基于动力响应主分量瞬时频率和幅值的非线性模型修正

Nonlinear model updating based on instantaneous frequencies and amplitudes of principal dynamic response components

提出了一种基于动力响应主分量的瞬时频率和幅值的非线性模型修正方法。首先通过解析模式分解和希尔伯特变换提取结构动力响应主分量的瞬时频率和瞬时幅值;然后选取瞬时幅值和瞬时频率慢变部分的有限多个时间点值来反映结构的非线性特性;最后采用响应面模型,并基于试验数据和有限元模型数据之间瞬时幅值和频率的残差建立目标函数,进行结构的非线性模型修正。通过三层框架的数值模拟分析,其结果表明该方法能精确有效地修正非线性结构模型。

In this paper, a new method based on instantaneous frequencies and amplitudes of principal dynamic response compo- nents is proposed for nonlinear model updating. The instantaneous frequencies and amplitudes of principal dynamic response components are firstly extracted by analytical mode decomposition with Hilbert transformation. Then, limited point-values of the extracted instantaneous frequencies and amplitudes are applied to reflect the nonlinear characteristics of structure. Finally, the response surface method is introduced with an objective function based on the residuals of instantaneous frequencies and am- plitudes between experimental structure and finite element model, so as to update the nonlinear structure model. A three-story building is simulated as an example for nonlinear model updating, The results show that the proposed method can effectively update the nonlinear structure model with high accuracy.