基于贝叶斯估计的结构固有频率不确定性分析

Uncertainty analysis of structural natural frequencies based on Bayesian estimation

在结构振动测试中,由于测试环境影响、试验设备、操作人员以及模态分析过程中的简化,试验获取的结构模态参数中包含了不确定因素。为了正确的估计结构物理参数的统计特性,在贝叶斯估计方法中选择共轭先验分布,结合试验数据导出后验分布,得到了结构固有频率均值及方差的估计值。对一个4层钢筋混凝土框架结构模型进行了振动测试。试验结果表明:在不能获得大量样本信息时,充分利用先验信息,结合现场测试数据,对频率参数进行估计,能够有效地减小均值与方差的可信区间长度,具有工程实用参考价值。

In modal experiment of a structure,because of environment effect,instrument equipment,error of operators,and simplification in modal analysis,some uncertainty factors were involved into the measured modal parameters.In order to evaluate the statistical characteristics of physical parameters correctly,it was necessary to take the uncertainty of modal parameters measured in testing into account.Based on Bayesian evaluatiom,here,a conjugate priori probability density function was seclected,the posterior probability density function was deduced combining with test data,then the mean and the variance of the structural natural frequencies were obtained.A modal experiment was conducted on a four-story reinforced concrete frame structure.The test results showed that when a large amount of samples is not available,the length of the confident interval for the mean and the variance are shortened effectively by taking full use of priori information and test data on line to evaluate the uncertainties of the natural frequencies,it is meaningful in practice.