模态参数不确定性分析的贝叶斯方法研究

在结构损伤诊断和参数识别中,实测结构模态参数不可避免地存在误差。本文将模态参数视为随机变量,采用贝叶斯方法对模态参数的不确定性进行分析。分析中选用高斯联合概率密度函数作为先验密度函数,通过多次独立的模态参数测试,得到传递函数的条件概率密度函数和模态参数的后验估计表达式,再利用拉普拉斯渐近方法求解边缘概率密度函数,得到模态参数的最大后验估计。在钢筋混凝土框架结构的模态试验中,利用本文方法给出了结构模态参数的估计值,结果表明,本文方法具有良好的收敛性。

A study on the uncertainty of model parameters by Bayesian method

In structural damage diagnosis and parameters identification,errors are inevitably intermixed in the measured model parameters of a structure.In this paper the model parameters are considered as the random variables,and the uncertainty of model parameters are analyzed by the Bayesian method.The Gaussian joint probability density function(PDF) is selected as a prior PDF in the analysis.By several independent measurements on the transfer function of a structure,the conditional PDF of the transfer function and then the formula of the posterior PDF of model parameters can be obtained.The integral of the margin PDF is approximated by using Laplace's method for asymptotic approximation,and the estimation of model parameters with maximal posterior probability can be found.In an experimental model analysis of a reinforced concrete frame structure,the estimation of model parameters is computed with this method and good convergence is shown by the results.