Smart Structures and Systems

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An iterative method for damage identification of skeletal structures utilizing biconjugate gradient method and reduction of search space

  • Sotoudehnia, Ebrahim (Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad) ;
  • Shahabian, Farzad (Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad) ;
  • Sani, Ahmad Aftabi (Civil Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad)
  • Received : 2018.07.04
  • Accepted : 2018.12.26
  • Published : 2019.01.25
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Abstract

This paper is devoted to proposing a new approach for damage detection of structures. In this technique, the biconjugate gradient method (BCG) is employed. To remedy the noise effects, a new preconditioning algorithm is applied. The proposed preconditioner matrix significantly reduces the condition number of the system. Moreover, based on the characteristics of the damage vector, a new direct search algorithm is employed to increase the efficiency of the suggested damage detection scheme by reducing the number of unknowns. To corroborate the high efficiency and capability of the presented strategy, it is applied for estimating the severity and location of damage in the well-known 31-member and 52-member trusses. For damage detection of these trusses, the time history responses are measured by a limited number of sensors. The results of numerical examples reveal high accuracy and robustness of the proposed method.

Keywords

References

  1. Cheng, L., Xie, H., Spencer Jr, B.F. and Giles, R. (2009), "Optimized finite element model updating method for damage detection using limited sensor information", Smart Struct. Syst., 5(6), 681-697. https://doi.org/10.12989/sss.2009.5.6.681
  2. Doebling, S.W., Farrar, C.R. and Prime, M.B. (1998), "A summary review of vibration-based damage identification methods", Shock Vib. Digest, 30(2), 91-125. https://doi.org/10.1177/058310249803000201
  3. Entezami, A. and Shariatmadar, H. (2014), "Damage detection in structural systems by improved sensitivity of modal strain energy and Tikhonov regularization method", International J. Dynam. Control, 2(4), 509-520. https://doi.org/10.1007/s40435-014-0071-z
  4. Entezami, A. and Shariatmadar, H. (2014), "Damage localization in shear buildings by direct updating of physical properties", Int. J. Adv. Struct. Eng., 6(2), 1-12. https://doi.org/10.1007/s40091-014-0058-1
  5. Entezami, A. and Shariatmadar, H. (2015), "New sensitivity-based methods for structural damage diagnosis by least square minimal residual techniques", Iran. J. Sci. Technol.-T.Civil Eng., 39(2), 231-251.
  6. Entezami, A., Shariatmadar, H. and Ghalehnovi, M. (2014), "Damage detection by updating structural models based on linear objective functions", J. Civil Struct. Health Monit., 4(3), 165-176. https://doi.org/10.1007/s13349-014-0072-9
  7. Esfandiari, A. (2017), "An innovative sensitivity-based method for structural model updating using incomplete modal data", Struct. Control Health Monit., 24(4), 1-13. https://doi.org/10.1002/stc.1905
  8. Esfandiari, A. and Vahedi, M. (2017), "Enhanced sensitivity for structural damage detection using incomplete modal data", Int. J. Struct. Stab. Dynam., 18(4), 1-26.
  9. Golub, G.H. and Van Loan, C.F. (2012), Matrix Computations, JHU Press.
  10. Hanke, M. and Groetsch, C.W. (1998), "Nonstationary iterated Tikhonov regularization", J. Optimz. Theory and Appl., 98(1), 37-53. https://doi.org/10.1023/A:1022680629327
  11. Kaveh, A. and Zolghadr, A. (2011), "Shape and size optimization of truss structures with frequency constraints using enhanced charged system search algorithm", Asian J. Civil Eng., 12(4), 487-509.
  12. Lei, Y., Liu, C., Jiang, Y. and Mao, Y. (2013), "Substructure based structural damage detection with limited input and output measurements", Smart Struct. Syst., 12(6), 619-640. https://doi.org/10.12989/sss.2013.12.6.619
