In this paper, a new vibration-based damage detection method for damage localization in shear frames is presented. For this purpose, a new damage index is proposed by means of static displacements estimated using only the first several mode data and Grey Relation Theory. The efficiency of the presented method has been demonstrated through studying several damage scenarios on three examples of shear frames with a different number of stories. The effects of various situations such as the existence random noises in the recorded data, number of available modes, different damage scenarios and irregularity in the structural characteristics have been studied on the applicability of the presented method. The obtained results show the robustness and good performance of the presented method in the damage diagnosis of shear frames. Some of the most important advantages of the suggested method can be summarized as its ability in damage localization by means of only the first mode data, low sensitivity to the random noises, and high speed and accuracy in estimating damage locations.


1. Rytter, A., “Vibration Based Inspection of Civil Engineering Structures”, Ph.D. Thesis, Aalborg University, Denmark, 1993.
2. Fan, W., and Qiao, P., “Vibration-Based Damage Identification Methods: A Review and Comparative Study”, Structural Health Monitoring, Vol. 10, No. 1, pp. 83–111, 2011.
3. Kim, J-T., Ryu, Y-S., Cho, H-M., and Stubbs, N., “Damage Identification in Beam-type Structures: Frequency-Based Method vs Mode-Shape-Based Method”, Engineering Structures, Vol. 25, No. 1, pp. 57–67, 2003.
4. Kim, J-T., and Stubbs, N., “Crack Detection in Beam-Type Structures using Frequency Data”, Journal of Sound and Vibration, Vol. 259, no. 1, pp. 145–160, 2003.
5. Xia, Y., and Hao, H., “Statistical Damage Identification of Structures with Frequency Changes”, Journal of Sound and Vibration, Vol. 263, pp. 853–870, 2003.
6. Zhu, H-P., He, B., and Chen, X-Q., “Detection of Structural Damage through Changes in Frequency”, Wuhan University Journal of Natural Sciences, Vol. 10, no. 6, pp. 1069–1073, 2005.
7. Yang, Z., and Wang, L., “Structural Damage Detection by Changes in Natural Frequencies”, Journal of Intelligent Material Systems and Structures, Vol. 21, No. 3, pp. 309–319, 2010.
8. Suresh, S., Omkar, S. N., Ganguli, R., and Mani, V., “Identification of Crack Location and Depth in A Cantilever Beam using A Modular Neural Network Approach”, Smart Materials and Structures, Vol. 13, pp. 907–915, 2004.
9. Salawu, O. S., “Detection of Structural Damage through Changes in Frequency: A Review”, Engineering Structures, Vol. 19, no. 9, pp. 718–723, 1997.
10. Perera, R., Fang, S-E., and Ruiz, A., “Application of Particle Swarm Optimization and Genetic Algorithms to Multiobjective Damage Identification Inverse Problems with Modelling Errors”, Meccanica, Vol. 45, pp. 723–734, 2010.
11. Hu, N., Wang, X., Fukunaga, H., Yao, Z. H., Zhang, H. X., and Wu, Z. S., “Damage Assessment of Structures using Modal Test Data”, International Journal of Solids and Structures, Vol. 28, pp. 3111–3126, 2001.
12. Duan, Z., Yan, G., Ou, J., and Spencer, B. F., “Damage Detection in Ambient Vibration using Proportional Flexibility Matrix with Incomplete Measured DOFs”, Structural Control and Health Monitoring, Vol. 14, No. 2, pp. 186–196, 2007.
13. Jaishi, B., and Ren, W. X., “Finite Element Model Updating Based on Eigenvalue and Strain Energy Residuals using Multiobjective Optimization Technique”, Mechanical Systems and Signal Processing, Vol. 21, pp. 2295–2317, 2007.
14. Yang, Q. W., and Liu, J. K., “Structural Damage Identification Based on Residual Force Vector”, Journal of Sound and Vibration, Vol. 305, pp. 298–307, 2007.
15. Kang, F., Li, J. J., and Xu, Q., “Damage Detection based on Improved Particle Swarm Optimization using Vibration Data”, Applied Soft Computing, Vol. 12, pp. 8, pp. 2329–2335, 2012.
