KSCE Journal of Civil Engineering

, Volume 23, Issue 2, pp 678–690 | Cite as

Time-domain Spectral Element Method for Impact Identification of Frame Structures using Enhanced GAs

  • Zexing Yu
  • Seyed Hossein MahdaviEmail author
  • Chao Xu
Structural Engineering


This paper develops an Enhanced Genetic Algorithm (GA) strategy in conjunction with a time-domain Spectral Finite Element Method (SFEM) for impact identification of framed structures. For this purpose, a spatial truss spectral element is proposed for impact response simulation. In this regard, Gauss-Lobatto-Legendre quadrature rules and points configuration are adopted to construct a diagonal matrix and to gain an optimum computational demands. A decimal and a mixed GA coding system are implemented to locate and re-construct the impact features, respectively. An improved GA-based fitness assessment is designed to significantly accelerate the convergence rate of the optimization strategy. The impact identification of two frame structures is investigated taking into account the influence of externally applied loading. It is concluded that, the proposed mixed coding GA strategy effectively overcomes the main drawbacks of classical GA approach. The developed SFEM is superior to conventional FEM because of its high order interpolation and integration rules. For large structures, impact localization is successfully accomplished very fast, which provides the excellent ability in developing an on-line health monitoring system. It is included that, the robustness of the proposed SFEM lies on the considerably higher computational efficiency in achieving the most accurate results with the less computational costs.


