Modal data-based approach to structural damage identification by means of imperialist competitive optimization algorithm


1 Department of Civil Engineering, University of Kurdistan, Sanandaj, Iran

2 Center of Excellence for Fundamental Studies in Structural Engineering, School of Civil Engineering, Iran University of Science & Technology, Tehran, Iran


In this paper, an effective method for structural damage detection is put forth in which an objective function based on the natural frequencies and modal shapes of the structure is established to identify and detect structural damage. The problem is defined and solved as an optimization problem employing Imperialist Competition Algorithm (ICA). Moreover, four numerical examples are examined each of which has different damage scenarios in order that the applicability of the method would be clearly proved. The results show the efficiency of the method in detecting single and multiple damages in different structures. Afterwards, the effects of measurement noises are included in some of the examples so that the method can be more consistent with real situations. Besides, a comparison among several evolutionary optimization algorithms in the research is made to enlighten the accuracy, robustness and reliability of the method. All of the results lead to the conclusion that the suggested method of the paper is of good accuracy, and, therefore, can be both used and trusted in solving damage detection problems, even in cases that measurement noises are encountered.


Main Subjects


1. Farrar, C.R. and Worden, K. \An introduction to
structural health monitoring", Phil. Trans. R. Soc. A.,
365(1851), pp. 303-315 (2007).
2. Yan, Y.J., Cheng, L., Wu, Z.Y., and Yam, L.H.
\Development in vibration-based structural damage
H. Dabbagh et al./Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 1070{1082 1081
detection techniques", Mech sys signal process, 21(5),
pp. 2198-2211(2007).
3. Shi, Z.Y., Law, S.S., and Zhang, L.M. \Structural
damage detection from modal strain energy change",
J. Eng Mech ASCE, 126(12), pp. 1216-1223 (2000).
4. Gawronski, W. Sawicki, J.T. \Structural damage detection
using modal norms", J. Sound Vib, 229(1), pp.
194-198 (2000).
5. Kawiecki, G. \Modal damping measurement for damage
detection", Smart Mat. Struct, 10(3), pp. 466-471
6. Shi, Z.Y., Law, S.S., and Zhang, L.M., \Improved
damage quanti cation from elemental modal strain
energy change", J. Eng. Mech-ASCE, 128(5), pp. 521-
529 (2002).
7. Abdo, M.A.B. and Hori, M. \A numerical study
of structural damage detection using changes in the
rotation of mode shapes", J. Sound. Vib., 251(2), pp.
227-239 (2002).
8. Sampaio, R.P.C., Maia, N.M.M., and Silva, J.M.M.
\The frequency domain assurance criterion as a tool for
damage detection, damage assessment of structures",
Proceedings Key Eng. Mat., 245, pp. 69-76 (2003).
9. Doebling, S.W., Farrar, C.R., and Prime, M.B. \A
summary review of vibration-based damage identi -
cation methods", Shock Vib. Dig., 30(2), pp. 91-105
10. Yan, Y.J., Cheng, L.,Wu, Z.Y., and Yam, L.H. \Development
in vibration-based structural damage detection
technique", Mech. Sys. Signal Process., 21(5), pp.
2198-2211 (2007).
11. Fang, S.E., Perera, R, De., and Roeck, G. \Damage
identi cation of a reinforced concrete frame by nite
element model updating using damage parameterization",
J. Sound. Vib., 313(3). pp. 544-559 (2008).
12. Tabrizian, Z., Ghodrati Amiri, G., and Hossein Ali
Beygi, M. \Charged system search algorithm utilized
for structural damage detection", Shock Vib., 13 pages
13. Gau, H.Y. and Li, Z.L. \Structural damage identi cation
based on Bayesian theory and improved immune
genetic algorithm", Expert Syst. Appl., 39(7), pp.
6426-6436 (2012).
14. Salawu, O.S. \Detection of structural damage through
changes in frequency: a review", Eng Struct, 19(9),
pp. 718-723 (1997).
15. Ren, W.X. and De Roeck, G. \Structural damage identi
cation using modal data. I: Simulation veri cation",
J. Struct. Eng. ASCE, 128(1), pp. 87-95 (2002).
16. Ren, W.X. and De Roeck, G. \Structural damage
identi cation using modal data. II: Test veri cation",
J. Struct. Eng. ASCE, 128(1), pp. 96-104 (2002).
17. Abdel Wahab, M.M. and De Roeck, G. \Damage detection
in bridges using modal curvatures: application
to a real damage scenario", J. Sound. Vib., 226(2), pp.
217-235 (1999).
18. Shi, Z.Y., Law, S.S., and Zhang, L.M. \Structural
damage detection from modal strain energy change",
J. Eng. Mech. ASCE, 126(12), pp. 1216-1223 (2000).
19. Jaishi, B. and Ren, W.X. \Structural nite element
model updating using ambient vibration test results",
J. Struct. Eng. ASCE, 131(4), pp. 617-628 (2005).
20. Jaishi, B. and Ren, W.X. \Damage detection by
