Damage detection in a double-beam system using proper orthogonal decomposition and teaching-learning based algorithm

Document Type : Article

Authors

1 School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, 16846, Iran.

2 School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, 16846, Iran., Narmak, Tehran, 16846, Iran

Abstract

This study deals with inverse approach for damage detection in a double-beam system. A double-beam system made of two parallel beams connected through an elastic layer. Degradation in stiffness of beams element, crack occurrence and partly destruction of inner layer has been considered as different types of damage. The time domain acceleration response of the system measured and proper orthogonal decomposition has been applied to the collected data in order to derive the proper orthogonal values (POV) and proper orthogonal modes (POM) of the system. Effect of single damage in different locations on the POV has been analyzed and an objective function has been defined using the dominant POV and POM of each beam separately. In order to increase robustness of the method against noise, the objective function enriched by adding statistical property of time domain response. The teaching-learning based optimization algorithm has been employed to solve optimization problem. Efficiency of the proposed method for detecting single and multiple damages in the system demonstrated with and without noise. Simulation results show good accuracy of the proposed method for detection single and multiple damages of different types in the system.

Keywords

Main Subjects

References

References:
1. Fan, W. and Qiao, P. "Vibration-based damage identification methods: a review and comparative study", Structural Health Monitoring, 10, pp. 83-111 (2011).
2. Ruotolo, R. and Surace, C. "Damage assessment of multiple cracked beams: numerical results and experimental validation", Journal of Sound and Vibration, 206(4), pp. 567-588 (1997).
3. Meruane, V. and Heylen, W. "An hybrid real genetic algorithm to detect structural damage using modal properties", Mechanical Systems and Signal Processing, 25(5), pp. 1559-1573 (2011).
4. Raich, A.M. and Liszkai, T.R. "Improving the performance of structural damage detection methods using advanced genetic algorithms", Journal of Structural Engineering, 133(3), pp. 449-461 (2007).
5. Dabbagh, H., Ghodrati Amiri, G., and Shaabani, S. "Modal data-based approach to structural damage identification by means of imperialist competitive optimization algorithm", Scientia Iranica, 25(3), pp. 1070-1082 (2018).
6. Kaveh, A., Hosseini Vaez, S.R., and Hosseini, P. "Enhanced vibrating particles system algorithm for damage identification of truss structures", Scientia Iranica, 20(1), pp. 246-256 (2019). DOI: 10.24200/sci.2017.4265.
7. Seyedpoor, S.M., Shahbandeh, S., and Yazdanpanah, O. "An efficient method for structural damage detection using a differential evolution algorithm-based optimisation approach", Civil Engineering and Environmental Systems, 32(3), pp. 230-250 (2015).
8. Fatahi, L. and Moradi, S. "Multiple crack identification in frame structures using a hybrid Bayesian model class selection and swarm-based optimization methods", Structural Health Monitoring, 17, pp. 39-58 (2018).
9. Fallahian, S., Joghataie, A., and Kazemi, M.T. "Structural damage detection using time domain responses and teaching-learning-based optimization (TLBO) algorithm", Scientia Iranica, 25(6), pp. 3088-3100 (2018). DOI: 10.24200/sci.2017.4238.
10. Rezvani, K., Maia, N.M.M., and Sabour, M.H. "A comparison of some methods for structural damage detection", Scientia Iranica, 25(3), pp. 1312-1322 (2018).
11. Cao, S. and Ouyang, H. "Robust multi-damage localisation using common eigenvector analysis and covariance matrix changes", Mechanical Systems and Signal Processing, 111, pp. 663-677 (2018).
12. Civera, M., Zanotti Fragonara, L., and Surace, C. "A novel approach to damage localisation based on bispectral analysis and neural network", Smart Structures and Systems, 20(6), pp. 669-682 (2017).
13. Oniszczuk, Z. "Free transverse vibrations of elastically connected simply supported double-beam complex system", Journal of Sound and Vibration, 232(2), pp. 387-403 (2000).
14. Palmeri, A. and Adhikari, S. "A Galerkin-type statespace approach for transverse vibrations of slender double-beam systems with viscoelastic inner layer", Journal of Sound and Vibration, 330, pp. 6372-6386 (2011).
15. Stojanovic, V., Kozic, P., and Janevski, G. "Exact closed-form solutions for the natural frequencies and stability of elastically connected multiple beam system using Timoshenko and high-order shear deformation theory", Journal of Sound and Vibration, 332, pp. 563-576 (2013). 
16. Huang, M. and Liu, J.K. "Substructural method for vibration analysis of the elastically connected doublebeam system", Advances in Structural Engineering, 16(2), pp. 365-377 (2013).
