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Published in: Mechanics of Composite Materials 2/2022

21-05-2022

Delamination Quantification by Haar Wavelets and Machine Learning

Authors: L. Jaanuska, H. Hein

Published in: Mechanics of Composite Materials | Issue 2/2022

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Abstract

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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Literature
1.
go back to reference 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). 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).
2.
go back to reference 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).CrossRef 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).CrossRef
3.
go back to reference 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).CrossRef 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).CrossRef
4.
go back to reference 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). 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.
go back to reference R. L. Ramkumar, S.V. Kulkarni, and B. Pipes, “Free vibration frequencies of a delaminated beam”, 34th Annual Technical Conference Proceedings, 1-5 (1979). 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.
go back to reference J. T. S. Wang, Y. Liu, and J. A. Gibby, “Vibration of split beams”, Journal of Sound and Vibration, 84, 491-502 (1982).CrossRef J. T. S. Wang, Y. Liu, and J. A. Gibby, “Vibration of split beams”, Journal of Sound and Vibration, 84, 491-502 (1982).CrossRef
7.
go back to reference P. Mujumdar and S. Suryanarayan, “Flexural vibration of beams with delaminations,” Journal of Sound and Vibration, 125, 441-461 (1988).CrossRef P. Mujumdar and S. Suryanarayan, “Flexural vibration of beams with delaminations,” Journal of Sound and Vibration, 125, 441-461 (1988).CrossRef
8.
go back to reference 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).CrossRef 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).CrossRef
9.
go back to reference 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).CrossRef 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).CrossRef
10.
go back to reference 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). 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).
11.
go back to reference 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).CrossRef 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).CrossRef
12.
go back to reference A. Pupurs, M. Loukil, and J. Varna, “Bending stiffness of damaged cross-ply laminates,” Mech. Compos. Mater., 57, No. 1, 31-46 (2021).CrossRef A. Pupurs, M. Loukil, and J. Varna, “Bending stiffness of damaged cross-ply laminates,” Mech. Compos. Mater., 57, No. 1, 31-46 (2021).CrossRef
13.
go back to reference 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).CrossRef 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).CrossRef
14.
go back to reference D. Chakraborty, “Artificial neural network based delamination prediction in laminated composites,” Materials and Design, 26, 1-7 (2005).CrossRef D. Chakraborty, “Artificial neural network based delamination prediction in laminated composites,” Materials and Design, 26, 1-7 (2005).CrossRef
15.
go back to reference P. Adams, “Damage detection in composite structures using piezoelectric materials (and neural net),” Smart Material Structures, 3, 318-328 (1994).CrossRef P. Adams, “Damage detection in composite structures using piezoelectric materials (and neural net),” Smart Material Structures, 3, 318-328 (1994).CrossRef
16.
go back to reference M. Krawczuk and W. Ostachowicz, “Identification of delamination in composite beams by genetic algorithm,” Science and Engineering of Composite Materials, 10, 147-155 (2002).CrossRef M. Krawczuk and W. Ostachowicz, “Identification of delamination in composite beams by genetic algorithm,” Science and Engineering of Composite Materials, 10, 147-155 (2002).CrossRef
17.
go back to reference 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).CrossRef 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).CrossRef
18.
go back to reference 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).CrossRef 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).CrossRef
19.
go back to reference 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).CrossRef 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).CrossRef
20.
go back to reference 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).CrossRef 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).CrossRef
21.
go back to reference C. Chui, Wavelets: a Mathematical Tool for Signal Analysis, Society for Industrial and Applied Mathematics, USA (1997).CrossRef C. Chui, Wavelets: a Mathematical Tool for Signal Analysis, Society for Industrial and Applied Mathematics, USA (1997).CrossRef
22.
go back to reference 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).CrossRef 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).CrossRef
23.
go back to reference 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).CrossRef 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).CrossRef
24.
go back to reference Ü. Lepik, “Numerical solution of differential equations using Haar wavelets,” Mathematics and Computers in Simulation, 68, No. 2, 127-143 (2005).CrossRef Ü. Lepik, “Numerical solution of differential equations using Haar wavelets,” Mathematics and Computers in Simulation, 68, No. 2, 127-143 (2005).CrossRef
25.
go back to reference 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).CrossRef 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).CrossRef
26.
go back to reference 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).CrossRef 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).CrossRef
27.
go back to reference 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).CrossRef 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).CrossRef
28.
go back to reference 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).CrossRef 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).CrossRef
29.
go back to reference 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).CrossRef 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).CrossRef
30.
go back to reference 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).CrossRef 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).CrossRef
31.
go back to reference 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).CrossRef 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).CrossRef
32.
go back to reference H. Luo and S. Hanagud, “Dynamics of delaminated beams,” International Journal of Solids and Structures, 37, 1501-1519 (2000).CrossRef H. Luo and S. Hanagud, “Dynamics of delaminated beams,” International Journal of Solids and Structures, 37, 1501-1519 (2000).CrossRef
33.
go back to reference 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).CrossRef 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).CrossRef
34.
go back to reference 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).CrossRef 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).CrossRef
35.
go back to reference 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). 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).
36.
go back to reference 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).CrossRef 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).CrossRef
Metadata
Title
Delamination Quantification by Haar Wavelets and Machine Learning
Authors
L. Jaanuska
H. Hein
Publication date
21-05-2022
Publisher
Springer US
Published in
Mechanics of Composite Materials / Issue 2/2022
Print ISSN: 0191-5665
Electronic ISSN: 1573-8922
DOI
https://doi.org/10.1007/s11029-022-10025-2

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