基于贝叶斯方法的模态参数识别的不确定度分析

振动模态分析和模态参数识别是动态测试的一个重要研究方向。模态参数在模型的修正、响应的预测、系统的健康检测及控制等方面有着重要的作用。但动态测试的不确定度分析,尤其是模态参数的不确定度的研究还十分缺乏。本文主要基于贝叶斯方法,通过傅立叶变换(FFT)建立时域数据和频域数据之间的对应关系。根据共振频带内的多个模态的响应数据得到相对应的模态参数,优化得到模态参数的最佳估计值,评定模态参数识别的不确定度。在固支梁的模态实验中,加速度传感器采集环境激励中的振动数据,运用贝叶斯法进行处理得到模态参数的最佳估计值。在此基础上,通过模态参数的最佳估计值,以及仪器的检定报告数据,结合合成不确度分析方法,系统分析了模态参数识别的不确定度。

Analysis of Uncertainty of Modal Parameters Identification based on Bayesian Method

Vibration modal analysis and modal parameters identification are important for dynamic testing. Modal parameters are essential for the model updating, response forecasting, system health monitoring and vibration control. However, the uncertainty analysis of dynamic testing, especially for modal parameters, is inadequate. In this paper, the corresponding relationship between time domain data and frequency domain data is established by using fast Fourier transform (FFT) based on Bayesian method. According to the response data of multiple modes in the resonance frequency band, the most probable value and the uncertainty of modal parameters identification are obtained. In the modal experiment of solid supported beam, the acceleration transducers were used to collect vibration data of system under ambient excitation. The modal identification and the most probable value of modal parameters were obtained by Bayesian method. The total uncertainty and uncertainty component of modal parameters identification were analyzed systematically by using the most probable value and instrument calibration report.