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.