Advertisement

Structural and Multidisciplinary Optimization

, Volume 57, Issue 2, pp 605–623 | Cite as

Identification of multiple flaws in 2D structures using dynamic extended spectral finite element method with a universally enhanced meta-heuristic optimizer

  • M. A. Livani
  • N. KhajiEmail author
  • P. Zakian
RESEARCH PAPER
  • 270 Downloads

Abstract

In this paper, flaw detection of two-dimensional structures is carried out using the extended spectral finite element method (XSFEM) associated with particle swarm optimization (PSO) algorithm enhanced by a new so-called active/inactive flaw (AIF) strategy. The AIF strategy, which is inspired from earthquake engineering concepts, is proposed for the first time in this paper. The XSFEM is employed to model the cracked and holed structures, while the PSO, which is a suitable non-gradient method for solving such problems, is employed to find crack location as an optimizer. The XSFEM consists of remarkable capabilities with the main features of spectral finite element method (SFEM) and extended finite element method (XFEM) to analyze the damaged structures without remeshing, leading it to be a proper approach in iterative processes. Moreover, the XSFEM enhances the accuracy of wave propagation analysis, and decreases computational cost as well in comparison with the XFEM. The application of XSFEM in damage detection of structures is studied for the first time in this paper. Furthermore, the AIF strategy is proposed in order to handle a simultaneously discrete and continuous optimization in an efficient way reducing computational effort. Considering the AIF as a universal strategy, it can be used in any meta-heuristic optimizer. In this research, the PSO is seeking for geometrical properties and the number of flaws in order to detect them by minimizing an error function based on sensor measurements. To overcome the challenge of unknown number of flaws, the proposed AIF strategy is employed in the PSO. Several benchmark examples are examined to evaluate capability and accuracy of the proposed algorithm for detection of cracks and holes.

Keywords

Extended spectral finite element method Structural damage detection Inverse problem Enhanced particle swarm optimization Active/inactive flaw (AIF) strategy Multiple flaw 

Notes

Acknowledgements

The authors wish to acknowledge and express their special gratitude to anonymous reviewers, for their constructive advices that improved the manuscript.

