Prediction of Ultrasonic Guided Wave Propagation in Fluid–Structure and Their Interface under Uncertainty Using Machine Learning
Publication: Journal of Engineering Mechanics
Volume 148, Issue 3
Abstract
Structural health monitoring (SHM) systems use nondestructive testing principles for damage identification. As part of SHM, the propagation of ultrasonic guided waves (UGW) is tracked and analyzed for the changes in the associated wave pattern. These changes help identify the location of a structural damage, if any. We advance the existing research by accounting for uncertainty in the material and geometric properties of a structure. The physics model employed in this study comprises a monolithically coupled system of elastic and acoustic wave equations, known as the wave propagation in fluid–structure and their interface (WpFSI) problem. Because the numerical simulation of the WpFSI problem becomes computationally extremely expensive for many realizations of the uncertainty, we developed an efficient algorithm in this work that employs machine learning techniques like Gaussian process regression and convolutional neural networks to predict UGW propagation in a fluid–structure and their interface under uncertainty. First, a small set of training images for different realizations of the uncertain parameters of the inclusion inside the structure is generated using the computationally costly physics model. Next, Gaussian processes trained with these images are used for predicting the propagated wave with convolutional neural networks for further enhancement to produce high-quality images of the wave patterns for new realizations of the uncertainty. The results indicate that the proposed approach provides an accurate prediction for the WpFSI problem in the presence of uncertainty.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Trained Gaussian processes and neural network that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This paper describes the technical results and analysis of the research conducted during the visit of the corresponding author to Smead Aerospace Engineering Sciences Department, University of Colorado, Boulder, CO, USA. The author would like to acknowledge his host, Prof. Kurt Maute, and support from the Helmut Schmidt University—University of the Federal Armed Forces, Hamburg, Germany. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the Federal Armed Forces of Germany.
References
Adam, P., G. Sam, C. Soumith, C. Gregory, Y. Edward, D. Zachary, L. Zeming, D. Alban, A. Luca, and L. Adam. 2017. “Automatic differentiation in PyTorch.” In Proc., Neural Information Processing Systems. London: Neural Information Processing System Foundation.
Agustsson, E., and R. Timofte. 2017. “NTIRE 2017 challenge on single image super-resolution: Dataset and study.” In Proc., IEEE Conf. on Computer Vision and Pattern Recognition (CVPR) Workshops. New York: IEEE.
Ahn, N., B. Kang, and K.-A. Sohn. 2018. “Fast, accurate, and lightweight super-resolution with cascading residual network.” In Proc., European Conference on Computer Vision (ECCV), 252–268. New York: Springer.
Baker, N., et al. 2019. Workshop report on basic research needs for scientific machine learning: Core technologies for artificial intelligence. Washington, DC: USDOE Office of Science.
Bangerth, W., R. Hartmann, and G. Kanschat. 2007. “deal.II: A general purpose object-oriented finite element library.” ACM Trans. Math. Software 33 (4): 1–27. https://doi.org/10.1145/1268776.1268779.
Bottou, L., F. E. Curtis, and J. Nocedal. 2018. “Optimization methods for large-scale machine learning.” SIAM Rev. 60 (2): 223–311. https://doi.org/10.1137/16M1080173.
Ciarlet, P. G. 1978. Vol. 4 of The finite element method for elliptic problems. Amsterdam, Netherlands: North-Holland.
Ciarlet, P. G., and P. A. Raviart. 1974. “A mixed finite element method for the biharmonic equation.” In Mathematical aspects of finite elements in partial differential equations, edited by C. de Boor, 125–145. Cambridge: Academic Press.
Davis, T. A., and I. S. Duff. 1997. “An unsymmetric-pattern multifrontal method for sparse LU factorization.” SIAM J. Matrix Anal. Appl. 18 (1): 140–158. https://doi.org/10.1137/S0895479894246905.
De, S. 2021. “Uncertainty quantification of locally nonlinear dynamical systems using neural networks.” J. Comput. Civ. Eng. 35 (4): 04021009. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000965.
De, S., J. Britton, M. Reynolds, R. Skinner, K. Jansen, and A. Doostan. 2020a. “On transfer learning of neural networks using bi-fidelity data for uncertainty propagation.” Int. J. Uncertainty Quantif. 10 (6): 543–573. https://doi.org/10.1615/Int.J.UncertaintyQuantification.2020033267.
