Research on Damage Diagnosis Based on Flexibility Matrix Decomposition

LI Guoqing; LUO Shuai; SU Rui; WANG Zeming; WANG Cheng

doi:10.21656/1000-0887.410257

Volume 42 Issue 3

Mar. 2021

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Article Navigation > Applied Mathematics and Mechanics > 2021 > 42(3): 292-298

LI Guoqing, LUO Shuai, SU Rui, WANG Zeming, WANG Cheng. Research on Damage Diagnosis Based on Flexibility Matrix Decomposition[J]. Applied Mathematics and Mechanics, 2021, 42(3): 292-298. doi: 10.21656/1000-0887.410257

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Research on Damage Diagnosis Based on Flexibility Matrix Decomposition

doi: 10.21656/1000-0887.410257

School of Civil Engineering, Shaoxing University, Shaoxing, Zhejiang 312000, P.R.China

Received Date: 2020-09-01
Rev Recd Date: 2021-01-07
Publish Date: 2021-03-01

Abstract

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.
- damage positioning,
- proportional flexibility matrix,
- matrix decomposition method,
- model reduction,
- noise immunity analysis

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References(15)

References

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