基于解析模式分解的密集工作模态参数识别

长大跨度的桥梁结构或者高层建筑的工作环境振动响应中经常包含密集的模态成分，并会出现模态叠混现象，而传统的信号分析方法往往难以识别结构的密集模态参数。提出一种基于解析模式分解理论与随机减量技术相结合的方法识别环境激励下的结构密集模态参数。对于工作环境激励下的结构振动响应，通过随机减量技术可以提取结构的自由振动响应，利用解析模式分解方法对具有密集模态的自由振动响应进行有效的分解，对每一阶自由振动响应利用最小二乘拟合方法识别出频率与阻尼比。通过两层框架的数值模拟以及对密集频率的密集程度指数和信号时程长度等参数分析，其结果表明通过随机减量技术提取的自由振动响应可以有效的减少模态叠混的影响，虽然提取的自由振动响应的时程长度比实际的信号时程要短，然而解析模式分解仍然能够十分有效的对短时程具有密集模态成分的信号进行有效的分解。最后，通过对一具有密集模态的36层框架的数值模拟，以及对一具有密集模态的3层框架的振动台实验，验证该方法可以有效的识别出环境激励下的结构密集模态参数。

Parameter Identification of Closely Spaced Structural Modals Based on Analytical Mode Decomposition

There exist closely spaced modes in dynamic responses of long- span bridges and high- rise buildings. However, up to present, it is still difficult to identify structural modal parameters of these structures with closely spaced modes using traditional signal analysis method. In this paper, a method combining the random decrement technique （RDT） with the analytical mode decomposition method was proposed for parameter identification of the closely spaced modals under operational vibration condition. In this method, the random decrement technique was used to extract the free vibration information from the measured response, while the analytical mode decomposition was developed with Hilbert transform to decompose the extracted free vibration. The frequency and damping ratio of the free vibration response of each order were evaluated using linear fitting technique. A 2-story building was simulated as an example for parametric study. The results show that the modal mixing problem can be eliminated by extracting the free vibration with short time duration using random decrement technique. With enhanced analytical mode decomposition method, each short-time-duration modal response can be separated and used for modal parameter identification. Finally, the new method was applied to the simulation of a 36-story building with closely spaced modes, and validated by shake table testing of a 3-story building frame installed with a tunable mass damper. Both simulations and experiments showed high accuracy and effectiveness of the new method for identification of the modal parameters of building systems.