A New Method for Damage Detection in Symmetric Beams Using Artificial Neural Network and Finite Element Method

Abstract

In this paper a new method for crack detection in symmetric beams is presented. Natural frequency is frequently used as a parameter to detect cracks in structures. In symmetric structures, it isn’t possible to identify the location and the depth of a crack using only the natural frequencies. This is due to the fact that the natural frequencies for any symmetric position of a crack with respect to symmetry plane of the structure are the same. In this research it is assumed that the structure is a rectangular beam which is fixed at both ends. Finite Element Method (FEM) was used to obtain natural frequencies of beam in different conditions of cracks. Then assumed the crack is located at the right side of the structure. Based on data were obtained from FEM, two distinct Artificial Neural Networks (ANNs) were trained for crack location and depth detection in some different conditions and then were tested. As it was assumed that the crack is at the right side of the beam, two symmetric positions could exist for a crack. Finally using an algorithm based on first vibrational mode shape of structure, locations and depths of cracks have been identified with good approximations

Keywords

• Crack Detection, Symmetric Beam, Mode Shape, Natural Frequency, Artificial Neural Network

References

1. [1] Vandive, J.K., Detection of structural failures on fixed platforms by measurement of dynamic responses, Proceedings of the 7th Annual Offshore Technology Conference, Houston, Texas, 1975.
2. [2] Crohas, H. and Lepert, P., Damage detection monitoring method for offshore platforms is field tested, Oil& Gas J., 80, 94-103, 1982.
3. [3] Cawley, P. and Adams, R.D., The location of defects in structures from measurements of natural frequencies, J. Strain Anal., 14, 49-57, 1979.
4. [4] Pandey, A.K., Biswas, M. And Samman, M.M., Damage detection from changes in curvature mode shapes, J. Sound Vib, 145, 321-332, 1991.
5. [5] Chance, J., Tomlinson, G.R. and Worden, K., A simplified approach to the numerical and experimental modeling of the dynamics of a cracked beam, Proceedings of the 12th International Modal Analysis Conference, Honolulu, Hawaii, 1994.
6. [6] Stubbs, N. And Osegueda, R., Global non-destructive damage evaluation in solids, Int. j. analyt. exp. modal anal., 5, 67-79, 1990.
7. [7] Wu, X., Ghaboussi, J. and Garrett, J. H., Use of neural networks in detection of structural damage, Comput. Struct., 42, 649-659, 1992.
8. [8] Kaouk, M. and Zimmerman, D.C., Structural damage assessment using a generalized minimum rank perturbation theory, AIAA J., 32, 836–842, 1994.

9. [9] Kim, J.T. and Stubbs, N., Model uncertainty and damage detection accuracy in plate-girder bridges, J. Struct. Eng., 121, 1409-1417, 1995.
10. [10] Dimarogonas, A.D., Vibration of cracked structures: a state of the art review, Eng. Fract. Mech., 55, 831-857, 1996.
11. [11] Douka, E., Loutridis, S. and Trochidis, A., Crack identification in beams using wavelet analysis, Int J Solids Struct., 40, 3557-3569, 2003.
12. [12] Dimarogonas, A.D., Vibration Engineering, West Publishers, St Paul, Minesota, 1976.
13. [13] Paipetis, S.A. Dimarogonas, A.D., Analytical method in rotor dynamics, Appl. Sci. London,1986.
14. 14] Adams, A.D. and Cawley, P., The location of defects in structures from measurements of natural frequencies, J. Strain Anal., 14, 49-57, 1979.
15. [15] Chondros, T.G. and Dimarogonas, A.D., Identification of cracks in welded joints of complex structures, J. Sound Vib., 69, 531-538, 1980.
16. [16] Goudmunson, P., Eigenfrequency change of structures: a state of the art review, Eng. Frac. Mech., 55, 831-857, 1982.
17. [17] Masoud, A., Jarrad, M.A. and Al-Maamory, M., Effect of crack depth on the natural frequency of a prestressed fixed-fixed beam, J. Sound Vib., 214, 201-212, 1998.
18. [18] Shen, M.-H. and Taylor, J.E., An identification problem for vibrating cracked beams, J. Sound Vib., 84, 150-457, 1991.
19. [19] Liang, R.Y., Hu, J. and Choy, F., Theoretical study of crack-induced eigenfrequency changes on beam structures, J. Eng. Mech., 118, 384-396, 1992.
20. [20] Kim, J.-T. and Stubbs, N., Crack detection in beam-type structures using frequency data, J. Sound Vib., 259, 145–160, 2003.
21. [21] Wu, X., Ghaboussi, J. and Garret, J.H., Use of neural networks in detection of structural damage, Comput. Struct., 42 , 649-659, 1992.
22. [22] Kao, C.Y. and Hung, S.L., Detection of structural damage via free vibration responses generated by approximating artificial neural networks, Comput. Struct., 81, 2631-2644, 2003.
23. [23] Chen, Q., Chan, Y.W. and Worden, K., Structural fault diagnosis and isolation using neural networks based on response-only data, Comput. Struct., 81, 2165-2172, 2003.
24. [24] Khaji, N. Shafiei, M. And Jalalpour, M., Closed-form solutions for crack detection problem of Timoshenko beams with various boundary conditions, Int. J. Mech. Sci., 51, 667-681, 2009.
25. [25] McClelland, J.L. and Rumelhart, D.E., Parallel distributed processing: Explorations in the Microstructure of Cognition, Volumes I and II, MIT Press, Cambridge, Massachusetts, USA, 1986.