De, S., and A. Doostan. 2021. “Neural network training using ℓ1-regularization and bi-fidelity data.” Preprint, submitted May 27, 2021. http://arxiv.org/abs/13011.
De, S., J. Hampton, K. Maute, and A. Doostan. 2020b. “Topology optimization under uncertainty using a stochastic gradient-based approach.” Struct. Multidiscip. Optim. 62 (5): 2255–2278. https://doi.org/10.1007/s00158-020-02599-z.
De, S., K. Maute, and A. Doostan. 2020c. “Bi-fidelity stochastic gradient descent for structural optimization under uncertainty.” Comput. Mech. 66 (4): 745–771. https://doi.org/10.1007/s00466-020-01870-w.
Deraemaeker, A., and K. Worden, eds. 2010. New trends in vibration based structural health monitoring. New York: Springer.
Dong, C., C. C. Loy, K. He, and X. Tang. 2014. “Learning a deep convolutional network for image super-resolution.” In Proc., European Conf. on Computer Vision, 184–199. New York: Springer.
Dong, C., C. C. Loy, K. He, and X. Tang. 2015. “Image super-resolution using deep convolutional networks.” IEEE Trans. Pattern Anal. Mach. Intell. 38 (2): 295–307. https://doi.org/10.1109/TPAMI.2015.2439281.
Ebna Hai, B. S. M. 2017. “Finite element approximation of ultrasonic wave propagation under fluid-structure interaction for structural health monitoring systems.” Ph.D. thesis, Faculty of Mechanical Engineering, Helmut Schmidt Univ.
Ebna Hai, B. S. M., and M. Bause. 2017. “Finite element approximation of fluid-structure interaction with coupled wave propagation.” Proc. Appl. Math. Mech. 17 (1): 511–512. https://doi.org/10.1002/pamm.201710225.
Ebna Hai, B. S. M., and M. Bause. 2019. “Numerical study and comparison of alternative time discretization schemes for an ultrasonic guided wave propagation problem coupled with fluid–structure interaction.” Comput. Math. Appl. 78 (9): 2867–2885. https://doi.org/10.1016/j.camwa.2019.01.009.
Ebna Hai, B. S. M., M. Bause, and P. Kuberry. 2019a. “Modeling and simulation of ultrasonic guided waves propagation in the fluid-structure domain by a monolithic approach.” J. Fluids Struct. 88 (Jul): 100–121. https://doi.org/10.1016/j.jfluidstructs.2019.04.014.
Ebna Hai, B. S. M., M. Bause, and P. A. Kuberry. 2019b. “Modeling concept and numerical simulation of ultrasonic wave propagation in a moving fluid-structure domain based on a monolithic approach.” Appl. Math. Modell. 75 (Nov): 916–939. https://doi.org/10.1016/j.apm.2019.07.007.
Ebna Hai, B. S. M., S. De, and M. Bause. 2021. Automatic differentiation technique and study of uncertainties effect on the coupled waves propagation problem in a fluid-composite structure domain. Hamburg, Germany: Faculty of Mechanical Engineering, Helmut Schmidt University-University of the Federal Armed Forces Hamburg.
Emmerich, M. T., K. C. Giannakoglou, and B. Naujoks. 2006. “Single- and multiobjective evolutionary optimization assisted by Gaussian random field metamodels.” IEEE Trans. Evol. Comput. 10 (4): 421–439. https://doi.org/10.1109/TEVC.2005.859463.
Forrester, A., A. Sobester, and A. Keane. 2008. Engineering design via surrogate modelling: A practical guide. Hoboken, NJ: Wiley.
Gharaibeh, Y., R. Sanderson, P. Mudge, C. Ennaceur, and W. Balachandran. 2011. “Investigation of the behaviour of selected ultrasonic guided wave modes to inspect rails for long-range testing and monitoring.” Proc. Inst. Mech. Eng., Part F: J. Rail Rapid Transit. 225 (3): 311–324. https://doi.org/10.1243/09544097JRRT413.
Giurgiutiu, V. 2014. Structural health monitoring with piezoelectric wafer active sensors. Amsterdam, Netherlands: Academic Press.
Goll, C., T. Wick, and W. Wollner. 2017. “DOpElib: Differential equations and optimization environment: A goal oriented software library for solving PDEs and optimization problems with PDEs.” Arch. Numer. Software 5 (2): 1–14. https://doi.org/10.11588/ans.2017.2.11815.
