Artificial intelligence

Abstract: This article is devoted to the problem of prediction of the stress-strain state of a ring plate using neural networks. The article shows how to train the neural network to estimate the von Mises stress of a ring plate under external uniform pressure. Machine learning, one of the six disciplines of Artificial Intelligence (AI) without which problems of having machines acting humanly could not be accomplished. Applications of ANNs to engineering structures arise in a variety of industries such as engineering, automotive, space structures, etc. ANNs allow to develop models e.g. for the stress-strain state estimation of some type of solids. Thus, the development of machine learning methods for predicting the behavior of engineering structures is urgent. The paper describes the scheme for using machine learning in the stress-strain state analysis of a ring plate. Additional input parameters of the data set are the following: outer radius, inner radius, thickness of the plate, Young’s modulus, Poison’s coefficient, and pressure load. The training set is generated by the finite element method. Initial parameters of the training set have been randomly generated. The artificial neural network merges numerical and one-hot input layers. One hot The developed regression model allows to predict von Mises stresses for a ring plate. The developed model allows to predict the von Mises stress with 10% of the mean absolute percentage error. The key advantage of an artificial neural network is the speed of prediction. The ANN predicts the von Mises stress almost instantaneously (milliseconds) comparing the finite element method.

Keywords: Machine Learning, Artificial Neural Network, Stress-Strain State, Ring Plate, Prediction, Regression

References:

