环境激励下基于相关函数的脉冲响应函数重构

在白噪声激励下,结构响应的相关函数作为脉冲响应函数的近似可以进行模态参数辨识,但其物理意义始终缺乏明确解释;相比于脉冲响应函数,基于相关函数的辨识缺少了模态参与因子或者说质量信息,这也是工况模态分析(OMA)方法的主要缺陷。简要回顾了复模态下的自然激励技术原理,证明了白噪声激励下位移响应的相关函数等价于系统在特定初始条件下的自由响应,给出相应初始条件的计算方法;进一步提出了一种系统质量分布的辨识方法,并藉此重构得到系统脉冲响应函数。讨论了相关函数误差与信号时长及激励带宽之间的关系。通过仿真和试验验证了所得结论。

Reconstruction of impulse response function based on correlation function under ambient excitation

The correlation functions (CFs) are treated as substitution of the impulse response functions (IRFs) for modal parameters identification under white noise excitation.However, a clear explanation of CFs is still absent.As is known, all the dynamic characteristics can be described with IRFs, however, the modal participation factors, or the mass information, cannot be identified using CFs, which is the main defect of operational modal analysis (OMA) as well.Under the complex mode assumption, the natural excitation technique (NExT) was reviewed.Then, the equivalence between CFs of displacements subjected to white noise excitation and the free responses under certain initial condition was derived.In addition, the initial condition for the free responses was provided.Furthermore, a mass distribution identification method was proposed and IRFs were reconstructed.The influence of time length and excitation bandwidth on the CF errors was discussed.Finally, a numerical simulation example and an experiment was designed to illustrate the effectiveness of the proposed method.