16. Ge, M., and Lui, E. M., “Structural Damage Identification using System Dynamics Properties”, Computers & Structures, Vol. 83, no. 27, pp. 2185–2196, 2005.
17. Ghodrati Amiri, G., Seyed Razaghi, S. A., and Bagheri, A., “Damage Detection in Plates Based on Pattern Search and Genetic Algorithms”, Smart Structures and Systems, Vol. 7, no. 2, pp. 117–132, 2011.
18. Yan, W-J., Ren, W-X., and Huang, T-L., “Statistic Structural Damage Detection Based on the Closed-form of Element Modal Strain Energy Sensitivity”, Mechanical Systems and Signal Processing, Vol. 28, pp. 183–194, 2012.
19. Limongelli, M. P., “The Interpolation Damage Detection Method for Frames under Seismic Excitation”, Journal of Sound and Vibration, Vol. 330, No. 22, pp. 5474–5489, 2011.
20. Tabrizian, Z., Afshari, E., Ghodrati Amiri, G., Hosseinali Beigy, M., and Pourhoseini Nejad, S. M., “A New Damage Detection Method: Big Bang-Big Crunch (BB-BC) Algorithm”, Shock and Vibration, Vol. 20, pp. 633–648, 2013.
21. Kourehli, S. S., Ghodrati Amiri, G., Ghafory-Ashtiany, M., and Bagheri, A., “Structural Damage Detection Based on Incomplete Modal Data using Pattern Search Algorithm”, Journal of Vibration and Control, Vol. 19, pp. 821–833, 2012.
22. Seyedpoor, S. M., “A Two Stage Method for Structural Damage Detection using A Modal Strain Energy based Index and Particle Swarm Optimization”, International Journal of Non-Linear Mechanics, Vol. 47, pp. 1–8, 2013.
23. Chen, X-Z., Zhu, H-P., and Chen, C-Y., “Structural Damage Identification using Test Static Data based on Grey System Theory”, Journal of Zhejiang University SCIENCE A, Vol. 6A, No. 8, pp. 790–796, 2005.
24. Abdo, M. A. B., “Parametric Study of using Only Static Response in Structural Damage Detection”, Engineering Structures, Vol. 34, pp. 124–131, 2012.
25. Zare Hosseinzadeh, A., Bagheri, A., and Ghodrati Amiri, G., “Two-Stage Method for Damage Localization and Quantification in High-Rise Shear Frames Based on the First Mode Shape Slope”, International Journal of Optimization in Civil Engineering, Vol. 3, no. 4, pp. 653–672, 2013.
26. Deng, J. L., “Introduction to Grey System Theory”, Journal of Grey System, Vol. 1, No. 1, pp.1–24, 1989.
27. Fu, C. Y., and Zheng, J. S., “Application of Grey Relational Analysis for Corrosion Failure of Oil Tubes”, Corrosion Science, Vol. 43, No. 5, pp. 881–889, 2001.
28. Seyedpoor, S. M., and Yazdanpanah, O., “An Efficient Indicator for Structural Damage Localization using the Change of Strain Energy Based on Static Noisy Data”, Applied Mathematical Modelling, Vol. 38, pp. 2661–2672, 2014.
29. Allemang, R. J., and Brown, D. L., “A Correlation Coefficient for Modal Vector Analysis”, 1st International Modal Analysis Conference, pp. 110–116, 1982.
30. Randall, J. A., “The Modal Assurance Criterion– Twenty Years of Use and Abuse”, Sound and Vibration, pp. 14–21, August 2003.
31. West, W. M., “Illustration of the Use of Modal Assurance Criterion to Detect Structural Changes in An Orbiter Test Specimen”, Proceedings of Air Force Conference on Aircraft Structural Integrity, pp.1–6, 1984.
32. Yang, Q-W., and Liu, J-K., “Damage Identification by the Eigenparameter Decomposition of Structural Flexibility Change”, International Journal for Numerical Methods in Engineering, Vol. 78, pp. 444–459, 2009.

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