前后向时间序列模型联合估计的时变结构模态参数辨识

为提高时变结构模态参数辨识精度和抗噪声能力，提出一种前后向泛函向量时变自回归滑动平均（FS-VTARMA）时间序列模型联合估计的模态参数辨识方法。首先建立前后向FS-VTARMA模型联合估计的均方误差形式的费用函数，其次引入非平稳信号中前向模型和后向模型估计系数的近似共轭关系，再利用两步最小二乘法（2SLS）得到时变模型系数，最后把时变模型特征方程转换为广义特征值问题提取出模态参数。利用时变刚度系统非平稳振动信号验证该方法，结果表明：能有效地克服前向模型估计中模态参数一步延迟以及起始时刻无法准确获得，以及后向模型估计中模态参数一步超前以及终止时刻无法准确获得的缺点，具有更高的模态参数辨识精度和更强的抗噪声能力。

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, this paper presents an identification approach using a forward-backward functional series vector time-dependent ARMA time series model (FS-VTARMA) based on joint estimation. Firstly, a cost function in the form of mean square error for joint forward-backward estimation of FS-VTARMA model is established. Secondly, the estimated parameters are approximately complex conjugate between forward and backward model for non-stationary signal. Once more, the time-varying model coefficients are obtained using two stages least square (2SLS) method. Finally, modal parameters are extracted from a generalized eigenvalue problem, which is transformed from an eigenvalue equation of the time-varying model. The identification approach is validated by non-stationary vibration signals of a system with time-varying stiffness. The results indicate that the proposed method not only can overcome the shortages of one-step delay and initial prediction error in forward model estimated parameter, but also one-step lead and terminal prediction error in backward model estimated parameters, and has higher modal parameter identification precision and better anti-noise performance.