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

Document Type : Article


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


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.


Main Subjects

1. Fan, W. and Qiao, P. Vibration-based damage identi
cation 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
identi cation 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 identi cation of truss structures", Scientia
Iranica, 20(1), pp. 246{256 (2019). DOI:
7. Seyedpoor, S.M., Shahbandeh, S., and Yazdanpanah,
O. An ecient method for structural damage detection
using a di erential evolution algorithm-based
optimisation approach", Civil Engineering and Environmental
Systems, 32(3), pp. 230{250 (2015).
8. Fatahi, L. and Moradi, S. Multiple crack identi -
cation in frame structures using a hybrid Bayesian
model class selection and swarm-based optimization
methods", Structural Health Monitoring, 17, pp. 39{58
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
770 A. Mirzabeigy and R. Madoliat/Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 757{771
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
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 sti ness 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 e ect 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. Garca, J.A.M. and Mena, A.J.G. Optimal distributed
generation location and size using a modi-
ed 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
A. Mirzabeigy and R. Madoliat/Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 757{771 771
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
37. Galvanetto, U., Surace, C., and Tassotti, A. Structural
damage detection based on proper orthogonal
decomposition: experimental veri cation", 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 di erential
evolution algorithm", Computers & Structures, 106,
pp. 228{244 (2012).