环境激励下基于柔度矩阵分解的损伤诊断

Abstract

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.