of high identification limitation and low identification rate in nonlinear system identification with fixed structure and parameters, a Subsystem-based Structural Adaptive Filtering (SSAF) method for nonlinear system identification was proposed with introducing structural adaptation into the optimization of identification. Multiple subsystems with linear-nonlinear hybrid structure were cascaded to form the model for this method. The linear part is a 1-order or 2-order Infinite Impulse Response (IIR) digital filter with uncertain parameters, and the nonlinear part is a static nonlinear function. In the initial stage, the parameters of the subsystems were randomly generated, and the generated subsystems were connected randomly according to the set connection rules, and the effectiveness of the nonlinear system was guaranteed by the connection mechanism with no feedback branches. An Adaptive Multiple-Elites-guided Composite Differential Evolution with a shift mechanism(AMECoDEs) algorithm was used for loop optimization of the adaptive model until the optimal structure and parameters were found, that is, the global optimal. The simulation results show that AMECoDEs performs well on nonlinear test functions and real data sets with high identification rate and good convergence rate. Compared with the Focused Time Lagged Recurrent Neural Network (FTLRNN), the number of parameters used in SSAF is reduced to 1/10, and the accuracy of fitness is improved by 7%, which proves the effectiveness of the proposed method.