基于贝叶斯的钢筋混凝土梁模型修正方法

Finite Element Model Updating of Reinforced Concrete Beam Based on Bayesian Method

本文提出了一个基于贝叶斯原理的钢筋混凝土梁有限元模型修正方法。针对钢筋混凝土梁模型修正中的方程病态问题及模态测试中测点信息不完整和模态信息不完备的实际情况,建立了适用于有限测点的目标函数和似然函数,且在目标函数中同时考虑了频率和振型信息。采用延迟拒绝自适应算法(DRAM)对待修正参数的后验概率进行了计算。数值算例表明本方法在仅使用低阶测量模态信息和不完整振型信息的情况下,仍能准确修正结构参数;实验算例表明,修正后的钢筋混凝土梁有限元模型的动力特性和测量结果一致,修正后的模型参数值和梁的轻微裂缝的位置及大小基本对应,说明了本文方法的有效性。

This paper proposes a finite element model updating method for reinforced concrete beams based on Bayesian.Aiming at the ill-conditioned problem of the reinforced concrete beam model and the incompleteness of the measured point information and the incomplete modal information in the modal test,the objective function and likelihood function for the finite measuring point are established.And the frequency and mode shapes information are considered simultaneously in the objective function.The posterior probability of the modified parameters is calculated using a delayed rejection adaptive algorithm(DRAM).Numerical examples show that the proposed method can accurately update structural parameters only when using low-order measurement modal information and incomplete mode shapes information.The experimental example shows that the dynamic characteristics of the updated finite element model of reinforced concrete beam are consistent with the measured results.The updated model parameter values correspond to the position and size of the slight crack of the beam,which shows the effectiveness of the proposed method.