基于EM算法的运行模态参数识别

Operational Modal Parameter Identification Using the Expectation Maximization Algorithm

摘要:

结合随机状态空间方程和极大似然法的期望最大EM算法进行了结构运行模态分析。EM算法以迭代的方式更新模型参数，进而得到状态空间方程的极大似然估计。模态参数通过状态空间模型参数求得。应用了平方根卡尔曼滤波方程提高EM迭代过程的计算稳健性。考虑到状态空间方程中激励噪声和测量噪声的相关性，建立了更完善的参数化状态空间方程。通过数值模拟对比分析，结果表明：考虑噪声相关性的EM算法比假设噪声不相关的EM算法具有更高的识别精度，EM算法在采样数据较少的情况下比随机子空间方法更有优势。

Abstract:

Using the stochastic state-space model and expectation maximization (EM) algorithm, operational modal analysis for civil structures is performed in this paper. The EM algorithm is a process to obtain the maximum likelihood estimate of the model by updating the model parameters iteratively. The modal parameters could be obtained from the identified parameters of the state-space model. In this study, the square-root version of the Kalman filtering method is applied to improve the computational robustness of the EM algorithm. Considering the correlation between input and measurement noises in the state-space model, an extended parameterization for the state-space model is established. The performances of the stochastic subspace identification (SSI) method, the EM algorithm without considering the noise correlation, and the proposed EM algorithm considering the noise correlation, are comparatively studied, and the results show that the EM algorithm considering the noise correlation is more accurate than that without considering the correlation. In addition, the proposed EM algorithm performs better than the SSI method in the case of short-length data.