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Delamination Quantification by Haar Wavelets and Machine Learning

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Mechanics of Composite Materials Aims and scope

The inverse problem on determining the location of a delamination and its severity in composite uniform beams is considered. It is shown that the problem can be solved in terms of delamination-induced changes in the natural frequencies or mode shapes. Delaminations are quantified by the artificial neural networks or random forests. The machine learning methods can predict the delamination status based on parameters of the natural frequency or the Haar wavelet transform coefficients derived from the first mode shape. Simulation studies showed that the combined approach of natural frequencies, Haar wavelets, and random forests produced accurate predictions. The results presented in this article can help one to understand the behavior of more complex structures under similar conditions.

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References

  1. R. A. Patil and M.V. Kavade, “Delamination detection in composite sandwich beam: experimental study,” Journal of Advances in Science and Technology, 13, No. 1, 199-204 (2017).

    Google Scholar 

  2. Z. Yang, L. Wang, H. Wang, et al., “Damage detection in composite structures using vibration response under stochastic excitation,” Journal of Sound and Vibration, 325, No. 45, 755-768 (2009).

    Article  Google Scholar 

  3. L. H. Yam, Y. J. Yan, and J. S. Jiang, “Vibration-based damage detection for composite structures using wavelet transform and neural network identification,” Composite Structures, 60, No. 4, 403-412 (2003).

    Article  Google Scholar 

  4. A. Tuck and V. Kekoc, “KC–30A structural health monitoring system verification and validation; MRH 90 HUMS,” AIAC14 Fourteenth Australian International Aerospace Congress, 3-18 (2011).

  5. R. L. Ramkumar, S.V. Kulkarni, and B. Pipes, “Free vibration frequencies of a delaminated beam”, 34th Annual Technical Conference Proceedings, 1-5 (1979).

  6. J. T. S. Wang, Y. Liu, and J. A. Gibby, “Vibration of split beams”, Journal of Sound and Vibration, 84, 491-502 (1982).

    Article  Google Scholar 

  7. P. Mujumdar and S. Suryanarayan, “Flexural vibration of beams with delaminations,” Journal of Sound and Vibration, 125, 441-461 (1988).

    Article  Google Scholar 

  8. T. Nagashima and H. Suemasu, “X-FEM analyses of a thin-walled composite shell structure with a delamination,” Computers and Structures, 88, 549-557 (2010).

    Article  Google Scholar 

  9. S. K. Kumar, R. Ganguli, and D. Harursampath, “Partial delamination modeling in composite beams using a finite element method,” Finite Elements in Analysis and Design, 76, 1-12 (2013).

    Article  Google Scholar 

  10. C. Gowda, N. Rajanna, and N. G. S. Udupa, “Investigating the effects of delamination location and size on the vibration behaviour of laminated composite beams,” Materials Today, 4, 10944-10951 (2017).

    Google Scholar 

  11. D. Y. Yin, C. F. Zhu, X. C. Chen et al. “Finite-element analysis and an experimental study into the water jet reaming process of carbon-carbon composites,” Mech. Compos. Mater., 57, No. 2, 257-268 (2021).

    Article  CAS  Google Scholar 

  12. A. Pupurs, M. Loukil, and J. Varna, “Bending stiffness of damaged cross-ply laminates,” Mech. Compos. Mater., 57, No. 1, 31-46 (2021).

    Article  CAS  Google Scholar 

  13. A. Okafor, K. Chandrashekhara, and Y. P. Jiang, “Delamination prediction in composite beams with built-in piezoelectric devices using modal analysis and neural network,” Smart Materials and Structures, 5, 338 (1999).

    Article  Google Scholar 

  14. D. Chakraborty, “Artificial neural network based delamination prediction in laminated composites,” Materials and Design, 26, 1-7 (2005).

    Article  CAS  Google Scholar 

  15. P. Adams, “Damage detection in composite structures using piezoelectric materials (and neural net),” Smart Material Structures, 3, 318-328 (1994).

    Article  Google Scholar 

  16. M. Krawczuk and W. Ostachowicz, “Identification of delamination in composite beams by genetic algorithm,” Science and Engineering of Composite Materials, 10, 147-155 (2002).

    Article  CAS  Google Scholar 

  17. A. Nag, D. Mahapatra, and S. Gopalakrishnan, “Identification of delamination in composite beams using spectral estimation and a genetic algorithm,” Smart Materials and Structures, 11, 899 (2002).

    Article  Google Scholar 

  18. Z.Z. Wang, J. Zhao, X. Ma et al., “Numerical simulation of progressive delamination in composite laminates under mode I and mode II loadings,” Mech. Compos. Mater., 56, No. 6, 735-746 (2021).

    Article  Google Scholar 

  19. M. Rucka and K. Wilde, “Application of continuous wavelet transform in vibration based damage detection method for beams and plates,” Journal of Sound and Vibration, 297, No. 35, 536-550 (2006).

