环境激励下脉冲响应函数与相关函数的关系

单位脉冲响应函数中包含了系统所有的动力特性参数,提取系统的单位脉冲函数或频率响应函数是获取系统动态特性参数、进行系统辨识以及对系统进行健康监测与精确控制的前提。在受环境激励的系统中,由于激励无法直接测量,导致单位脉冲响应函数无法直接获取。在自然激励技术(natural excitation technique)的基础上,基于复模态系统的多输入多输出位移响应,讨论了环境激励下系统单位脉冲响应函数与响应的相关函数之间的关系。基于实模态系统并将质量矩阵进一步假设为对角矩阵,辨识出系统所受环境激励的强度分布。根据辨识的模态参数以及环境激励的强度,由响应的相关函数重构了系统的单位脉冲响应函数。最后通过仿真进一步验证了文中的结论。

Discussion on the Relation between Correlation Functions and Impulse Response Functions under Ambient Excitation

The impulse response functions (IRFs) contain all the dynamic characteristics of a structure. The extraction of IRFs or frequency response functions (FRF) is the premise of obtaining the dynamic characteristics of the structure, the structure identification, the health monitoring, and the precise control of the structure. However, in some real in-operation working conditions, the excitations cannot be measured. Thus the IRFs cannot be acquired directly. In this paper, the relation between the correlation functions and IRFs is meticulously deduced through natural excitation technique (NExT). Furthermore, considering that the structure is a real-modal system, the intensity of each excitation is identified when the structure is discrete and the mass matrix is diagonal. Using the identified mode parameters and the intensity of the excitations, the IRFs of the structure are reconstructed by correlation functions. A simulation is employed to validate the reliability of the relation derived between the correlation functions and the IRFs.