Goodfellow, I., Y. Bengio, and A. Courville. 2016. Deep learning. Cambridge, MA: MIT Press.
Gopalakrishnan, S., M. Ruzzene, and S. Hanagud. 2011. Computational techniques for structural health monitoring. London: Springer.
Gresil, M., A. Poohsai, and N. Chandarana. 2017. “Guided wave propagation and damage detection in composite pipes using piezoelectric sensors.” Procedia Eng. 188: 148–155. https://doi.org/10.1016/j.proeng.2017.04.468.
Hensman, J., N. Fusi, and N. D. Lawrence. 2013. “Gaussian processes for big data.” Preprint, submitted September 26, 2013. http://arxiv.org/abs/1309.6835.
Hinton, G. E., N. Srivastava, A. Krizhevsky, I. Sutskever, and R. R. Salakhutdinov. 2012. “Improving neural networks by preventing co-adaptation of feature detectors.” Preprint, submitted July 3, 2012. http://arxiv.org/abs/1207.0580.
Huang, G., F. Song, and X. Wang. 2010. “Quantitative modeling of coupled piezo-elastodynamic behavior of piezoelectric actuators bonded to an elastic medium for structural health monitoring: A review.” Sensors 10 (4): 3681–3702. https://doi.org/10.3390/s100403681.
Karbhari, V. M. 2013. Non-destructive evaluation (NDE) of polymer matrix composites. Oxford, UK: Woodhead Publishing.
Khurjekar, I. D., and J. B. Harley. 2019. “Accounting for physics uncertainty in ultrasonic wave propagation using deep learning.” Preprint, submitted November 7, 2019. http://arxiv.org/abs/1911.02743.
Kingma, D. P., and J. Ba. 2014. “Adam: A method for stochastic optimization.” Preprint, submitted December 22, 2014. http://arxiv.org/abs/1412.6980.
Koch, P., T. Wagner, M. T. Emmerich, T. Bäck, and W. Konen. 2015. “Efficient multi-criteria optimization on noisy machine learning problems.” Appl. Soft Comput. 29: 357–370. https://doi.org/10.1016/j.asoc.2015.01.005.
Krige, D. G. 1951. “A statistical approach to some basic mine valuation problems on the Witwatersrand.” J. South Afr. Inst. Min. Metall. 52 (6): 119–139.
Lamb, H. 1917. “On waves in an elastic plate.” Proc. Royal Soc. London, Ser. A 93 (648): 114–128. https://doi.org/10.1098/rspa.1917.0008.
Lammering, R., U. Gabbert, M. Sinapius, T. Schuster, and P. Wierach, eds. 2018. Lamb-wave based structural health monitoring in polymer composites. Cham, Switzerland: Springer.
Leckey, C. A., M. D. Rogge, and F. R. Parker. 2014. “Guided waves in anisotropic and quasi-isotropic aerospace composites: Three-dimensional simulation and experiment.” Ultrasonics 54 (1): 385–394. https://doi.org/10.1016/j.ultras.2013.05.007.
Lee, J.-R., J.-K. Jang, and C.-W. Kong. 2014. “Fully noncontact wave propagation imaging in an immersed metallic plate with a crack.” Shock Vib. 2004: 1–8. https://doi.org/10.1155/2014/895693.
Lino, M., C. Cantwell, S. Fotiadis, E. Pignatelli, and A. Bharath. 2020. “Simulating surface wave dynamics with convolutional networks.” Preprint, submitted December 1, 2020. http://arxiv.org/abs/2012.00718.
Luca, A. D., Z. Sharif-Khodaeib, M. H. Aliabadib, and F. Caputo. 2016. “Numerical simulation of the Lamb wave propagation in impacted CFRP laminate.” Procedia Eng. 167: 109–115. https://doi.org/10.1016/j.proeng.2016.11.676.
Melville, J., K. S. Alguri, C. Deemer, and J. B. Harley. 2018. “Structural damage detection using deep learning of ultrasonic guided waves.” In Vol. 1949 of Proc., AIP Conf., 230004. Melville, NY: AIP Publishing LLC.
Mitra, M., and S. Gopalakrishnan. 2016. “Guided wave based structural health monitoring: A review.” Smart Mater. Struct. 25 (5): 053001. https://doi.org/10.1088/0964-1726/25/5/053001.
