基于DLM的桥梁结构承载力的贝叶斯预测

Bayesian prediction of structural bearing capacity of aging bridges based on dynamic linear model

为结合检测信息和承载力的先验模型来对桥梁结构性能进行预测,认为结构性能随时间变化的动态测量为一个时间序列,然后引入了动态线性模型(DLM)对结构性能进行预测.考虑到桥梁结构性能的时变特性,运用贝叶斯动态模型建立了退化抗力的状态方程和观测方程,并通过贝叶斯因子来对检测信息进行监控,然后结合参数的先验信息,对退化抗力的状态参数进行贝叶斯后验概率推断,建立了一个动态线性模型来对结构抗力短期的变化趋势进行预测.为了结构性能线性模型的贝叶斯动态修正,确定了一步向前预测分布和滤波分布.基于检测信息,考虑到变量估计主观认识的不确定性,引入折扣因子来确定状态误差方差矩阵.最后,通过算例论证了本文方法的适用性.

To predict the bridge structure performance based on inspection information and the priori model of bearing capacity,the dynamic measure of structural performance over time is treated as a time series,a Bayesian dynamic linear model（DLM） is then introduced.Considering the time-dependent characteristics of structural performance of the considered bridge,this paper proposes the probability method of bridge resistance degradation predication.State equation and observation equation of resistance degradation are established with Bayesian dynamic linear model.Combining parameters＇ prior information with the early resistance observation data containing noise,the resistance degradation state parameters are deduced with Bayesian Posterior Probability.A dynamic linear model is built to forecast the short-term trend of structural resistance.The one-step-ahead forecast distribution and the filtering distribution are determined for Bayesian dynamic updating.To allow for the epistemic uncertainty in variance estimation based on inspection information,a discount factor approach is made for specification of unknown variance matrix.Finally,a RC girder is taken as an illustration example to demonstrate the applicability of the proposed method.