Skip to main content
Log in

Improved Stress Estimation with Machine Learning and Ultrasonic Guided Waves

  • Research paper
  • Published:
Experimental Mechanics Aims and scope Submit manuscript

Abstract

Background

Due to the acoustoelastic effect, ultrasonic guided waves have been used to estimate mechanical stress in a cheap and nondestructive fashion. Machine learning has been applied to map complex waveforms to stress estimates, though important aspects to construct and deploy real-time monitoring systems, such as accuracy and hardware consumption, to date, have not been concomitantly explored.

Objective

The goal of the present paper is to propose a data modeling methodology that optimizes accuracy and computational implementation, towards devising the best practices for real-time ultrasonic-based stress estimation.

Methods

We evaluate shallow and deep learning models with dimensionality reduction, which are compared to the most recent work showing overall better results for the approach presented herein both in terms of accuracy and hardware resources consumption. We generated a dataset to evaluate the models on a test rig with a plate measuring (i) ultrasonic guided waves excited by broadband signals and (ii) different stress conditions. The models are created and tested using a Monte-Carlo hold-out procedure with a repeated k-fold randomized hyperparameter search to evaluate their robustness in different stress conditions.

Results

We dramatically improve the current state of the art by proposing and evaluating a more efficient model construction procedure. Results show that by using shallow models and principal component analysis, we were able to improve the model performance in terms of predictive power and inference hardware consumption. Specifically, we obtained an accuracy improvement of about 10% and hardware consumption used for inference smaller in three orders of magnitude when compared to the state-of-the-art reported with deep neural network models.

Conclusions

Results herein depicted impact the way practitioners may proceed for building efficient embedded predictive models for stress estimation using guided waves, enabling more precise, decentralized, and real-time nondestructive monitoring.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Zhao R, Yan R, Chen Z, Mao K, Wang P, Gao RX (2019) Deep learning and its applications to machine health monitoring. Mech Syst Signal Process 115:213–237

    Article  Google Scholar 

  2. Silver D, Huang A, Maddison CJ, Guez A, Sifre L, Van Den Driessche G, Schrittwieser J, Antonoglou I, Panneershelvam V, Lanctot M et al (2016) Mastering the game of go with deep neural networks and tree search. Nature 529(7587):484–489

    Article  Google Scholar 

  3. Lai Z, Mylonas C, Nagarajaiah S, Chatzi E (2021) Structural identification with physics-informed neural ordinary differential equations. J Sound Vib 508

    Article  Google Scholar 

  4. Vieira R, Lambros J (2021) Machine learning neural-network predictions for grain-boundary strain accumulation in a polycrystalline metal. Exp Mech 61(4):627–639

    Article  Google Scholar 

  5. Liu Z, Peng Q, Li X, He C, Wu B (2020) Acoustic emission source localization with generalized regression neural network based on time difference mapping method. Exp Mech 60(5):679–694

    Article  Google Scholar 

  6. Wu R, Kong C, Li K, Zhang D (2016) Real-time digital image correlation for dynamic strain measurement. Exp Mech 56(5):833–843

    Article  Google Scholar 

  7. Zhang X-C, Gong J-G, Xuan F-Z (2021) A deep learning based life prediction method for components under creep, fatigue and creep-fatigue conditions. Int J Fatigue 148

    Article  Google Scholar 

  8. Lim H, Sohn H (2020) Online stress monitoring technique based on lamb-wave measurements and a convolutional neural network under static and dynamic loadings. Exp Mech 60(2):171–179

    Article  Google Scholar 

  9. Hu Z, Tariq S, Zayed T (2021) A comprehensive review of acoustic based leak localization method in pressurized pipelines. Mech Syst Signal Process 161

    Article  Google Scholar 

  10. Bao Y, Chen Z, Wei S, Xu Y, Tang Z, Li H (2019) The state of the art of data science and engineering in structural health monitoring. Engineering 5(2):234–242

