基于Hankel矩阵联合近似对角化的结构模态识别
Modal Analysis of Structures Based on Hankel Matrix Joint Approximate Diagonalization Method

针对基于二阶盲辨识（second order blind identification，简称SOBI）的模态参数识别方法存在的不足，提出了一种基于Hankel矩阵联合近似对角化（Hankel matrix joint approximate diagonalization，简称HJAD）技术的结构运行模态分析（operational modal analysis，简称OMA）的新方法。该方法通过对随机子空间类模态识别方法常用的Hankel矩阵进行联合近似对角化，以分离各阶模态响应，进行模态识别。与基于SOBI的模态识别方法相比，在具体实施过程中，仅需要在分析数据中添加与实测振动响应对应的时间延迟的数据，实现难度较小。数值算例和物理模型试验的分析结果表明，所提出的基于HJAD技术的结构运行模态分析方法，不仅具有鲁棒性强和计算效率高的优点，还可以克服传统的基于SOBI的模态识别方法的模态识别能力受测点数目限制的问题。
To overcome some limitations of the modal identification method based on the second-order blind identification (SOBI) algorithm, a new modal parameter identification method based on the Hankel matrix joint approximate diagonalization (HJAD) technique was proposed. In this method, the Hankel matrix, which is commonly used by the stochastic subspace identification method, was diagonalized using the joint approximate diagonalization technique in order to separate modal responses and identify modal parameters. Compared with the SOBI-based modal parameter identification method, the proposed method was easy to implement when only additional time-lagged response data was needed. The numerical and experimental analysis results show that the proposed modal parameter identification method overcame the limitation of not being able to estimate more active modes than the number of available sensors.