利用NARMA模型辨识非线性时变结构系统

为了有效地进行非线性时变结构系统的辨识,提出了一种基于Kalman滤波算法的利用时变非线性自回归滑动平均模型的用于非线性时变结构系统辨识的新方法.首先,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.建立系统参数的随机游动模型,引入Kalman滤波算法估计系统的参数,实现对非线性时变结构系统的辨识.最后对一个具有非线性时变刚度的三自由度结构系统进行了仿真,结果表明:该方法可以有效地跟踪非线性时变结构系统的参数变化.遗忘因子的对比试验表明只有选择合适的遗忘因子才能得到合理的结果.

Identifying nonlinear time-varying structural system based on NARMA model

To effectively identify the nonlinear time-varying structural system, a novel method used for nonlinear time-varying structural system identification is proposed based on NARMA (Nonlinear Auto-Regressive Moving Average) model using Kalman filter. At first, the nonlinear time-invariant structural dynamical model was transformed into a NARMA model using linear transformation. Then the nonlinear term was expanded to a polynomial of input and output data. According to the hypothesis of short time invariance, the time-variant parameters of system were tracked by changing parameters of the model, and then the nonlinear time-varying system identification was transformed into linear time-varying parameter estimation. Establishing a random walk process of model parameters and introducing the Kalman filter to estimate system parameters, realized the identification of time-varying nonlinear system. At last, the method was validated by a simulation of a three degrees of freedom structural system with nonlinear time-varying stiffness. It is important for the selection of forgetting factor to obtain a better result by the comparison of identification results using different forgetting factors.