    Article  Google Scholar 

  11. Alegre J, Díaz A, Cuesta I, Manso J (2019) Analysis of the influence of the thickness and the hole radius on the calibration coefficients in the hole-drilling method for the determination of non-uniform residual stresses. Exp Mech 59(1):79–94

    Article  Google Scholar 

  12. Wang C, Yu X, Jiang M, Xing Z, Wang C (2021) Numerical and experimental investigation into the evolution and distribution of residual stress in laser transmission welding of PC/Cu/PC. Opt Laser Technol 136

    Article  Google Scholar 

  13. Zhu X, di Scalea FL (2017) Thermal stress measurement in continuous welded rails using the hole-drilling method. Exp Mech 57(1):165–178

    Article  Google Scholar 

  14. Liu G, Liu H, Wei A, Xiao J, Wang P, Li S (2018) A new device for stress monitoring in continuously welded rails using bi-directional strain method. Journal of Modern Transportation 26(3):179–188

    Article  Google Scholar 

  15. Chu T, Ranson W, Sutton MA (1985) Applications of digital-image-correlation techniques to experimental mechanics. Exp Mech 25(3):232–244

    Article  Google Scholar 

  16. Wang W, Xu C, Jin H, Meng S, Zhang Y, Xie W (2017) Measurement of high temperature full-field strain up to 2000 \(^\circ\)c using digital image correlation. Measur Sci Tech 28(3):035007

  17. Hughes JM, Vidler J, Ng C-T, Khanna A, Mohabuth M, Rose LF, Kotousov A (2019) Comparative evaluation of in situ stress monitoring with rayleigh waves. Struct Health Monit 18(1):205–215

    Article  Google Scholar 

  18. Li Z, He J, Teng J, Huang Q, Wang Y (2019) Absolute stress measurement of structural steel members with ultrasonic shear-wave spectral analysis method. Struct Health Monit 18(1):216–231

    Article  Google Scholar 

  19. Mohabuth M, Kotousov A, Ng C-T (2016) Effect of uniaxial stress on the propagation of higher-order lamb wave modes. Int J Non-Linear Mech 86:104–111

    Article  Google Scholar 

  20. Wang W, Xu C, Zhang Y, Zhou Y, Meng S, Deng Y (2018) An improved ultrasonic method for plane stress measurement using critically refracted longitudinal waves. NDT & E International 99:117–122

    Article  Google Scholar 

  21. Mishakin VV, Dixon S, Potter MDG (2006) The use of wide band ultrasonic signals to estimate the stress condition of materials. J Phys D: Appl Phys 39(21):4681–4687

    Article  Google Scholar 

  22. Hughes D, Kelly J (1953) Second-order elastic deformation of solids. Phys Rev 92(5):1145–1149

    Article  MATH  Google Scholar 

  23. Pao Y, Sachse W, Fukuoka H (1984) Acoustoelasticity and ultrasonic measurements of residual stresses. Phys. Acoust. 17:61–143

    Google Scholar 

  24. Rose JL (2014) Ultrasonic Guided waves in solid media. Cambridge University Press

  25. Gandhi N, Michaels JE, Lee SJ (2012) Acoustoelastic lamb wave propagation in biaxially stressed plates. The Journal of the Acoustical Society of America 132(3):1284–1293

    Article  Google Scholar 

  26. Kubrusly AC, Braga MBA, vonder Weid JP (2016) Derivation of acoustoelastic lamb wave dispersion curves in anisotropic plates at the initial and natural frames of reference. J Acoust Soc Am 140(4):2412–2417

  27. Pau A, Lanzadi SF (2015) Nonlinear guided wave propagation in prestressed plates. J Acoust Soc Am 137(3):1529–1540

  28. Pei N, Bond LJ (2016) Higher order acoustoelastic lamb wave propagation in stressed plates. The Journal of the Acoustical Society of America 140(5):3834–3843

    Article  Google Scholar 

  29. Yang Y, Ng CT, Mohabuth M, Kotousov A (2019) Finite element prediction of acoustoelastic effect associated with lamb wave propagation in pre-stressed plates. Smart Materials and Structures 28(9):095007