  13. Li, H.B., Huang, T.Z., Zhang, Y., Liu, X.P. and Gu, T.X. (2011), "Chebyshev-type methods and preconditioning techniques", Appl. Math. Comput., 218(2), 260-270. https://doi.org/10.1016/j.amc.2011.05.036
  14. Li, W. and Li, Z. (2010), "A family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non-square matrix", Appl. Math. Comput., 215(9), 3433-3442. https://doi.org/10.1016/j.amc.2009.10.038
  15. Li, X. and Law, S. (2010), "Adaptive Tikhonov regularization for damage detection based on nonlinear model updating", Mech. Syst. Signal Pr., 24(6), 1646-1664. https://doi.org/10.1016/j.ymssp.2010.02.006
  16. Lu, Z. and Chen, X. (2017), "Generalized conjugate gradient methods for ℓ1 regularized convex quadratic programming with finite convergence", Math. Oper. Res., 43(1), 275-303. https://doi.org/10.1287/moor.2017.0865
  17. Lu, Z., and Law, S. (2007), "Features of dynamic response sensitivity and its application in damage detection", Journal of Sound and Vibration, 303(1), 305-329. https://doi.org/10.1016/j.jsv.2007.01.021
  18. Messina, A., Williams, E., and Contursi, T. (1998), "Structural damage detection by a sensitivity and statistical-based method'', J. Sound Vib., 216(5), 791-808. https://doi.org/10.1006/jsvi.1998.1728
  19. Naseralavi, S., Fadaee, M. and Salajegheh, J. (2011), "Subset solving algorithm: A novel sensitivity-based method for damage detection of structures'', Appl. Math. Model., 35(5), 2232-2252. https://doi.org/10.1016/j.apm.2010.11.045
  20. Naseralavi, S., Shojaee, S. and Ahmadi, M. (2016), "Modified gradient methods hybridized with Tikhonov regularization for damage identification of spatial structure", Smart Struct. Syst., 18(5), 839-864. https://doi.org/10.12989/sss.2016.18.5.839
  21. Pedram, M., Esfandiari, A. and Khedmati, M.R. (2017), "Damage detection by a FE model updating method using power spectral density: Numerical and experimental investigation", J. Sound Vib., 397, 51-76. https://doi.org/10.1016/j.jsv.2017.02.052
  22. Saad, Y. (2003), Iterative methods for sparse linear systems, SIAM, Philadelphia.
  23. Saffari, H., Maghami, A. and Mansouri, I. (2014), "Preconditioning improved bi-conjugate gradient in nonlinear analysis of space trusses", Asian J. Civil Eng., 15(4), 547-561.
  24. Saffari, H., Mirzai, N.M., Mansouri, I. and Bagheripour, M.H. (2012), "Efficient numerical method in second-order inelastic analysis of space trusses", J. Comput. Civil Eng., 27(2), 129-138. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000193
  25. Sarvi, F., Shojaee, S. and Torkzadeh, P. (2014), "Damage identification of trusses by finite element model updating using an enhanced Levenberg-Marquardt algorithm", Int. J. Optimiz. Civil Eng., 4(2), 207-231.
  26. Simoen, E., De Roeck, G., and Lombaert, G. (2015), "Dealing with uncertainty in model updating for damage assessment: A review", Mech. Syst. Signal Pr., 56, 123-149. https://doi.org/10.1016/j.ymssp.2014.11.001
  27. Toutounian, F. and Soleymani, F. (2013), "An iterative method for computing the approximate inverse of a square matrix and the Moore-Penrose inverse of a non-square matrix", Appl. Math. Comput., 224, 671-680. https://doi.org/10.1016/j.amc.2013.08.086
  28. Wang, J. and Yang, Q. (2012), "Modified Tikhonov regularization in model updating for damage identification", Struct. Eng. Mech., 44(5), 585-600. https://doi.org/10.12989/sem.2012.44.5.585
  29. Wu, L. and Casciati, F. (2014), "Local positioning systems versus structural monitoring: a review", Struct. Control Health Monit., 21(9), 1209-1221. https://doi.org/10.1002/stc.1643
  30. Yang, J. (2009), "Newton-conjugate-gradient methods for solitary wave computations", J. Comput. Phys., 228(18), 7007-7024. https://doi.org/10.1016/j.jcp.2009.06.012
  31. Yu, E. and Chung, L. (2012), "Seismic damage detection of a reinforced concrete structure by finite element model updating", Smart Struct. Syst., 9(3), 253-271. https://doi.org/10.12989/sss.2012.9.3.253