基于频域极大似然估计ARMA模型的运行模态辨识方法

Operational Modal Identification Method Based on Frequency-domain Maximum Likelihood Estimates of ARMA Models

摘要:

为提升运行模态参数识别精度,本文建立多变量ARMA模型的频域极大似然识别方法,以实现ARMA模型参数最优估计;基于所估计模型的AR部分,完成了模态参数识别。考虑到测量噪声对模态识别的影响,通过特征值分解与灵敏度分析,构造多变量ARMA模型参数估计的不确定性边界,从而实现了模态参数识别中不确定性的传递与量化。数值算例结果表明,所提方法能够精准提取模态参数并给出估计的置信区间,且识别精度显著优于基于多变量AR模型和辅助变量法的运行模态分析结果。

Abstract:

Aiming to enhance the identification accuracy and stability of structural operational modal parameters under actual working conditions, a frequency-domain maximum likelihood identification method for multivariate ARMA models was established, which enabled the optimal and high-precision estimation of ARMA model key parameters. Based on the accurately estimated model, operational modal parameter identification was further completed by analyzing and applying the AR component of the multivariate ARMA model. In practical modal identification tests, measurement noise from sensors and data acquisition processes inevitably interfered with identification results and reduced the reliability of modal parameters. Considering the adverse impact of measurement noise on operational modal identification, it constructed uncertainty bounds for the parameter estimates of multivariate ARMA models through eigenvalue decomposition and parameter sensitivity analysis, which effectively realized the propagation and quantitative evaluation of uncertainty in the entire modal parameter identification process. Numerical example results verified that the proposed method can accurately extract structural modal parameters and provide reliable estimation confidence intervals for identification results. Moreover, compared with the traditional operational modal analysis methods, including multivariate AR models and the instrumental variable method, the proposed approach delivered remarkably higher identification accuracy and better anti-noise performance.