  30. Ma Y, Yang Z, Zhang J, Liu K, Wu Z, Ma S (2019) Axial stress monitoring strategy in arbitrary cross-section based on acoustoelastic guided waves using pzt sensors. AIP Adv 9(12)

    Article  Google Scholar 

  31. Shi F, Michaels JE, Lee SJ (2013) In situ estimation of applied biaxial loads with lamb waves. The Journal of the Acoustical Society of America 133(2):677–687

    Article  Google Scholar 

  32. Kubrusly AC, Perez N, Oliveira TF, Adamowski JC, Braga AMB, Vonde Weid JP (2016) Mechanical strain sensing by broadband time reversal in plates. IEEE Trans Ultrason, Ferroelect, Freq Cont 63:746–756

  33. Martinho LM, Kubrusly AC, Perez N, von der Weid JP (2021) Strain sensitivity enhancement of broadband ultrasonic signals in plates using spectral phase filtering. Appl Sci 11:6

    Article  Google Scholar 

  34. Quiroga J, Mujica L, Villamizar R, Ruiz M, Camacho J (2017) PCA based stress monitoring of cylindrical specimens using pzts and guided waves. Sensors 17:12

    Article  Google Scholar 

  35. Domingos P (2012) A few useful things to know about machine learning. Commun ACM 55(10):78–87

    Article  Google Scholar 

  36. Mehta P, Bukov M, Wang CH, Day AG, Richardson C, Fisher CK, Schwab DJ (2019) A high-bias, low-variance introduction to machine learning for physicists. Physics Reports. A high-bias, low-variance introduction to Machine Learning for physicists 810:1–124

  37. Nord JH, Koohang A, Paliszkiewicz J (2019) The internet of things: Review and theoretical framework. Expert Syst Appl 133:97–108

    Article  Google Scholar 

  38. Liao Y, Deschamps F, Loures EFR, Ramos LFP (2017) Past, present and future of industry 4.0 - a systematic literature review and research agenda proposal. Int J Prod Res 55(12):3609–3629

  39. Amancio DR, Comin CH, Casanova D, Travieso G, Bruno OM, Rodrigues FA, da FontouraCosta L (2014) A systematic comparison of supervised classifiers. PLOS ONE 9(4):1–14

  40. Fernández-Delgado M, Cernadas E, Barro S, Amorim D (2014) Do we need hundreds of classifiers to solve real world classification problems? J Mach Learn Res 15(90):3133–3181

    MathSciNet  MATH  Google Scholar 

  41. Zhang C, Liu C, Zhang X, Almpanidis G (2017) An up-to-date comparison of state-of-the-art classification algorithms. Expert Syst Appl 82:128–150

    Article  Google Scholar 

  42. Hastie T, Tibshirani R, Friedman J (2008) The elements of statistical learning, 2 ed. Springer

  43. Wu X, Kumar V, Ross Quinlan J, Ghosh J, Yang Q, Motoda H, McLachlan GJ, Ng A, Liu B, Yu PS, Zhou Z-H, Steinbach M, Hand DJ, Steinberg D (2007) Top 10 algorithms in data mining. Knowl Inf Syst 14(1):1–37

    Article  Google Scholar 

  44. Smola AJ, Schölkopf B (2004) A tutorial on support vector regression. Stat Comput 14(3):199–222

    Article  MathSciNet  Google Scholar 

  45. Vapnik VN (1998) Statistical Learning Theory. Wiley, New York, NY

    MATH  Google Scholar 

  46. Sabzekar M, Hasheminejad SMH (2021) Robust regression using support vector regressions. Chaos, Solitons & Fractals 144:110738

  47. James G, Witten D, Hastie T, Tibshirani R (2014) An Introduction to Statistical Learning: With Applications in R. Springer, New York, USA

