基于贝叶斯DLM的桥梁结构可靠度预测

Reliability Prediction of Aging Bridges Based on Bayesian Dynamic Linear Model

桥梁结构的性能是时变的,可利用时间序列模型来描述,本文引入贝叶斯动态线性模型(DLM)。运用贝叶斯DLM建立桥梁结构退化抗力的观测方程和状态方程,通过贝叶斯因子对桥梁结构检测信息进行监控,通过检测信息和退化抗力状态参数的先验信息,对退化抗力的状态参数进行贝叶斯后验概率推断,通过不断的"概率预测-修正"递推运算,获得最优退化抗力的状态概率估计预测老化桥梁的退化抗力,建立一个DLM预测桥梁抗力的变化趋势。DLM以及DLM的概率递推过程类似于著名的卡尔曼滤波算法,可以实现桥梁退化抗力的贝叶斯动态预测(向前预测和向后预测),考虑到状态变量的不确定性,本文引入折扣因子确定状态误差方差。基于贝叶斯动态修正的抗力概率模型建立桥梁结构可靠度的预测公式。通过算例验证了本文所建模型的合理性。

The performance of bridge structures was time-dependent ,which was able to be depicted by time se-ries models . The Bayesian dynamic linear model（DLM ） was then introduced . The state equation and observa-tion equation of resistance degradation of the bridge structures were established by applying the Bayesian dy-namic linear model . The resistance degradation state parameters were deduced with the Bayesian posterior probability . Through continuous recursion operation of probability forecast-updating the optimal resistance degradation state probability was obtained to predict the bridge degradation resistance . The DLM was built to predict the changing tendency of bridge resistances . To allow for the epistemic uncertainty of state variants , the discount factor was used to specify the variance of state errors . The prediction formula of bridge reliability was built on the basis of the Bayesian DLM of bridge resistance probability . Finally numerical examples verify the applicability of the proposed model .