基于动力特性灵敏度解析代数算法的结构损伤识别:理论与数值分析

Structural Damage Detection Based on the Analytical Sensitivity Analysis of Dynamic Properties

基于结构动力特性灵敏度解析解,建立了结构损伤方程组代数表达式,该损伤方程组通过矩阵运算实现,简洁紧凑,有效地避免模态截断问题.同时,基于经典的随机子空间模态算法(stochastic subspace method,SSI)实现结构损伤前与损伤后的模态参数识别.将结构损伤前后模态参数识别结果代入损伤方程组,可以检测出桥梁结构损伤的位置和损伤的程度,该方法无需迭代.利用简支梁桥算例对该模态参数识别方法和损伤识别方法进行了验证和分析.数值计算结果表明,在噪声水平较低地工况下,本文提出的方法对单损伤梁和多损伤梁均能实现损伤定位和损伤程度的判别,计算效率较高.

The structural damage equations are established based on the algebraic solution of eigensolution sensitivity. The equations are compact and their error caused by the mode truncation can be well addressed. At the same time, the classic stochastic subspace method （SSI） is adopted to extract the modal parameters before and after the structural damage. Based on the damage equations and the modal parameters, the damage location and the damage degree of the structure can be solved properly. The damage identification method is verified and analyzed by using simple beam as an example. The results show that the method can identify the location and extent of damage in different scenarios including single damage and multi damages.