Abstract: Using the timevarying NARMA (Nonlinear Auto Regressive Moving Average) model and the improved recursive least square algorithm, an identification method for nonlinear timevarying structure system is proposed. Firstly, the dynamic model of the timeindependent structure system is changed to an autoregressivemovingaverage model by means of linear transform method. Then the nonlinear function of this model is expanded to a polynomial about input and output using Taylor expansion, and the polynomial timevarying NARMA model, which is a linear combination of parameters, is obtained. Using the basic sequences to fit the timevarying parameters of the model, the nonlinear timevarying system is then transformed into a linear timeinvariant system, whose parameters can be estimated by improved recursive least square algorithm. Finally, the proposed method is validated by the simulation of a 3DOF structural system with nonlinear timevarying stiffness.

Key words: vibration and wave, nonlinear timevarying system, system identification, recursive least square, NARMA

摘要： 基于时变非线性自回归滑动平均模型利用改进的递推最小二乘算法提出一种用于非线性时变结构系统辨识的方法。利用线性变换将非线性时不变结构系统的动力学模型转化为非线性自回归滑动平均模型，然后将非线性项展开为系统输出数据的多项式的形式。利用短时时不变假设，通过改变模型的参数跟踪系统参数的变化，将非线性时变系统的辨识问题转化为线性时变系统的辨识问题，再利用改进的递推最小二乘算法实现对非线性时变结构系统的辨识。最后通过一个具有非线性时变刚度的三自由度结构系统的仿真算例表明,该方法可以有效地辨识非线性时变结构系统。

关键词: 振动与波, 非线性时变系统, 系统辨识, 递推最小二乘, 自回归滑动平均