基于模态参数考虑边界条件变异的桥梁结构损伤识别

根据桥梁结构的实际工程特性,分析其边界条件变异、结构损伤及其参数变化,采用约束优化理论,建立以实测和理论模态参数误差平方和最小为目标函数的优化反演问题。基于矩阵摄动理论引入与结构动力方程对应的特征值和特征向量的一阶、二阶摄动量,将优化反演问题简化为非线性最小二乘法优化反演问题。针对桥梁结构边界条件对模态参数影响显著的实际情况,实施桥梁结构边界条件预识别,采用单元模态应变能方法预定位损伤,提出考虑边界条件变异的桥梁结构损伤识别具体流程。以一磁浮轨道梁方案为例,采用数值模拟进行边界条件变异及损伤的识别验证,结果表明:该方法能够有效识别边界条件的变异及构件损伤,识别参数的相对误差最大为12.48%,具有较高的识别精度。

Damage detection of bridge structure accounting for boundary condition variation based on mode parameters

According to the engineering characteristic of bridge structure,boundary condition variation and structure damages as well as the parameterization of them are analyzed in detail.The optimization inversion question is established with target function of minimum sum of square errors between mode parameters tested and calculated by using constrained optimization theory.The first and second order eigenvalues and eigenvectors of the corresponding dynamic equation are introduced into the optimization inversion question based on matrix perturbation theory,so the question is simplified as optimization inversion of the nonlinear least square.According to the fact that boundary condition of bridge structure has much more effect on mode parameters,pre-identification of boundary condition is used.Then the detailed method and process of bridge structure damage detection are put forward accounting for the boundary condition,in which pre-location method of element mode strain energy is adopted.At last,the numerical analysis results of a maglev railway girder show that the damage detection method can effectively detect change of boundary condition and structure damages with fairly well precision and the maximum relative detection error is 12.48%.