环境激励下的Bayesian SFFT模态参数识别法及不确定性量化研究

Bayesian SFFT modal parametric identification method and uncertainty quantification under environmental excitation

针对传统Bayesian模态参数识别方法存在识别结果不确定性和量化指标单一的问题,提出了贝叶斯缩放快速傅里叶变换(Bayesian scaled fast Fourier transform,Bayesian SFFT)模态参数识别法,通过求解四维数值的优化,得到模态参数的最佳估值,并采用蒙特卡罗抽样的方法得到后验协方差矩阵和信息熵,实现对识别结果进行双重不确定性量化的目的。最后,通过数值模拟与工程应用验证了该方法的有效性,并研究了频带宽度系数k对识别结果的影响以及对比了变异系数与信息熵的量化效果。结果表明,将频带宽度系数k限制在7~9之间能够确保误差与不确定性的平衡;在阻尼比识别结果的量化中,信息熵的量化效果优于变异系数的量化效果。

Here,aiming at problems of uncertainty of identification results and single quantification index existing in traditional Bayesian modal parametric identification method,Bayesian scaled FFT(SFFT)modal parametric identification method was proposed.By solving a 4-dimensional numerical optimization problem,optimal estimations of modal parameters were obtained,and Monte Carlo sampling was used to obtain posterior covariance matrix and information entropy,and realize the purpose of dual-uncertainty quantification of identification results.Finally,the effectiveness of the proposed method was verified with numerical simulation and engineering applications,and effects of the bandwidth coefficient k on the recognition results were studied,and the quantification effects of variation coefficient and information entropy were compared.The results showed that limiting the bandwidth coefficient k within the range of 7~9 can ensure a balance between error and uncertainty;in quantification of damping ratio recognition results,the quantization effect of information entropy is better than that of variation coefficient.