References

  1. Ahmadi HR, Daneshjoo F, Khaji N (2015) New damage indices and algorithm based on square time–frequency distribution for damage detection in concrete piers of railroad bridges. Struct Control Health Monit 22:91–106. doi: 10.1002/stc.1662 CrossRefGoogle Scholar
  2. Barroso ES, Parente E, Cartaxo de Melo AM (2016) A hybrid PSO-GA algorithm for optimization of laminated composites. Struct Multidiscip Optim 55(6):2111–2130. doi: 10.1007/s00158-016-1631-y
  3. Begambre O, Laier JE (2009) A hybrid particle swarm optimization–simplex algorithm (PSOS) for structural damage identification. Adv Eng Softw 40:883–891CrossRefzbMATHGoogle Scholar
  4. Belytschko T, Liu WK, Moran B (2000) Finite elements for nonlinear continua and structures J WileyGoogle Scholar
  5. Benaissa B, Aït Hocine N, Belaidi I, Hamrani A, Pettarin V (2016) Crack identification using model reduction based on proper orthogonal decomposition coupled with radial basis functions. Struct Multidiscip Optim 54:265–274. doi: 10.1007/s00158-016-1400-y MathSciNetCrossRefGoogle Scholar
  6. Chang W-D (2015) A modified particle swarm optimization with multiple subpopulations for multimodal function optimization problems. Appl Soft Comput 33:170–182CrossRefGoogle Scholar
  7. Chatzi EN, Hiriyur B, Waisman H, Smyth AW (2011) Experimental application and enhancement of the XFEM–GA algorithm for the detection of flaws in structures. Comput Struct 89:556–570CrossRefGoogle Scholar
  8. Doebling SW, Farrar CR, Prime MB (1998) A summary review of vibration-based damage identification methods. Shock and vibration digest 30:91–105CrossRefGoogle Scholar
  9. Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150CrossRefzbMATHGoogle Scholar
  10. Edke MS, Chang K-H (2011) Shape optimization for 2-D mixed-mode fracture using extended FEM (XFEM) and level set method (LSM). Struct Multidiscip Optim 44:165–181. doi: 10.1007/s00158-010-0616-5 CrossRefGoogle Scholar
  11. Fatemi M, Greenleaf JF (1999) Vibro-acoustography: an imaging modality based on ultrasound-stimulated acoustic emission. Proc Natl Acad Sci 96:6603–6608CrossRefGoogle Scholar
  12. Fleming M, Chu Y, Moran B, Belytschko T, Lu Y, Gu L (1997) Enriched element-free Galerkin methods for crack tip fields. Int J Numer Methods Eng 40:1483–1504MathSciNetCrossRefGoogle Scholar
  13. Giurgiutiu V, Zagrai A (2005) Damage detection in thin plates and aerospace structures with the electro-mechanical impedance method. Struct Health Monit 4:99–118CrossRefGoogle Scholar
  14. Hellier C (2001) Handbook of nondestructive evaluationGoogle Scholar
  15. Jia H, Takenaka T, Tanaka T (2002) Time-domain inverse scattering method for cross-borehole radar imaging. IEEE Trans Geosci Remote Sens 40:1640–1647CrossRefGoogle Scholar
  16. Jung J, Taciroglu E (2014) Modeling and identification of an arbitrarily shaped scatterer using dynamic XFEM with cubic splines. Comput Methods Appl Mech Eng 278:101–118MathSciNetCrossRefGoogle Scholar
  17. Jung J, Jeong C, Taciroglu E (2013) Identification of a scatterer embedded in elastic heterogeneous media using dynamic XFEM. Comput Methods Appl Mech Eng 259:50–63MathSciNetCrossRefzbMATHGoogle Scholar
  18. Kaveh A (2014) Advances in metaheuristic algorithms for optimal design of structures. Springer,Google Scholar
  19. Kaveh A, Zakian P (2013) Optimal design of steel frames under seismic loading using two meta-heuristic algorithms. J Constr Steel Res 82:111–130CrossRefGoogle Scholar
  20. Kaveh A, Zakian P (2014) Optimal seismic design of reinforced concrete shear wall-frame structures KSCE. J Civ Eng 18:2181–2190Google Scholar
  21. Kaveh A, Aghakouchak A, Zakian P (2015) Reduced record method for efficient time history dynamic analysis and optimal design. Earthquakes and Structures 8:639–663CrossRefGoogle Scholar
  22. Khaji N, Kazemi Noureini H (2012) Detection of a through-thickness crack based on elastic wave scattering in plates part I forward solution. Asian Journal of Civil Engineering (BHRC) 13:301–318Google Scholar
  23. Kudela P, Żak A, Krawczuk M, Ostachowicz W (2007) Modelling of wave propagation in composite plates using the time domain spectral element method. J Sound Vib 302:728–745CrossRefzbMATHGoogle Scholar
  24. Lakshmi K, Mohan Rao AR (2013) Optimal design of laminate composite isogrid with dynamically reconfigurable quantum PSO. Struct Multidiscip Optim 48:1001–1021. doi: 10.1007/s00158-013-0943-4 CrossRefGoogle Scholar
  25. Legay A, Wang H, Belytschko T (2005) Strong and weak arbitrary discontinuities in spectral finite elements. Int J Numer Methods Eng 64:991–1008MathSciNetCrossRefzbMATHGoogle Scholar
  26. Lei W, Xiaojun W, Xiao L (2016) Inverse system method for dynamic loads identification via noisy measured dynamic responses. Eng Comput 33:1070–1094. doi: 10.1108/EC-04-2015-0103 CrossRefGoogle Scholar
  27. Liu Z, Menouillard T, Belytschko T (2011) An XFEM/spectral element method for dynamic crack propagation. Int J Fract 169:183–198CrossRefzbMATHGoogle Scholar
  28. Luh G-C, Lin C-Y (2011) Optimal design of truss-structures using particle swarm optimization. Comput Struct 89:2221–2232CrossRefGoogle Scholar
  29. Mehrjoo M, Khaji N, Moharrami H, Bahreininejad A (2008) Damage detection of truss bridge joints using artificial neural networks. Expert Syst Appl 35:1122–1131. doi: 10.1016/j.eswa.2007.08.008 CrossRefGoogle Scholar
  30. Mehrjoo M, Khaji N, Ghafory-Ashtiany M (2013) Application of genetic algorithm in crack detection of beam-like structures using a new cracked Euler–Bernoulli beam element. Appl Soft Comput 13:867–880. doi: 10.1016/j.asoc.2012.09.014 CrossRefGoogle Scholar
  31. Menouillard T, Song J-H, Duan Q, Belytschko T (2010) Time dependent crack tip enrichment for dynamic crack propagation. Int J Fract 162:33–49CrossRefzbMATHGoogle Scholar