Miyanawala, T. P., and R. Jaiman. 2018. “A hybrid data-driven deep learning technique for fluid-structure interaction.” Preprint, submitted July 20, 2018. http://arxiv.org/abs/1807.09591.
Moseley, B., A. Markham, and T. Nissen-Meyer. 2018. “Fast approximate simulation of seismic waves with deep learning.” Preprint, submitted December 1, 2020. http://arxiv.org/abs/1807.06873.
Mukhopadhyay, S. C. 2011. New developments in sensing technology for structural health monitoring. Berlin: Springer.
Niezrecki, C., J. Baqersad, and A. Sabato. 2018. “Digital image correlation techniques for NDE and SHM.” In Handbook of advanced non-destructive evaluation. Cham, Switzerland: Springer.
Ostachowicz, W., and J. A. Güemes, eds. 2013. New trends in structural health monitoring. New York: Springer.
Park, B., H. Sohn, C.-M. Yeum, and T. Truong. 2013. “Laser ultrasonic imaging and damage detection for a rotating structure.” Struct. Health Monit. 12 (5–6): 494–506. https://doi.org/10.1177/1475921713507100.
Raghavan, A., and C. E. S. Cesnik. 2007. “Review of guided-wave structural health monitoring.” Shock Vib. Dig. 39 (2): 91–114. https://doi.org/10.1177/0583102406075428.
Raissi, M., and G. E. Karniadakis. 2018. “Hidden physics models: Machine learning of nonlinear partial differential equations.” J. Comput. Phys. 357 (Mar): 125–141. https://doi.org/10.1016/j.jcp.2017.11.039.
Raissi, M., P. Perdikaris, and G. E. Karniadakis. 2017. “Physics informed deep learning (part I): Data-driven solutions of nonlinear partial differential equations.” Preprint, submitted November 28, 2017. http://arxiv.org/abs/1711.10561.
Rasmussen, C. E., and C. K. Williams. 2006. Gaussian processes for machine learning. Cambridge, MA: MIT Press.
Rautela, M., and S. Gopalakrishnan. 2021. “Ultrasonic guided wave based structural damage detection and localization using model assisted convolutional and recurrent neural networks.” Expert Syst. Appl. 167: 114189. https://doi.org/10.1016/j.eswa.2020.114189.
Ren, H., X. Chen, and Y. Chen. 2017. Reliability based aircraft maintenance optimization and applications. London: Academic Press.
Richter, T. 2017. Vol. 118 of Fluid-structure interactions: Models, analysis and finite elements. Cham, Switzerland: Springer.
Rizzo, P., J.-G. Han, and X.-L. Nit. 2010. “Structural health monitoring of immersed structures by means of guided ultrasonic waves.” J. Intell. Mater. Syst. Struct. 21 (14): 1397–1407. https://doi.org/10.1177/1045389X10384170.
Rose, J. L. 2014. Ultrasonic guided waves in solid media. Cambridge, UK: Cambridge University Press.
Salamone, S., I. Bartoli, F. L. D. Scalea, and S. Coccia. 2009. “Guided-wave health monitoring of aircraft composite panels under changing temperature.” J. Intell. Mater. Syst. Struct. 20 (9): 1079–1090. https://doi.org/10.1177/1045389X08101634.
Scalea, F. L. D., and S. Salamone. 2008. “Temperature effects in ultrasonic Lamb wave structural health monitoring systems.” J. Acoust. Soc. Am. 124 (1): 161–174. https://doi.org/10.1121/1.2932071.
Sorteberg, W. E., S. Garasto, A. S. Pouplin, C. D. Cantwell, and A. A. Bharath. 2018. “Approximating the solution to wave propagation using deep neural networks.” Preprint, submitted December 4, 2018. http://arxiv.org/abs/1812.01609.
Stengel, K., A. Glaws, and R. King. 2019. “Physics-informed super resolution of climatological wind and solar resource data.” In Vol. 2019 of AGU fall meeting abstracts, A43E-04. Washington, D.C: American Geophysical Union.
Su, Z., and L. Ye. 2009. Vol. 48 of Processing of Lamb wave signals—Identification of damage using Lamb waves. Applied and computational mechanics. London: Springer.
