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Mathematical Problems in Engineering
Volume 2017, Article ID 1089645, 11 pages
Research Article

Damage Detection in Grid Structures Using Limited Modal Test Data

1State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China
2Jiangsu Key Laboratory of Environmental Impact and Structural Safety in Engineering, School of Mechanics and Civil Engineering, Xuzhou 221116, China

Correspondence should be addressed to Bei-dou Ding; moc.361@ratsdbd

Received 12 January 2017; Revised 13 March 2017; Accepted 2 April 2017; Published 1 June 2017

Academic Editor: Michele Betti

Copyright © 2017 Bei-dou Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The detection of potentially damaged elements in grid structures is a challenging topic. By using limited measured test data, damage detection for grid structures is developed by the modal strain energy (MSE) method. Two critical problems are considered in this paper in developing the MSE method to detect potential damage to the grid structure by using limited modal test data. First, an updated mode shape expansion method based on the modal assurance criterion is adopted to ensure that the modal shape obtained from the reference baseline model is reliable and has explicit physical meanings. Second, after identifying the location of the element damage by the element MSE method with expanded mode shapes, multivariable parameters denoting element damage severity are simultaneously determined. These parameters are included in the column vector and matched with the corresponding element stiffness matrix while the error tolerance value of the Frobenius norm of the column vector is undercontrolled. Finally, a three-dimension numerical model of the grid structure is used to represent different damage cases and to demonstrate the effectiveness of the present method. The application of the three-dimension physical model to a full-scale grid structure is also verified. Analysis results demonstrate that the presented damage detection method effectively locates and quantifies single- and multimember damage in grid structures and can be applied in engineering practice.