基于最优结构多维泰勒网的含噪声非线性时变系统辨识

Identification of nonlinear time-varying system with noise based on multi-dimensional Taylor network with optimal structure

针对具有噪声干扰的非线性时变系统建模时存在的困难,建立了一种具有最优结构和最佳泛化能力的多维泰勒网模型,以实现对该系统的辨识.首先,为了能够快速反映系统输入/输出的变化,以多维泰勒网的连接权系数作为时变参数,并由带可变遗忘因子的递推最小二乘算法对其进行训练,进而讨论了辨识方案的稳定性.然后,为了避免维数灾难并满足实时性要求,给出了选择多维泰勒网有效回归项的改进权衰减法,以使多维泰勒网同时具有最小结构和最佳的泛化能力.最后,通过算例说明基于最优结构的多维泰勒网在含噪声非线性时变系统辨识问题中应用的方法,算例结果验证了该方法的有效性.

Aiming at the modeling difficulties of the nonlinear time-varying system with noise disturbance,a multi-dimensional Taylor network(MTN) model with optimal structure and optimum generalization ability is established to implement the identification of the system.Firstly,to rapidly reflect the input-output changes of the system,the link weight coefficients of MTN are taken as the time-varying parameters,and then the recursive least-squares algorithm with a variable forgetting factor is adopted to train the system and the stability of the identification scheme is addressed.Secondly,to avoid the dimension curse and meet the real-time requirements,an improved pruning algorithm is developed to choose the effective regression items of MTN,which provides the network with the simplest structure and optimum generalization ability.Finally,an example is given to illustrate the application of the MTN with minimum structure in the identification of a nonlinear time-varying system with noise disturbance,and the experimental results demonstrate the effectiveness of the proposed method.