impact identification spectral finite element enhanced genetic algorithms 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Douma, J., Niederleithinger, E., and Snieder, R. (2015). “Locating events using time reversal and deconvolution: Experimental application and analysis.” Journal of Nondestructive Evaluation, Vol. 34, No. 2, pp. 1–9, DOI: 10.1007/s10921-015-0276-x.Google Scholar
  2. Doyle, J. F. (1994). “A genetic algorithm for determining the location of structural impacts.” Experimental Mechanics, Vol. 34, No. 1, pp. 37–44, DOI: 10.1007/BF02328440.MathSciNetGoogle Scholar
  3. Dziendzikowski, M., Dragan, K., and Katunin, A. (2017). “Localizing impact damage of composite structures with modified RAPID algorithm and non-circular PZT arrays.” Archives of Civil & Mechanical Engineering, Vol. 17, No. 1, pp. 178–187, DOI: 10.1016/j.acme.2016.09.005.Google Scholar
  4. Gaul, L. and Hurlebaus, S. (1998). “Identification of the impact location on a plate using wavelets.” Mechanical Systems & Signal Processing, Vol. 12, No. 6, pp. 783–795, DOI: 10.1006/mssp.1998.0163.Google Scholar
  5. Ge, L., Wang, X., and Wang, F. (2014). “Accurate modeling of PZTinduced Lamb wave propagation in structures by using a novel spectral finite element method.” Smart Materials & Structures, Vol. 23, No. 9, pp. 095018, DOI: 10.1088/0964-1726123/91095018Google Scholar
  6. Ghajari, M., Sharifkhodaei, Z., Aliabadi, M. H., and Apicella, A. (2013). “Identification of impact force for smart composite stiffened panels.” Smart Materials & Structures, Vol. 22, No. 8, pp. 085014, DOI: 10.1088/0964-1726/22/8/085014.Google Scholar
  7. Ha, S. and Chang, F. K. (2010). “Optimizing a spectral element for modeling PZT-induced Lamb wave propagation in thin plates.” Smart Materials & Structures, Vol. 19, No. 1, pp. 015015, DOI: 10.1088/0964-1726/19/1/015015.Google Scholar
  8. Haywood, J., Coverley, P. T., Staszewski, W. J., and Worden, K. (2005). “An automatic impact monitor for a composite panel employing smart sensor technology.” Smart Material Structures, Vol. 14, No. 1, pp. 265, DOI: 10.1088/0964-1726/14/1/027.Google Scholar
  9. Hollandsworth, P. E. and Busby, H. R. (1989). “Impact force identification using the general inverse technique.” International Journal of Impact Engineering, Vol. 8, No. 4, pp. 315–322, DOI: 10.1016/0734-743X (89)90020-1.Google Scholar
  10. Hossain, M. S., Zhi, C. O., Ng, S. C., Ismail, Z., and Khoo, S. Y. (2017). “Inverse identification of impact locations using multilayer perceptron with effective time-domain feature.” Inverse Problems in Science & Engineering, Vol. 26, No. 3, pp. 1–19, DOI: 10.1080/17415977.2017.1316496.Google Scholar
  11. Katunin, A. (2015). “Stone impact damage identification in composite plates using modal data and quincunx wavelet analysis.” Archives of Civil & Mechanical Engineering, Vol. 15, No. 1, pp. 251–261, DOI: 10.1016/j.acme.2014.01.010.MathSciNetGoogle Scholar
  12. Kazemi, M. and Hematiyan, M. R. (2009). “An efficient inverse method for identification of the location and time history of an elastic impact load.” Journal of Testing & Evaluation, Vol. 37, No. 6, pp. 545–555, DOI: 10.1520/JTE102179.Google Scholar
  13. Khoo, S. Y., Ismail, Z., Kong, K. K., Ong, Z. C., Noroozi, S., Chong, W. T., and Rahman, A. G. A. (2014). “Impact force identification with pseudo-inverse method on a lightweight structure for under-determined, even-determined and over-determined cases.” International Journal of Impact Engineering, Vol. 63, pp. 52–62, DOI: 10.1016/j.ijimpeng.2013.08.005.Google Scholar
  14. Kudela, P., Krawczuk, M., and Ostachowicz, W. (2007). “Wave propagation modelling in 1D structures using spectral finite elements.” Journal of Sound & Vibration, Vol. 300, Nos. 1–2, pp. 88–100, DOI: 10.1016/j.jsv.2006.07.031.zbMATHGoogle Scholar
  15. Mahdavi, S. H. and Razak, H. A. (2016). “Optimal sensor placement for time-domain identification using a wavelet-based genetic algorithm.” Smart Materials & Structures, Vol. 25, No. 6, pp. 065006, DOI: 10.1088/0964-1726/25/6/065006.Google Scholar
  16. Martin, M. T. and Doyle, J. F. (1996). “Impact force location in frame structures.” International Journal of Impact Engineering, Vol. 18, No. 1, pp. 79–97, DOI: 10.1016/0734—743X(95)00016-9.Google Scholar
  17. Ostachowicz, W., Kudela, P., Krawczuk, M., and Zak, A. (2011). Guided waves in structures for SHM, Wiley & Sons, New Delhi. pp. 47–78.Google Scholar
  18. Patera, A. T. (1984). “A spectral element method for fluid dynamics: Laminar flow in a channel expansion.” Journal of Computational Physics, Vol. 54, No. 3, pp. 468–488, DOI: 10.1016/0021-9991(84) 90128–1.zbMATHGoogle Scholar
  19. Perry, M. J., Koh, C. G., and Choo, Y. S. (2006). “Modified genetic algorithm strategy for structural identification.” Computers & Structures, Vol. 84, Nos. 8–9, pp. 529–540, DOI: 10.1016/j.compstruc.2005.11.008.Google Scholar
  20. Sanchez, N., Ortizbernardin, A., and Meruane, V. (2016). “A novel impact identification algorithm based on a linear approximation with maximum entropy.” Smart Materials & Structures, Vol. 25, No. 9, pp. 15, DOI: 10.1088/0964-1726/25/9/095050.Google Scholar
  21. Xu, Q. (2013). “Impact detection and location for a plate structure using least squares support vector machines.” Structural Health Monitoring, Vol. 13, No. 1, pp. 5–18, DOI: 10.1177/1475921713495083.Google Scholar
  22. Xu, C., Wu, M. Z., and Hamdaoui, M. (2016). “Mixed integer multiobjective optimization of composite structures with frequencydependent interleaved viscoelastic damping layers.” Computers & Structures, Vol. 172, pp. 81–92, DOI: 10.1016/j.compstruc.2016.05.006.Google Scholar
  23. Xu, C. and Yu, Z. X. (2017). “Numerical simulation of elastic wave propagation in functionally graded cylinders using time-domain spectral finite element method.” Advances in Mechanical Engineering, Vol. 9, No. 11, pp. 1–17, DOI: 10.1177/1687814017734457.Google Scholar
  24. Yan, G. and Zhou, L. (2009). “Impact load identification of composite structure using genetic algorithms.” Journal of Sound & Vibration, Vol. 319, Nos. 3–5, pp. 869–884, DOI: 10.1016/j.jsv.2008.06.051.Google Scholar

Copyright information

© Korean Society of Civil Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of AstronauticsNorthwestern Polytechnic UniversityXi’anChina

Personalised recommendations