模态识别的Bayesian TDD-FFT法及其应用

Bayesian TDD-FFT method for modal identification and its application

针对Bayesian FFT(Fast Fourier Transform)在多自由度下的病态Hessian矩阵求逆和模态参数不确定性评估问题,提出了Bayesian TDD-FFT模态方法。提出Bayesian TDD(Time Domain Decomposition)方法,将多测点多自由度信号转变为单测点单自由度信号;结合Bayesian FFT和蒙特卡罗方法获取模态参数的最佳估计和后验概率分布,进行不确定性分析,并通过数值模拟验证了Bayesian TDD-FFT法的有效性;基于上海中心大厦实测数据,通过对比分析指出Bayesian TDD-FFT法能够获得Fast Bayesian FFT法的结果精度,同时发现频率和阻尼没有相关性,而激励谱密度和预测误差谱密度存在明显的相关性。

Here, aiming at problems of ill Hessian matrix inversion under multi-DOF conditions using Bayesian FFT method and uncertainty evaluation of modal parameters, Bayesian TDD-FFT(time domain decomposition-fast Fourier transform) modal identification method was proposed. Firstly, Bayesian TDD method was used to convert a multi-DOF signal into SDOF(single degree of freedom) signals. Then, Bayesian FFT method combined with Monte-Carlo one was used to acquire the optimal estimation and posterior probability distribution of modal parameters, and do uncertainty analysis. The effectiveness of Bayesian TDD-FFT method was verified with numerical simulation. Finally, the contrastive analysis was performed for the actual measured data at Shanghai center tower. The results showed that the proposed Bayesian TDD-FTT method can be used to acquire the same result accuracy as that of the fast Bayesian FFT one;there is no correlation between frequency and damping, while there is an obvious correlation between excitation spectral density and prediction error one.