nite element model updating using modal
residual", J. Sound. Vib., 290(1). pp. 369-387 (2006).
21. Jaishi, B. and Ren, W.X. \Finite element model updating
based on eigenvalue and strain energy residuals
using multiobjective optimisation technique", Mech.
Sys. Signal Process, 21(5), pp. 2295-2317 (2007).
22. Jaishi, B., Kim, H.J., Kim, M.K., Ren, W.X., and Lee,
S.H. \Finite element model updating of concrete- lled
steel tubular arch bridge under operational condition
using modal
exibility", Mech. Sys. Signal Process,
21(6), pp. 2406-2426 (2007).
23. Perera, R. and Ruiz, A. \A multistage FE updating
procedure for damage identi cation in large-scale
structures based on multiobjective evolutionary optimization",
Mech. Sys. Signal Process, 22(4). pp. 970-
991 (2008).
24. Kaveh, A. and Talatahari, S. \Optimum design of
skeletal structures using imperialist competitive algorithm",
Comput. struct., 88(21), pp. 1220-1229 (2010).
25. Kaveh, A. and Zolghadr, A. \An improved CSS for
damage detection of truss structures using changes in
natural frequencies", Advances in Eng. Soft., 80, pp.
93-100 (2015).
26. Saada, M., Arafa, M., and Nassef, A. \Finite element
model updating approach to damage identi cation in
beams using particle swarm optimization", Eng. Opt.,
45(6), pp. 677- 696 (2013).
27. Kaveh, A., Javadi, S.M. and Maniat, M. \Damage
detection via modal data with a mixed particle swarm
strategy, ray optimizer, and harmony search", Asian
J. Civil Eng. (BHRC), 15(1), pp. 95-106 (2014).
28. Zare Hosseinzadeh, A., Bagheri, A., and Ghodrati
Amiri, G. \Two-stage method for damage localization
and quanti cation in high- rise shear frames based on
the rst mode shape slope", Int. J. Optim. Civil Eng.,
3(4), pp. 653-672 (2013).
29. Pandey, A.K., Biswas, M., and Samman, M.M., \Damage
detection from changes in curvature mode shapes",
J. Sound Vib., 145(2), pp. 321-332 (1991).
30. Moreno-Garca, P., Dos Santos, J.V.A., and Lopes. H.,
\A new technique to optimize the use of mode shape
derivatives to localize damage in laminated composite
plates", Composite Struct, 108, pp. 548-554 (2014).
31. Pandey, A.K. and Biswas, M., \Damage detection in
structures using changes in
exibility", J. Sound Vib.,
169(1), pp. 3-17 (1994).
32. Balsamo, L., Mukhopadhyay, S., and Betti. R., \A statistical
framework with sti ness proportional damage
sensitive features for structural health monitoring",
Smart Struct. Sys., 15(3), pp. 699-715 (2015).
1082 H. Dabbagh et al./Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 1070{1082
33. Dos Santos, J.V.A., Soares, C.M.M., Soares, C.A.M.,
and Pina, H.L.G., \A damage identi cation numerical
model based on the sensitivity of orthogonality
conditions and least squares techniques", J. Comput.
Struct., 78(1), pp. 283-291 (2000).
34. Perera, R., Fang, S. and Huerta, C. \Structural crack
detection without updated baseline model by single
and multiobjective optimization", Mech. Sys. Signal
Process., 23(3), pp. 752-768 (2009).
35. Nouri Shirazi, M.R. and Mollamahmoudi, H. \Structural
damage identi cation using an adaptive multistage
optimization method based on a modi ed particle
swarm algorithm", J. Optim. Theory Appl., 160(3),
pp. 1009-1019.
36. Yu, L. and Fu, Y. \Structural damage detection by
fusion of GA and PSO", Advanced Mat. Research, 919,
pp. 338-343 (2014).
37. Kaveh, A. and Maniat, M. \Damage detection based
on MCSS and PSO using modal data", Smart Struct.
Sys., 15(5), pp. 1253-1270 (2015).
38. Seyedpoor, S.M. and Yazdanpanah, O. \Structural
damage detection by di erential evolution as a global
optimization algorithm", Iranian J. Struct. Eng., 1(1),
pp. 52-62 (2015).
39. Xu, H.J., Liu, J.K., and Lv, Z.R. \Structural damage
identi cation based on modi ed cuckoo search algorithm",
Struct. Eng. Mech., 58(1), pp. 163-179 (2016).
40. Allemang, R.J. and Brown D.L., \A correlation coe
cient for modal vector analysis", Proceed. 1st Int.
Modal. Analysis Conf., Kissimmee, FL, USA, 1, pp.
110-116 (1982).
41. Atashpaz-Gargari, E. and Lucas, C. \Imperialist competitive
algorithm: an algorithm for optimization inspired
by imperialistic competition", IEEE Cong Evolutionary
Comput, Singapore, pp. 4661-4667 (2007).
42. Ghodrati Amiri, G., Zare Hosseinzadeh, A., Bagheri,
A., et al. \Damage prognosis by means of modal residual
force and static de
ections obtained by modal
based on the diagonalization method", Smart
Mter. Struct., 22(7), 075032 (2013).
43. Ghodrati Amiri, G., Zare Hosseinzadeh, A., and Seyed
Razzaghi, S.A. \Generalized
exibility- based model
updating approach via democratic particle swarm optimization
algorithm for structural damage prognoisis",
Int. J. Optim. Civil Eng., 5(4), pp. 445-464 (2015).