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Structural damage detection based on l 1 regularization using natural frequencies and mode shapes
Author(s) -
Hou Rongrong,
Xia Yong,
Zhou Xiaoqing
Publication year - 2018
Publication title -
structural control and health monitoring
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.587
H-Index - 62
eISSN - 1545-2263
pISSN - 1545-2255
DOI - 10.1002/stc.2107
Subject(s) - tikhonov regularization , regularization (linguistics) , regularization perspectives on support vector machines , backus–gilbert method , algorithm , computer science , vibration , mathematics , inverse problem , mathematical optimization , artificial intelligence , physics , mathematical analysis , acoustics
Summary Conventional vibration‐based damage detection methods employ the Tikhonov regularization in model updating to deal with the problems of underdeterminacy and measurement noise. However, the Tikhonov regularization technique tends to provide over smooth solutions that the identified damage is distributed to many structural elements. This result does not match the sparsity property of the actual damage scenario, in which structural damage typically occurs at a small number of locations only in comparison with the total elements of the entire structure. In this study, an l 1 regularization‐based model updating technique is developed by utilizing the sparsity of the structural damage. Both natural frequencies and mode shapes are employed during the model updating. A strategy of selecting the regularization parameter for the l 1 regularization problem is also developed. A numerical and an experimental examples are utilized to demonstrate the effectiveness of the proposed damage detection method. The results showed that the proposed l 1 regularization‐based method is able to locate and quantify the sparse damage correctly over a large number of elements. The effects of the mode number on the damage detection results are also investigated. The advantage of the present l 1 regularization over the traditional l 2 regularization method in damage detection is also demonstrated.