  32. Mian A, Han X, Islam S, Newaz G (2004) Fatigue damage detection in graphite/epoxy composites using sonic infrared imaging technique. Compos Sci Technol 64:657–666CrossRefGoogle Scholar
  33. Michaels JE (2008) Detection, localization and characterization of damage in plates with an in situ array of spatially distributed ultrasonic sensors. Smart Mater Struct 17:035035CrossRefGoogle Scholar
  34. Nanthakumar S, Lahmer T, Rabczuk T (2013) Detection of flaws in piezoelectric structures using extended FEM international. Journal for Numerical Methods in Engineering 96:373–389MathSciNetCrossRefzbMATHGoogle Scholar
  35. Nanthakumar S, Lahmer T, Rabczuk T (2014) Detection of multiple flaws in piezoelectric structures using XFEM and level sets. Comput Methods Appl Mech Eng 275:98–112MathSciNetCrossRefzbMATHGoogle Scholar
  36. Noël L, Duysinx P (2016) Shape optimization of microstructural designs subject to local stress constraints within an XFEM-level set framework. Struct Multidiscip Optim 55(6):2323–2338. doi: 10.1007/s00158-016-1642-8
  37. Papila M, Haftka RT (2003) Implementation of a crack propagation constraint within a structural optimization software. Struct Multidiscip Optim 25:327–338. doi: 10.1007/s00158-003-0329-0 CrossRefGoogle Scholar
  38. Patera AT (1984) A spectral element method for fluid dynamics: laminar flow in a channel expansion. J Comput Phys 54:468–488. doi: 10.1016/0021-9991(84)90128-1 CrossRefzbMATHGoogle Scholar
  39. Peng H, Meng G, Li F (2009) Modeling of wave propagation in plate structures using three-dimensional spectral element method for damage detection. J Sound Vib 320:942–954CrossRefGoogle Scholar
  40. Rabinovich D, Givoli D, Vigdergauz S (2007) XFEM-based crack detection scheme using a genetic algorithm. Int J Numer Methods Eng 71:1051–1080. doi: 10.1002/nme.1975 MathSciNetCrossRefzbMATHGoogle Scholar
  41. Rabinovich D, Givoli D, Vigdergauz S (2009) Crack identification by ‘arrival time’ using XFEM and a genetic algorithm international. Journal for Numerical Methods in Engineering 77:337–359. doi: 10.1002/nme.2416 MathSciNetCrossRefzbMATHGoogle Scholar
  42. Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: Proceedings of the IEEE Conference on Evolutionary Computation, ICEC. IEEE World Congress on Computational Intelligence. pp 69–73Google Scholar
  43. Shi Q, Wang X, Wang L, Li Y, Chen X (2017) Set-membership identification technique for structural damage based on the dynamic responses with noises. Struct Control Health Monit 24:e1868. doi: 10.1002/stc.1868 CrossRefGoogle Scholar
  44. Sohn H, Farrar CR, Hemez FM, Shunk DD, Stinemates DW, Nadler BR, Czarnecki JJ (2003) A review of structural health monitoring literature: 1996–2001 Los Alamos National Laboratory, USAGoogle Scholar
  45. Sridhar R, Chakraborty A, Gopalakrishnan S (2006) Wave propagation analysis in anisotropic and inhomogeneous uncracked and cracked structures using pseudospectral finite element method international. Journal of Solids and Structures 43:4997–5031CrossRefzbMATHGoogle Scholar
  46. Sukumar N, Chopp DL, Moës N, Belytschko T (2001) Modeling holes and inclusions by level sets in the extended finite-element method. Comput Methods Appl Mech Eng 190:6183–6200MathSciNetCrossRefzbMATHGoogle Scholar
  47. Sun H, Waisman H, Betti R (2013) Nondestructive identification of multiple flaws using XFEM and a topologically adapting artificial bee colony algorithm. Int J Numer Methods Eng 95:871–900MathSciNetCrossRefzbMATHGoogle Scholar
  48. Sun H, Waisman H, Betti R (2014a) A multiscale flaw detection algorithm based on XFEM. Int J Numer Methods Eng 100:477–503CrossRefzbMATHGoogle Scholar
  49. Sun H, Waisman H, Betti R (2014b) A two-scale algorithm for detection of multiple flaws in structures modeled with XFEM. In: SPIE Smart Structures and Materials+ Nondestructive Evaluation and Health Monitoring. International Society for Optics and Photonics, pp 906322–906322-906314Google Scholar
  50. Sun H, Waisman H, Betti R (2016) A sweeping window method for detection of flaws using an explicit dynamic XFEM and absorbing boundary layers international. Journal for Numerical Methods in Engineering 105:1014–1040MathSciNetCrossRefGoogle Scholar
  51. Urban M, Alizad A, Aquino W, Greenleaf J, Fatemi M (2011) A review of vibro-acoustography and its applications in medicine. Current Medical Imaging Reviews 7:350–359CrossRefGoogle Scholar
  52. Waisman H, Chatzi E, Smyth AW (2010) Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms. Int J Numer Methods Eng 82:303–328zbMATHGoogle Scholar
  53. Wang L, Wang X, Li Y, Lin G, Qiu Z (2016) Structural time-dependent reliability assessment of the vibration active control system with unknown-but-bounded uncertainties. Struct Control Health Monit. doi: 10.1002/stc.1965
  54. Yan G, Sun H, Waisman H (2015) A guided Bayesian inference approach for detection of multiple flaws in structures using the extended finite element method. Comput Struct 152:27–44CrossRefGoogle Scholar
  55. Yuan H, Guzina BB (2012) Topological sensitivity for vibro-acoustography applications. Wave Motion 49:765–781MathSciNetCrossRefzbMATHGoogle Scholar
  56. Zakian P, Khaji N (2016a) A novel stochastic-spectral finite element method for analysis of elastodynamic problems in the time domain. Meccanica 51:893–920. doi: 10.1007/s11012-015-0242-9 MathSciNetCrossRefzbMATHGoogle Scholar
  57. Zakian P, Khaji N (2016b) Spectral finite element simulation of seismic wave propagation and fault dislocation in elastic media. Asian Journal of Civil Engineering (BHRC) 17:1189–1213Google Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Faculty of Civil and Environmental EngineeringTarbiat Modares UniversityTehranIran

Personalised recommendations