    MATH  Google Scholar 

  48. Duda RO, Hart PE, Stork DG (2000) Pattern Classification, 2nd edn. Wiley, New York, USA

    MATH  Google Scholar 

  49. Zhang S (2021) Challenges in knn classification. IEEE Trans Knowl Data Eng (in press)

  50. Breiman L (2001) Random forests. Machine learning 45(1):5–32

    Article  Google Scholar 

  51. Kingma DP, Ba JL (2015) Adam: A method for stochastic optimization. In 3rd International Conference on Learning Representations (San Diego, CA, USA)

  52. Strang G (2019) Linear Algebra and Learning from Data. Wellesley-Cambridge Press, Wellesley, USA

    MATH  Google Scholar 

  53. Liu W, Wang Z, Liu X, Zeng N, Liu Y, Alsaadi FE (2017) A survey of deep neural network architectures and their applications. Neurocomputing 234:11–26

    Article  Google Scholar 

  54. Schmidhuber J (2015) Deep learning in neural networks: An overview. Neural Netw 61:85–117

    Article  Google Scholar 

  55. Lecun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444

    Article  Google Scholar 

  56. Bishop C (2006) Pattern Recognition and Machine Learning. Information science and statistics. Springer, New York, NY, USA

    MATH  Google Scholar 

  57. Gewers FL et al (2021) Principal component analysis: A natural approach to data exploration. ACM Computing Surveys 54:4

    Google Scholar 

  58. Brunton S, Kutz J (2019) Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control. Cambridge University Press, New York, NY, USA

    Book  MATH  Google Scholar 

  59. Kuhn M, Johnson K (2013) Applied Predictive Modeling. Springer, New York, USA

    Book  MATH  Google Scholar 

  60. Bergstra J, Bengio Y (2012) Random search for hyper-parameter optimization. J Mach Learn Res 13(10):281–305

    MathSciNet  MATH  Google Scholar 

  61. Pedregosa F et al (2011) Scikit-learn: Machine learning in Python. J Mach Learn Res 12:2825–2830

    MathSciNet  MATH  Google Scholar 

  62. Abadi M et al (2016) Tensorflow: A system for large-scale machine learning. In 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI 16), pp. 265–283

  63. Lecun Y et al (1998) Gradient-based learning applied to document recognition. Proc IEEE 86(11):2278–2324

    Article  Google Scholar 

  64. Allen M (2018) Raincloud plots: a multi-platform tool for robust data visualization. PeerJ Preprints 6:e27137v1

  65. Deb K (2001) Multi-objective optimisation using evolutionary algorithms: an introduction. In Multi-objective evolutionary optimisation for product design and manufacturing. Springer. pp. 3–34

  66. Ren P, Xiao Y, Chang X, Huang P-Y, Li Z, Chen X, Wang X (2021) A comprehensive survey of neural architecture search: Challenges and solutions. ACM Computing Surveys 54:4

    Google Scholar 

  67. Ayala HVH et al (2017) Efficient hardware implementation of radial basis function neural network with customized-precision floating-point operations. Control Eng Pract 60:124–132

    Article  Google Scholar 

  68. Duarte J et al (2018) Fast inference of deep neural networks in FPGAs for particle physics. J Instrum 13(07):P07027–P07027

    Article  Google Scholar 

  69. Huang C-H (2021) An fpga-based hardware/software design using binarized neural networks for agricultural applications: A case study. IEEE Access 9:26523–26531

    Article  Google Scholar 

  70. Shawahna A et al (2019) Fpga-based accelerators of deep learning networks for learning and classification: A review. IEEE Access 7:7823–7859

    Article  Google Scholar 

  71. Siracusa M, Ferrandi F (2020) Tensor optimization for high-level synthesis design flows. IEEE Trans Comput Aided Des Integr Circuits Syst 39(11):4217–4228

    Article  Google Scholar 

  72. Zhu J et al (2020) An efficient task assignment framework to accelerate dpu-based convolutional neural network inference on fpgas. IEEE Access 8:83224–83237

    Article  Google Scholar 

  73. Bharadwaj HK et al (2021) A review on the role of machine learning in enabling iot based healthcare applications. IEEE Access 9:38859–38890

