基于Gibbs抽样的马尔科夫蒙特卡罗方法在结构物理参数识别及损伤定位中的研究

通过对结构动力特征方程进行的一系列变化,得到了线性结构识别模型,并由贝叶斯更新理论得到其后验分布形式.利用结构的模态参数,并考虑其随机性,应用基于Gibbs抽样的马尔科夫蒙特卡罗方法对线性结构识别模型中各参数的条件后验分布进行了抽样,成功地实现了结构物理参数识别及损伤定位.数值算例表明:Gibbs抽样结果可以以不同的方...

The identification of physical parameters and damage locations using the Gibbs sampling based on the Markov Chain Monte Carlo method

At first, the linear structural identification model is obtained based on a series of conversions of the dynamic characteristic equation, then the posterior distribution of the model is achieved by using the Bayesian updating theory. Utilize the structural modal parameters, and take their randomness into consideration, the samples of the parameters from the conditional posterior distribution of the linear structural identification model is achieved. During the process, the Gibbs sampling based on the Markov Chain Monte Carlo method is taken. The numerical examples show that the Gibbs sampling can not just identify the damage degree and locations in different ways with little error, but can make a probability measure of the identified values.