Sun, J., K. A. Innanen, and C. Huang. 2021. “Physics-guided deep learning for seismic inversion with hybrid training and uncertainty analysis.” Geophysics 86 (3): R303–R317. https://doi.org/10.1190/geo2020-0312.1.
Tai, Y., J. Yang, and X. Liu. 2017. “Image super-resolution via deep recursive residual network.” In Proc., IEEE Conf. on Computer Vision and Pattern Recognition, 3147–3155. New York: IEEE.
Turek, S., and J. Hron. 2006. “Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow.” In Vol. 53 of Fluid-structure interaction, 371–385. New York: Springer.
Wang, G. G., and S. Shan. 2007. “Review of metamodeling techniques in support of engineering design optimization.” J. Mech. Des. 129 (4): 370–380. https://doi.org/10.1115/1.2429697.
Wang, L., and Y. Liu. 2020. “A novel method of distributed dynamic load identification for aircraft structure considering multi-source uncertainties.” Struct. Multidiscip. Optim. 61 (5): 1929–1952. https://doi.org/10.1007/s00158-019-02448-8.
Wang, L., Y. Liu, K. Gu, and T. Wu. 2020. “A radial basis function artificial neural network (RBF ANN) based method for uncertain distributed force reconstruction considering signal noises and material dispersion.” Comput. Methods Appl. Mech. Eng. 364: 112954. https://doi.org/10.1016/j.cma.2020.112954.
Wang, Z., A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli. 2004. “Image quality assessment: From error visibility to structural similarity.” IEEE Trans. Image Process. 13 (4): 600–612. https://doi.org/10.1109/TIP.2003.819861.
Whisenant, M. J., and K. Ekici. 2020. “Galerkin-free technique for the reduced-order modeling of fluid-structure interaction via machine learning.” In AIAA Scitech 2020 Forum. Reston, VA: American Institute of Aeronautics and Astronautics.
Wick, T. 2011a. “Adaptive finite element simulation of fluid-structure interaction with application to heart-valve dynamics.” Ph.D. thesis, Dept. of Mathematics, Univ of Heidelberg.
Wick, T. 2011b. “Fluid-structure interactions using different mesh motion techniques.” Comput. Struct. 89 (13–14): 1456–1467. https://doi.org/10.1016/j.compstruc.2011.02.019.
Wick, T. 2016. “Coupling fluid–structure interaction with phase-field fracture.” J. Comput. Phys. 327: 67–96. https://doi.org/10.1016/j.jcp.2016.09.024.
Willard, J., X. Jia, S. Xu, M. Steinbach, and V. Kumar. 2020. “Integrating physics-based modeling with machine learning: A survey.” Preprint, submitted March 10, 2020. http://arxiv.org/abs/2003.04919.
Yan, F., R. L. Royer Jr., and J. L. Rose. 2009. “Ultrasonic guided wave imaging techniques in structural health monitoring.” J. Intell. Mater. Syst. Struct. 21 (3): 377–384. https://doi.org/10.1177/1045389X09356026.
Yang, W., X. Zhang, Y. Tian, W. Wang, J.-H. Xue, and Q. Liao. 2019. “Deep learning for single image super-resolution: A brief review.” IEEE Trans. Multimedia 21 (12): 3106–3121. https://doi.org/10.1109/TMM.2019.2919431.
Yuan, F.-G. 2016. Structural health monitoring (SHM) in aerospace structures. Duxford, UK: Woodhead Publishing, Elsevier.
Zhang, D., L. Lu, L. Guo, and G. E. Karniadakis. 2019. “Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems.” J. Comput. Phys. 397 (Nov): 108850. https://doi.org/10.1016/j.jcp.2019.07.048.
Zhu, W., Y. Sheng, and Y. Sun. 2017. Wave-dynamics simulation using deep neural networks. Stanford, CA: Stanford Univ.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 148 • Issue 3 • March 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Mar 31, 2021
Accepted: Sep 7, 2021
Published online: Dec 23, 2021
Published in print: Mar 1, 2022
Discussion open until: May 23, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Mikhail V. Golub, Olga V. Doroshenko, Mikhail A. Arsenov, Artem A. Eremin, Yan Gu, Ilya A. Bareiko, Improved Unsupervised Learning Method for Material-Properties Identification Based on Mode Separation of Ultrasonic Guided Waves, Computation, 10.3390/computation10060093, 10, 6, (93), (2022).