Modal parameter identification of time-varying structures using a forward-backward time series model based on joint estimation

To improve modal parameter identification precision and anti-noise performance for time-varying structures an identification approach using a forward-backward functional series vector time-dependent ARMA time series model (FS-VTARMA) based on joint estimation was presented. Firstly, a cost function in the form of mean square error for joint forward-backward estimation of FS-VTARMA model was established. Secondly, the estimated parameters of forward and backward models for a non-stationary signal were approximately complex conjugate. Then, the time-varying model coefficients were obtained using the two-stage least square (2SLS) method. Finally, its modal parameters were extracted from a generalized eigenvalue problem transformed from an eigenvalue equation of the time-varying model. The identification approach was validated with non-stationary vibration signals of a system with time-varying stiffness. The results indicated that the proposed method can not only overcome shortages of one-step delay and initial prediction error in the forward model's modal parameter estimation, but also overcome shortages of one-step step lead and terminal prediction error in the backward model's modal parameter estimation, it has higher modal parameter identification precision and better anti-noise performance.