    Article  Google Scholar 

  74. Peddeti K, Santhanam S (2018) Dispersion curves for lamb wave propagation in prestressed plates using a semi-analytical finite element analysis. The Journal of the Acoustical Society of America 143(2):829–840

    Article  Google Scholar 

  75. Zuo P, Yu X, Fan Z (2020) Acoustoelastic guided waves in waveguides with arbitrary prestress. J Sound Vib 469

    Article  Google Scholar 

  76. Ou Y, Tatsis KE, Dertimanis VK, Spiridonakos MD, Chatzi EN (2021) Vibration-based monitoring of a small-scale wind turbine blade under varying climate conditions. part i: An experimental benchmark. Struct Cont Health Mon 28(6):e2660

  77. Ribeiro MGDC, Kubrusly AC, Ayala HVH, Dixon S (2021) Machine learning-based corrosion-like defect estimation with shear-horizontal guided waves improved by mode separation. IEEE Access 9:40836–40849

  78. Tatsis K, Ou Y, Dertimanis VK, Spiridonakos MD, Chatzi EN (2021) Vibration-based monitoring of a small-scale wind turbine blade under varying climate and operational conditions. part ii: A numerical benchmark. Structural Control and Health Monitoring 28(6):e2734

  79. Figueiredo E, Figueiras J, Park G, Farrar CR, Worden K (2011) Influence of the autoregressive model order on damage detection. Computer-Aided Civil and Infrastructure Engineering 26(3):225–238

    Article  Google Scholar 

  80. Avci O, Abdeljaber O, Kiranyaz S, Hussein M, Gabbouj M, Inman DJ (2021) A review of vibration-based damage detection in civil structures: From traditional methods to machine learning and deep learning applications. Mech Syst Signal Process 147

    Article  Google Scholar 

  81. Feng D-C, Liu Z-T, Wang X-D, Jiang Z-M, Liang S-X (2020) Failure mode classification and bearing capacity prediction for reinforced concrete columns based on ensemble machine learning algorithm. Advanced Engineering Informatics 45

    Article  Google Scholar 

  82. Feng D-C, Wang W-J, Mangalathu S, Hu G, Wu T (2021) Implementing ensemble learning methods to predict the shear strength of rc deep beams with/without web reinforcements. Eng Struct 235

    Article  Google Scholar 

  83. Blaiech AG et al (2019) A survey and taxonomy of fpga-based deep learning accelerators. J Syst Archit 98:331–345

    Article  Google Scholar 

  84. Danopoulos D et al (2021) Utilizing cloud fpgas towards the open neural network standard. Sustainable Computing: Informatics and Systems 30

    Google Scholar 

  85. Kowsalya T (2020) Area and power efficient pipelined hybrid merged adders for customized deep learning framework for fpga implementation. Microprocess Microsyst 72

    Article  Google Scholar 

  86. Giubilato R et al (2019) An evaluation of ros-compatible stereo visual slam methods on a nvidia jetson tx2. Measurement 140:161–170

    Article  Google Scholar 

  87. Mittal S (2019) A survey on optimized implementation of deep learning models on the nvidia jetson platform. J Syst Archit 97:428–442

    Article  Google Scholar 

  88. Pinto de Aguiar AS et al (2020) Vineyard trunk detection using deep learning an experimental device benchmark. Comp Electron Agri 175:105535

  89. Tabani H et al (2021) Performance analysis and optimization opportunities for nvidia automotive gpus. Journal of Parallel and Distributed Computing 152:21–32

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to H. V. Hultmann Ayala.

Ethics declarations

Conflict of Interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Villares Holguin, C.D., Hultmann Ayala, H.V. & Kubrusly, A.C. Improved Stress Estimation with Machine Learning and Ultrasonic Guided Waves. Exp Mech 62, 237–251 (2022). https://doi.org/10.1007/s11340-021-00787-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11340-021-00787-6

Keywords

Navigation