    Article  Google Scholar 

  20. S. Zheng, Z. Li, and H. Wang, “Research on delamination monitoring for composite structures based on HHGAWNN,” Applied Soft Computing, 9, No. 3, 918-923 (2009).

    Article  Google Scholar 

  21. C. Chui, Wavelets: a Mathematical Tool for Signal Analysis, Society for Industrial and Applied Mathematics, USA (1997).

    Book  Google Scholar 

  22. C.K. Chen and C.H. Hsiao, “Haar wavelet method for solving lumped and distributed-parameter systems,” Control Theory and Applications, 144, No. 1, 87-94 (1997).

    Article  Google Scholar 

  23. C.-H. Hsiao and W.-J. Wang, “State analysis of time-varying singular nonlinear systems via Haar wavelets,” Mathematics and Computers in Simulation, 51, No. 12, 91-100 (1999).

    Article  Google Scholar 

  24. Ü. Lepik, “Numerical solution of differential equations using Haar wavelets,” Mathematics and Computers in Simulation, 68, No. 2, 127-143 (2005).

    Article  Google Scholar 

  25. M. Ratas, A. Salupere, and J. Majak, “Solving nonlinear PDEs using the higher order Haar wavelet method on nonuniform and adaptive grids,” Mathematical Modelling and Analysis, 1, No. 26, 147-169 (2021).

    Article  Google Scholar 

  26. M. Sorrenti, M. Di Sciuva, J. Majak, and F. Auriemma, “Static response and buckling loads of multilayered composite beams using the refined Zigzag theory and higher-order Haar wavelet method,” Mech. Compos. Mater., 57, No. 1, 1-18 (2021).

    Article  CAS  Google Scholar 

  27. Z. Chun and Z. Zheng, “Three-dimensional analysis of functionally graded plate based on the Haar wavelet method,” Acta Mechanica Solida Sinica, 20, No. 2, 95-102 (2007).

    Article  Google Scholar 

  28. B. Shvartsman and J. Majak, “Numerical method for stability analysis of functionally graded beams on elastic foundation,” Applied Mathematical Modelling, 40, No. 5, 3713-3719 (2016).

    Article  Google Scholar 

  29. M. Cao, L. Ye, L. Zhou, et al., “Sensitivity of fundamental mode shape and static deflection for damage identification in cantilever beams,” Mechanical Systems and Signal Processing, 25, 630-643 (2011).

    Article  Google Scholar 

  30. D. Shu and C. N. Della, “Free vibration analysis of composite beams with two non-overlapping delaminations,” International Journal of Mechanical Sciences, 46, No. 4, 509-526 (2004).

    Article  Google Scholar 

  31. M.-H. H. Shen and C. Pierre, “Natural modes of Bernoulli–Euler beams with symmetric cracks,” Journal of Sound and Vibration, 138, No. 1, 115-134 (1990).

    Article  Google Scholar 

  32. H. Luo and S. Hanagud, “Dynamics of delaminated beams,” International Journal of Solids and Structures, 37, 1501-1519 (2000).

    Article  Google Scholar 

  33. H. Hein and L. Feklistova, “Free vibrations of non-uniform and axially functionally graded beams using Haar wavelets,” Engineering Structures, 33, No. 12, 3696 - 3701(2011).

    Article  Google Scholar 

  34. H. Hein and L. Feklistova, “Computationally efficient delamination detection in composite beams using Haar wavelets,” Mechanical Systems and Signal Processing, 25, No. 6, 2257-2270 (2011).

    Article  Google Scholar 

  35. L. Feklistova and H. Hein, “Delamination identification using machine learning methods and Haar wavelets,” Computer Assisted Methods in Engineering and Science, 19, No. 4, 351-360 (2012).

    Google Scholar 

  36. H. Mustafidah, S. Hartati, and A. Harjoko, “Selection of most appropriate backpropagation training algorithm in data pattern recognition,” International Journal of Computer Trends and Technology, 14, 92-95 (2014).

    Article  Google Scholar 

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Authors and Affiliations

  1. University of Tartu, Institute of Computer Science, Narva mnt 18, 51009, Tartu, Estonia

    L. Jaanuska & H. Hein

Authors
  1. L. Jaanuska
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  2. H. Hein
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Correspondence to L. Jaanuska.

Additional information

Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 58, No. 2, pp. 353-368, March-April, 2022. Russian DOI: https://doi.org/10.22364/mkm.58.2.07.

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Jaanuska, L., Hein, H. Delamination Quantification by Haar Wavelets and Machine Learning. Mech Compos Mater 58, 249–260 (2022). https://doi.org/10.1007/s11029-022-10025-2

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  • DOI: https://doi.org/10.1007/s11029-022-10025-2

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