一种AR模型的稀疏模态参数估计方法
A Sparse Modal Parameter Estimation Method Based on AR Model

基于自回归模型（autoregressive，AR）的模态参数估计方法需要进行阶次估计，阶次确定错误会使结果中包含虚假模态或者遗漏模态。针对这种情形，通过将模态选择的问题转化为带有稀疏约束的振型系数问题，提出了一种基于AR模型的稀疏模态参数估计方法。先假设一个较大的系统阶次，采用基于AR模型的估计方法计算模态参数，然后构造振型系数的稀疏优化模型，多次稀疏求解后用统计和聚类的方法对结果进行校正，最后根据振型系数鉴定对应模态的真假。这种无需提前确定阶次的估计方法既避免了定阶次引起的误差，又能有效地将噪声模态分离，适合复杂环境下的参数估计。在斜拉索桥模型上验证结果表明，该方法具有良好的识别效果。
The modal parameter estimation method based on the autoregressive (AR) modal may produce inaccurate modal parameters as well as a fake modal or miss some modals because of wrong orders. To solve this problem, this paper comes up with a new method by solving the coefficients of vibration mode with a sparse constraint so as to produce accurate modal parameters. It first uses the AR model to arrive at the modal parameters by assuming a larger order for the vibration mode and then constructs the sparse optimization model for the coefficient of vibration mode. After that, the statistical results obtained with the multiple solutions for the sparse optimization model are used to adjust the final results. Finally, the paper identifies modal parameters according to the coefficient of vibration mode. This method not only avoids the errors caused by assuming the large order but also enhances noise resistance. The test results on the cable demonstrate the stability and accuracy of this method