环境激励下基于柔度矩阵分解的损伤诊断

Research on Damage Diagnosis Based on Flexibility Matrix Decomposition

为了解决环境激励作用下结构自由度不完备对损伤诊断的影响,提出了一种基于自由度缩聚的比例柔度矩阵分解损伤诊断法.利用附加质量法求解出环境激励作用下振型关于质量归一化因子.进而根据质量归一化因子和比例柔度矩阵系数之间的关系,构建出其比例柔度矩阵,再通过使用QR矩阵分解法对构建出的比例柔度矩阵进行分解.以分解后得到的三角矩阵(R矩阵)作为研究对象,将R矩阵经过相应的数学算法处理得到最终损伤定位指标.算例研究表明:在环境激励作用下考虑自由度缩聚的影响,无论对于单损伤还是多损伤,所提损伤定位指标均表现出较高的准确性,且具有一定的鲁棒性.该文基于矩阵分解法推导出的损伤定位指标可以应用在环境激励作用下的损伤诊断,同时也为自由度不完备结构的损伤诊断提供了新研究思路.

To solve the influence of incomplete measured DOFs on structural damage detection under ambient excitation,based on model reduction a proportional flexibility matrix(PFM)decomposition method was proposed.By means of the additional mass method,the normalized factor of mode shapes under ambient excitation was solved.According to the relation between the normalized factor and the PFM factor,the new PFM was built.Then,with the QR matrix decomposition method,the new PFM was decomposed and the resulting triangular matrix(R matrix)was considered as the research object,which was processed with the corresponding mathematical algorithm to obtain the final damage position index.The results show that,the proposed damage position index has high accuracy and certain robustness for both a single damage and multiple damages under ambient excitation.The damage position index derived from the matrix decomposition method applies to structural damage diagnosis under environmental excitation,making a new research idea for damage diagnosis of incomplete-DOF structures.