17. Mirzabeigy, A., Dabbagh, V., and Madoliat, R. "Explicit formulation for natural frequencies of doublebeam system with arbitrary boundary conditions", Journal of Mechanical Science and Technology, 31(2),pp. 515-521 (2017).
18. Mirzabeigy, A., Madoliat, R., and Vahabi, M. "Free vibration analysis of two parallel beams connected together through variable stiness elastic layer with elastically restrained ends", Advances in Structural Engineering, 20(3), pp. 275-287 (2017).
19. Mirzabeigy, A. and Madoliat, R. "Free vibration analysis of partially connected parallel beams with elastically restrained ends", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 230(16), pp. 2851-2864 (2016).
20. Nguyen, K.V. "Crack detection of a double-beam carrying a concentrated mass", Mechanics Research Communications, 75, pp. 20-28 (2016). 
21. Liu, G.R. and Quek, S.S., The Finite Element Method: A Practical Course, Butterworth-Heinemann (2013). 
22. Newmark, N.M. "A method of computation for structural dynamics", Journal of the Engineering Mechanics Division, 85(3), pp. 67-94 (1959).
23. Mehrjoo, M. Khaji, N., and Ghafory-Ashtiany, M. "Application of genetic algorithm in crack detection of beam-like structures using a new cracked Euler- Bernoulli beam element", Applied Soft Computing, 13(2), pp. 867-880 (2013).
24. Ostachowicz, W.M. and Krawczuk, M. "Analysis of the effect of cracks on the natural frequencies of a cantilever beam", Journal of Sound and Vibration,150(2), pp. 191-201 (1991).
25. Rao, R.V., Savsani, V.J., and Vakharia, D.P. "Teaching-learning-based optimization: an optimization method for continuous non-linear large scale problems", Information Sciences, 183(1), pp. 1-15 (2012).
26. Singh, M., Panigrahi, B.K., and Abhyankar, A.R. "Optimal coordination of directional over-current relays using teaching learning-based optimization (TLBO) algorithm", International Journal of Electrical Power & Energy Systems, 50, pp. 33-41 (2013).
27. Garcia, J.A.M. and Mena, A.J.G. "Optimal distributed generation location and size using a modi- fied teaching-learning based optimization algorithm", International Journal of Electrical Power & Energy Systems, 50, pp. 65-75 (2013).
28. Basu, M. "Teaching-learning-based optimization algorithm for multi-area economic dispatch", Energy, 68, pp. 21-28 (2014).
29. Jordehi, A.R. "Optimal setting of TCSCs in power systems using teaching-learning-based optimisation algorithm", Neural Computing and Applications, 26(5), pp. 1249-1256 (2015).
30. Farshchin, M., Camp, C.V., and Maniat, M. "Multiclass teaching-learning-based optimization for truss design with frequency constraints", Engineering Structures, 106, pp. 355-369 (2016).
31. Kerschen, G., Golinval, J.C., Vakakis, A.F., and Bergman, L.A. "The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview",  Nonlinear Dynamics, 41(1), pp. 147-169 (2005).
32. Kerschen, G., Poncelet, F., and Golinval, J.C. "Physical interpretation of independent component analysis in structural dynamics", Mechanical Systems and Signal Processing, 21(4), pp. 1561-1575 (2007).
33. Feeny, B.F. and Kappagantu, R. "On the physical interpretation of proper orthogonal modes in vibrations", Journal of Sound and Vibration, 211(4), pp. 607-616 (1998).
34. Kerschen, G. and Golinval, J.C. "Physical interpretation of the proper orthogonal modes using the singular value decomposition", Journal of Sound and Vibration, 249(5), pp. 849-865 (2002).
35. Feeny, B.F. and Liang, Y. "Interpreting proper orthogonal modes of randomly excited vibration systems", Journal of Sound and Vibration, 265(5), pp. 953-966 (2003).
36. Galvanetto, U. and Violaris, G. "Numerical investigation of a new damage detection method based on proper orthogonal decomposition", Mechanical Systems and Signal Processing, 21(3), pp. 1346-1361(2007).
37. Galvanetto, U., Surace, C., and Tassotti, A. "Structural damage detection based on proper orthogonal decomposition: experimental verification", AIAA Journal, 46(7), pp. 1624-1630 (2008).
38. Thiene, M., Zaccariotto, M., and Galvanetto, U. "Application of proper orthogonal decomposition to damage  detection in homogeneous plates and composite beams", Journal of Engineering Mechanics, 139(11),pp. 1539-1550 (2013).
39. Rao, A.R.M., Lakshmi, K., and Venkatachalam, D. "Damage diagnostic technique for structural health monitoring using POD and self adaptive dierential evolution algorithm", Computers & Structures, 106,pp. 228-244 (2012).
Scientia Iranica
Volume 27, Issue 2
Transactions on Mechanical Engineering (B)
March and April 2020
Pages 757-771

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History

  • Receive Date: 26 February 2018
  • Revise Date: 08 August 2018
  • Accept Date: 03 December 2018

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