1. Hertzmann A, Fleet D. Machine Learning and Data Mining, Lecture Notes CSC 411/D11, Computer Science Department, University of Toronto, Canada (2012).
2. McCulloch WS, Pitts W. A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5(4):115–133 (1943).
3. Hern A. Google says machine learning is the future. Available at: www.theguardian.com/technology/2016/jun/28/all.
4. Choporova O., Lisnyak A. “Using machine learning to predict the stress-strain state of a rectangular plate with a circular cut-out” CEUR Workshop Proceeding s. 2020. Т. 2791. C. 1-6. URL:https://www.scopus.com/record/display.uri?eid=2-s2.0-85098720535 &origin= resultslist
5. Keras. URL: https://www.tensorflow.org/guide/keras.
6. Abambres M., Marcy M., Doz G. “Potential of Neural Networks for Structural Damage Localization”, engrXiv. 2018. URL: Available: engrxiv.org/rghpf/ doi: 10.31224/osf.io/rghpf.
7. C. Jin, S. Jang, X. Sun “Damage detection of a highway bridge under severe temperature changes using extended Kalman filter trained neural network” Journal of Civil Structural Health Monitoring. 2016. Vol. 6, Iss. 3, pp. 545–560.
8. Maksymova О. M. “Razvitie s primenenie neurosetevih tehnologiy dlia zadach mehaniki i stroitelnih konstrukcij”, Vestnik IrGTU. 2013. № 8 (79). pp. 81–88.
9. Oliynyk A. O., Subbotin S. O., Oliynyk O. O. “Evolyutsiyni obchyslennya ta prohramuvannya”. Zaporizhzhya: ZNTU. 2010. p. 324.
10. Kozyn I. V. “Evolyutsiyni modeli v dyskretnoyi optymizatsiyi”. Zaporizhzhya: ZNU. 2019. p. 204.
11. Maksymova О. M. “Neural network forecasting technologies for problems of the dynamics of building structures” XIV All-Russian Scientific and Technical Conference "Neuroinformatics-2012"; Moscow 2012.
12. Maksymova О. M. “Neuronet technology development and application for solving mechanical and engineering structures problems” Vestnik IrGTU. 2013. № 8 (79). p. 82.
13. M. Raissi, P. Perdikaris, and G. Em Karniadakis, ‘‘Multistep neural networks for data-driven discovery of nonlinear dynamical systems,’’ 2018, arXiv:1801.01236. [Online]. Available: http://arxiv.org/abs/1801.01236
14. Peter Z. Szewczyk Neural Net-work Based Extrapolation Strategies in Structural Analysis and Design, 1999. p.238 – 255.
15. M. Raissi, P. Perdikaris, and G. Em Karniadakis, ‘‘Multistep neural networks for data-driven discovery of nonlinear dynamical systems,’’ 2018, arXiv:1801.01236. [Online]. Available: http://arxiv.org/abs/1801.01236
16. F. Roewer-Despres, N. Khan, and I. Stavness, ‘‘Towards finite element simulation using deep learning,’’ in Proc. 15th Int. Symp. Comput. Methods Biomechan. Biomed. Eng., 2018, pp. 1–20.
17. J. Ghaboussi, ‘‘Neural networks in computational mechanics,’’ Arch. Comput. Methods Eng., vol. 3, no. 4, p. 435, 1996.
18. L. Liang, M. Liu, C. Martin, and W. Sun, ‘‘A deep learning approach to estimate stress distribution: A fast and accurate surrogate of finite-element analysis,’’ J. Roy. Soc. Interface, vol. 15, no. 138, Jan. 2018, Art. no. 20170844.
19. L. Liang, M. Liu, C. Martin, and W. Sun, ‘‘A machine learning approach as a surrogate of finite element analysis-based inverse method to estimate the zero-pressure geometry of human thoracic aorta,’’ Int. J. Numer. Methods Biomed. Eng., vol. 34, no. 8, p. e3103, May 2018.
20. Onur Avci P. O., Abdeljaber A. O. “Self-Organizing Maps for Structural Damage Detection: A Novel Unsupervised Vibration-Based Algorithm”, Journal of Performance of Constructed Facilities. 2016. Vol. 30, Iss. 3. pp. 1–11.
21. Tao S. “Deep Neural Network Ensembles”. Available: https://arxiv.org/abs/1904.05488
22. Hany Sallam, Carlo S. Regazzoni, Ihab Talkhan, and Amir Atiya “Evolving neural networks ensembles”. IAPR Workshop on Cognitive Information Processing, pp. 142-147
23. Webb A. M., Reynolds C., Iliescu D.-A., Reeve H., Lujan M., Brown G. “Joint Training of Neural Network Ensembles”. Available: https://arxiv.org/abs/1902.04422.
24. Abadi M., Agarwal A. Barham P. TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems. Proceedings of the 12th USENIX Symposium on Operating Systems Design and Implementation (OSDI ’16) (Savannah, GA, USA, November, 2 – 4, 2016). Savannah, GA, USA, 2016. P. 265 – 283.
25. Bahrampour S., Ramakrishnan N., Schott L., et al. Comparative Study of Deep Learning Software Frameworks. Available at: https://arxiv.org/abs/1511.06435
26. Chollet. F., et al. Keras. 2015. Available at: https://github.com/fchollet/keras
27. Jia Y., Shelhamer E., Donahue J., et al. Caffe: Convolutional Architecture for Fast Feature Embedding. Proceedings of the 22nd ACM International Conference on Multimedia (Orlando, FL, USA, November 03 – 07, 2014), Orlando, FL, USA 2014. P. 675–678. DOI: 10.1145/2647868.2654889.
28. Kruchinin D., Dolotov E., Kornyakov K. et al. Comparison of Deep Learning Libraries on the Problem of Handwritten Digit Classification. Analysis of Images, Social Networks and Texts. Communications in Computer and Information Science. 2015. vol. 542. P. 399 – 411. DOI: 10.1007/978-3-319-26123-2_38.
29. Peter Z. Szewczyk Neural Net-work Based Extrapolation Strategies in Structural Analysis and Design, 1999. p.238 – 255.
30. Abovskiy N.P., Maximova O.M. Neuro-Prognosis Based on Step Model with Teaching for Natural Tests Results of Building Structures. j. Optical Memory & Neural Networks (Information Optics), 2007, P. 40 – 46.
31. Kinnikar A., Husain M., Meena S.M. Face Recognition Using Gabor Filter And Convolutional Neural Network : proceedings of the International Conference on Informatics and Analytics (Pondicherry, India, August 25 – 26, 2016), Pondicherry, India, 2016. P. 113:1 – 113:4. DOI: 10.1145/2980258.2982104.
32. Boominathan L., Kruthiventi S.S., Babu R.V. CrowdNet: A Deep Convolutional Network for Dense Crowd Counting. Proceedings of the 2016 ACM on Multimedia Conference (Amsterdam, The Netherlands, October 15 – 19, 2016), Amsterdam, The Netherlands, 2016. P. 640 – 644. DOI: 10.1145/2964284.2967300.
33. Ranzato M.A., Huang F.J., Boureau Y.L., et al. Unsupervised Learning of Invariant Feature Hierarchies with Applications to Object Recognition. IEEE Conference on Computer Vision and Pattern Recognition (Minneapolis, MN, USA, 17 – 22 June 2007), Minneapolis, MN, USA, 2007. P. 1 – 8. DOI: 10.1109/cvpr.2007.383157.